15 big ideas that will revolutionize industries and economies, led by AI

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More tech-led transformation is coming and artifical intelligence (AI) will be at the heart of that change, says a report by  ARK Invest , which is an investment management firm that focuses on disruptive innovation in public equity markets. 

"We're all about finding the next big thing. Those hewing to the benchmarks, which are backwards looking, are not about the future. They are about what has worked. We're all about what is going to work," says  Cathie Wood , founder, CEO, and chief investment officer of ARK. 

Also: 4 ways to help your organization overcome AI inertia

ARK publishes a Big Ideas report annually, which provides a comprehensive analysis of technological convergence and its potential to revolutionize industries and economies:

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The ARK Big Ideas 2024 report is titled 'Disrupting the Norm, Defining the Future' and it highlights 15 big ideas, which are: 

  • Technological Convergence - The global equity market value associated with disruptive innovation could increase to 60% by 2030.
  • Artificial Intelligence - Scaling global intelligence and redefining work: AI training costs should continue to fall 75% per year.
  • Smart Contracts - Powering the internet-native financial system, smart contract networks could generate fees of $450bn in 2030.
  • Digital Wallets - Digital wallets could grow select vertical software platforms' revenues to $27-$50bn in 2030.
  • Robotics - Generalizing automation, thanks to the convergence of AI software and hardware. Generalizable robotics represent a $24 trillion-plus global revenue opportunity.
  • Digital Consumers - Transitioning toward digital leisure, where spending could teach $23 trillion in 2030.
  • Electric Vehicles - Lower battery costs powering adoption mean EV sales could reach 74 million in 2030.
  • Robotaxis - Robotaxi platforms could create $28 trillion in enterprise value in 2030.
  • Multiomic Tools & Technology - Translating biological insights into economic value: R&D spending could decline by more than 25%, thanks to multiomic tools and technology.
  • Reusable Rockets - Satellite connectivity revenues could exceed $130bn per year in 2030.
  • Autonomous Logistics - Global autonomous delivery revenue could reach $900bn by 2030.
  • Bitcoin Allocation - Growing the role of bitcoin in investment portfolios. During the last seven years, bitcoin's annualized return has averaged around 44%.
  • Bitcoin in 2023 - After challenges in 2022, bitcoin's price surged 155% last year, reaching $827 billion in market cap.
  • Precision Therapies - Curing disease more efficiently and less expensively. The enterprise value of companies focused on precision therapies could reach $4.5 trillion by 2030.
  • 3D Printing - Revenues could grow 40% at an annual rate to $180bn by 2030.

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The 2024 Big Ideas report by ARK identifies five innovation platforms converging and defining the technological era: AI, public blockchains, energy storage, robotics, and multiomic sequencing. ARK also looks at the historic impact of converging technologies and estimated economic impacts. 

The company identifies AI as the central technology catalyst. Let's take a deeper dive into the AI chapter of the 2024 BIg Ideas report. 

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AI: Redefining Work

The research suggests coding assistants are early success stories that have boosted the productivity and job satisfaction of software developers. AI-powered assistants are increasing the performance of knowledge workers and, interestingly, benefiting underperforming workers relatively more than high performers:

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Foundational models are improving across domains. With larger training datasets and more parameters, GPT-4 outperforms GPT-3.5 significantly . Increasingly, foundation models are becoming "multimodal" -- supporting text, images, audio, and video -- and are not only more dynamic and user-friendly, but also more performant. The analysis says the cost of authoring the written word has collapsed:

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AI-training performance is rapidly improving. What's more, training costs should continue to fall 75% per year.  The research notes that after focusing initially on large language model (LLM) training-cost optimization, researchers are now prioritizing inference costs. Based on enterprise-scale use cases, inference costs seem to be falling at an annual rate of around 86%, which is even faster than the fall in training costs. Today, the inference costs associated with GPT-4 Turbo are lower than those for GPT-3 a year ago:

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The open-source community is competing with private models. ARK states that the performance of open-source models is improving faster than closed-source models. LLM performance advances will require nuanced techniques, with the Stanford HELM framework highlighted as an example in the report. 

Also:  Why open-source generative AI models are still a step behind GPT-4

ARK also notes that computing power and high-quality training data appear to be the primary contributors to model performance. As models grow and require more training data, will a lack of fresh data cause model performance to plateau? Research institute Epoch AI estimates that high-quality language/data sources, such as books and scientific papers, could be exhausted by 2024, although a larger set of untapped vision data still exists:

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The reserach suggests the acceleration of employee productivity using AI could have a multi-trillion dollar impact. AI has the potential to automate most tasks in knowledge-based professions by 2030, dramatically increasing the average worker's productivity. Software solutions that automate and accelerate knowledge work tasks should be prime beneficiaries:

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The ARK Invest Big Idea 2024 report is the gold standard for detailing the disruptive technologies that will shape industries and economies for the next decade. The summary of the report's AI chapter includes potential possibilities for AI beyond 2030, and potential scenarios by 2040: 

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The report also includes other great content. The Digital Consumer and Digital Wallet chapters of the report are important for business leaders in any sector and any size. For example, the report suggests social commerce should grow 32% at an annual rate, from $730bn today to over $5 trillion in 2030. 

Also:  Five ways to use AI responsibly

The Big Ideas report is a comprehensive study of disruptive technologies, with more than 160 pages of analysis. To learn more about the research, you can visit here .

Artificial Intelligence

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Singapore looks to accelerate AI development with investment in compute and talent

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Microsoft and Google are proud AI is helping you (other companies not so much)

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AI is supercharging collaboration between developers and business users

Big Ideas Math

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Tools to Identify Big ideas

May 13, 2019

Light bulb with the words Big Idea

“Big Ideas are broad concepts that are explored in multiple ways and are relevant to the Learners, and the larger community (e.g., health).”

Challenge Based Learning Guide 

The starting point for developing a challenge experience is a Big Idea. It can be identified by the senior learner beforehand or with the junior learners as a first step of the journey. Big Ideas are “broad concepts that are explored in multiple ways and are relevant to the Learners and the larger community.” The beauty of the Big Idea is that they allow for contextualization and ownership. The Big Ideas of Health, Water and Resilience are going to be interpreted differently depending on context, circumstances, and timing and will lead to uniquely personal learning experiences and solutions.

Big Ideas are all around us. Read, look, talk with people, listen and the Big Ideas will emerge. They do not have to be earth-shattering or have the capacity to create solutions that are world changing – they first need to be relevant to the learners and their community. The learners include both the senior (teachers, parents) and the junior (students) participants. The community can be as large as the world or as small as the home and classroom.

When identifying and agreeing upon Big Ideas, it is critical to stop and get a pulse on what is relevant to the learners. If there is something of immediate relevance and concern, this is the optimal Big Idea because it creates an urgency to identify and solve the resulting challenge.

For example, if everyone is concerned about their upcoming AP test this should be the Big Idea because it is the most relevant issue to the learners and the local community (class). If we ignore the pressing Big Ideas and focus on ones with limited relevance, it will be a struggle.

With this said the learners could broaden the Big Idea from the test ( to assessment) and bring in other concerns (health, competition, definitions of success, statistics, etc.) through the essential questioning, challenge and guiding questions.

Here are some ideas for developing and reaching consensus on Big Ideas:

The passion (or concern) walk. Have all of the learners individually make a list of items that they are passionate (or concerned about). Decide ahead of time if it makes more sense to focus on passions or concerns and make sure to define these terms before the activity. Once the learners (and the senior leaners should participate as well) create a list have them select the top passion (or concern). Then work to reduce it to a keyword (a teachable moment on what keywords are and how they work) and write them on paper, card or a device if everyone has them. When everyone has selected their keyword (s) have them walk around the room with the words visible and discuss the Ideas. Finally, have them “clump” together around shared ideas and see if they can agree on a keyword that represents their concerns.

Tools: paper, pens

Create mind-maps (tools/apps) to help brainstorm, organize, categorize, and even prioritize ideas and how they connect. Having access to tools like these help provide a way to assess and adjust where needed. Instead of jumping into a narrative (start, middle, and end) document— learners can look at the structure of any project like this. Here is a quick example of a basic plan to help learners ask the right questions, generate the needed guiding activities to answer the questions.

Tools:  bubble.us , FreeMind, XMind

Photo Essay – Grab those phones, cameras, etc and take a walk around the community or school and take pictures of issues and concerns. Review and group the photos by Big Ideas (e.g. pollution, waste, graffiti, traffic). This activity can create a teachable moment for pattern recognition and understanding diagrams

Tools: For quick slideshows to help organize and showcase the collected images— you can use apps like Photos slideshow for iOS, Quick, Google SlideShow, FilmoraGo, PixGram.

Standards Word Cloud

Standards, Goals, Objectives Word Maps – Big Ideas can even be found in the official curriculum documents. In many schools, the standards are the most pressing concern of the adult learners. So take all the text for a specific area or unit and create a Word Map. For example, this is a Word Map of the Colorado 8th grade Physical Science Grade-level Expectations at a Glance . Looks like Energy and Change might be interesting Big Ideas to pursue. You can also mix subject area standards and get an interdisciplinary word map.

Tools: wordle.net, wordclouds.com

Big Idea Wall – keep a space in the room (or on the Internet) where students can post pictures, words, drawings, lyrics, etc. that strike them as Big Ideas. This collection can be mined throughout the year for Big Ideas to guide class, group or individual challenges. Tools: Bulletin board, tacks, paper. For digital collections – blogs, DropBox, Google Drive, Guest Speakers – work with local organizations or the city to speak to the learners about local issues and concerns. Most cities have identified a set of concerns and improvement goals. For example, one school worked with the city on the Big Idea of Graffiti and through their challenge learned about city government, laws and policies, human behavior, art, science, and math while developing solutions to pitch to city officials.

Tools: Websites, email, phone

Ted Talks Keyword Search – The Ted Talks website (https://www.ted.com/talks) includes a collection of presentations by “expert speakers on education, business, science, tech and creativity” Visit the site, select Topics > See All Topics and you can explore by Keyword. The extensive list contains a treasure trove of Big Ideas that are connected with expert presentations.

TED Talks Keywords

Tools: Web Browser

What ideas and tools do you have for generating Big Ideas? Let us know at #CBLWorld  or #BigIdeas

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ScienceDaily

Big new idea introduced with the help of tiny plankton

Researchers at Michigan State University and the Carnegie Institution for Science have developed a model that connects microscopic biology to macroscopic ecology, which could deepen our understanding of nature's laws and create new opportunities in ecosystem management.

Reporting in the journal Science on Feb. 16, the team showed how microscopic relationships in plankton -- such as between an organism's size and nutrient consumption -- scales up to predictably affect food webs.

"Using data that other researchers have measured at the microscale about these organisms, our model can predict what's happening at the scale of whole ecosystems," said Jonas Wickman, a postdoctoral research associate with MSU's College of Natural Science and first author of the new paper.

"We can now show how lower-level rules of life feed into these higher levels based on ecological interactions and evolutionary considerations," said Elena Litchman, a senior staff scientist at Carnegie's Biosphere Sciences and Engineering division. "Up until now, people had mostly considered these levels in isolation."

This new report will enable the team and its peers to design new experiments to test, refine and expand the model by extending it to other species and ecosystems. This could ultimately lead to the model being able to inform ecosystem management strategies in various environments around the globe.

Small organisms, global impact

The team is also interested in what more they can learn from their model and the plankton they study.

"We chose them as a model system for a few reasons," said Christopher Klausmeier, an MSU Research Foundation Professor at the W. K. Kellogg Biological Station. He's also a faculty member with the Department of Plant Biology, the Department of Integrative Biology and the Ecology, Evolution and Behavior, or EEB, program at MSU.

One of the reasons is that plankton are the primary research focus for the research group led by Litchman and Klausmeier.

"They're relatively simple organisms. If anything is going to follow the rules, plankton are a good candidate," Klausmeier said. "But they're also globally important. They're responsible for about half of the primary production on Earth and are the base of most aquatic food webs."

Primary producers use biochemical processes such as photosynthesis to turn the Earth's carbon and raw nutrients into compounds that are useful for the organisms themselves and their predators. This means plankton are a critical cog in the natural machinery that cycles the planet's life-essential elements, including carbon, nitrogen and oxygen.

Having this scaling model that describes plankton can thus be useful for better understanding those key processes, as well as if and how those are changing with the planet's climate.

The team did not include climate-associated variables like temperature in this study, but the researchers are already planning their next steps in that direction.

"The effects of global warming could alter the lower-level physiological processes," Litchman said. "We could then use this framework to see how those effects bubble up to different levels of organization."

Eye-popping simplicity

Wickman hasn't always been a plankton ecologist. His undergraduate degree was in physics, but he switched to ecology during his doctoral studies in Sweden before joining the Klausmeier-Litchman lab in 2020.

The team said his physics background shaped his approach to developing this model, which Litchman described as "beautiful -- stripping out everything except the essential processes."

To begin, Wickman built from fundamental theories describing his system of interest. Only in this case, the system wasn't, say, quantum mechanical particles. It was tiny organisms linked by a simple food web.

Within that web, phytoplankton are the primary producers and zooplankton are their predators.

"Well, grazers really," Wickman said of the zooplankton. "We don't usually call cows predators of grass."

To fully appreciate the workings of this important relationship and its global implications, researchers have been breaking it down into its components driven by ecology and evolution.

For example, microscopic considerations like the size of a phytoplankton affect its ability to compete for nutrients, which in turn influence how big cells can get and how likely it is to become food for zooplankton.

These microscopic factors are thus connected to macroscopic variables, including the distribution of nutrients and how densely or sparsely different plankton populate their environments.

Over the past several decades, scientists have formulated mathematics that describe important relationships at the micro scale and macro scale individually. Attempts to bridge the scales, however, have left researchers wanting, Wickman said.

That's because previous attempts to make that connection have had to make compromises. Some previous models have chosen simplicity at the expense of accuracy and realism. Others have confronted that complexity with brute computational force, making them less accessible and harder to work with.

"Our model includes actual ecological and evolutionary mechanisms but is simple enough to use," Wickman said.

The work began as pure theory, but Litchman suggested that it should be possible to test its predictions using existing data. "When I saw how well the model matched the observations, my eyes popped out," she said.

With support from the U.S. National Science Foundation, or NSF, the team had been working on this problem for several years and had published an earlier paper developing the eco-evolutionary modeling techniques they relied on.

Now, the team has showcased the potential of their model by uniting it with real-world data.

"The revelation that patterns emerging at macroecological scales can be explained by properties of individual organisms at microecological scales is as compelling as it is elegant," said Steve Dudgeon, program director in NSF's Directorate for Biological Sciences, which helped fund the work.

"The study provides new avenues of research that could enhance prediction of how ecosystems, and the relationships among the organisms in them, will change with eco-evolutionary dynamics interacting in changing environments."

Because of the natural variation of biological systems, the model and its results may seem messy to someone used to the precision of physics, but Wickman views them with excitement.

"We actually achieved quite good accuracy for ecology," he said. "We may not have the same level of theoretical elegance as physics, but that just means we have much more territory to explore."

  • Ecology Research
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  • Environmental Issues
  • Organic farming
  • Biodiversity
  • Trophic level
  • Overfishing
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Story Source:

Materials provided by Michigan State University . Original written by Matt Davenport. Note: Content may be edited for style and length.

Journal Reference :

  • Jonas Wickman, Elena Litchman, Christopher A. Klausmeier. Eco-evolutionary emergence of macroecological scaling in plankton communities . Science , 2024; 383 (6684): 777 DOI: 10.1126/science.adk6901

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NASA’s BIG Idea Challenge

The Breakthrough, Innovative, and Game-Changing (BIG) Idea Challenge is an engineering design competition that seeks innovative ideas from teams of undergraduate and graduate students, tackling new themes each year that support technologies needed to develop technology needed to support NASA’s exploration goals. Finalist teams receive up to $150,000 to build and test their concepts before presenting their projects to a panel of NASA and industry experts.  

Each year, the BIG Idea Challenge offers a real-world experience for college students and their advisors to develop technology needed to support NASA’s exploration goals.

“The BIG Idea Challenge proves time and time again that engaging the academic community in complex technology challenges is a worthwhile endeavor for everyone involved.”   — Niki Werkheiser, Director of Technology Maturation, NASA’s Space Technology Mission Directorate

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2024 BIG Idea Challenge: Lunar Inflatable Systems

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NASA’s 2024 BIG Idea Challenge invites student innovators to build and demonstrate how their concepts can benefit future missions to the Moon and beyond. Inflatable systems could greatly reduce the mass and stowed volume of science and exploration payloads, which is critical for lowering delivery costs to deep space destinations. Student innovators have been invited to develop concepts for truly novel solutions for future space exploration.

Finalists will be selected by a panel of NASA and industry experts based on a proposal and video package that includes a specific, compelling mission scenario/use case where an inflatable system would be applicable and advantageous. The proposal package is due February 1, 2024, and non-binding notices of intent (NOI) can be submitted on a rolling basis until that deadline.

NASA’s Space Technology Mission Directorate sponsors the BIG Idea Challenge through a collaboration between its Game Changing Development program , in coordination with the Lunar Surface Innovation Initiative , and NASA’s Office of STEM Engagement’s Space Grant project.  The BIG Idea Challenge is managed by a partnership between the National Institute of Aerospace and the Johns Hopkins Applied Physics Laboratory on behalf of NASA.

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Past challenges, lunar forge: producing metal products on the moon.

NASA’s 2023 BIG Idea Challenge

The 2023 BIG Idea Challenge provided undergraduate and graduate students the opportunity to design, develop, and demonstrate technologies that could enable the production of lunar infrastructure from ISRU-derived metals found on the Moon. Teams were invited to submit proposals that focused on any part of the metal product production pipeline from prospecting to testing. Key infrastructure products desired included storage vessels for liquids and gases, extrusions, pipes, power cables, and supporting structures (i.e., roads, landing pads, etc.).

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Extreme Terrain Access for Mobility

NASA’s 2022 BIG Idea Challenge

The 2022 BIG Idea Challenge provided undergraduate and graduate students the opportunity to design, develop, and demonstrate robotic systems with alternative rover locomotion modalities for use in off-world extreme lunar terrain applications. This competition was an open innovation challenge with minimal constraints so that proposing teams could genuinely create and develop out-of-the-box solutions. Teams were invited to submit proposals for robots with new mobility solutions in operating scenarios that required access to extreme terrain categories.

2022 BIG Idea Challenge: Extreme Terrain Mobility

Lunar Dust Mitigation

NASA’s 2021 BIG Idea Challenge

NASA asked university and college students around the country to help solve the pesky problem of lunar dust as the agency plans for sustainable human exploration of the Moon. Through the 2021 competitive BIG Idea Challenge and the Space Grant project, NASA awarded nearly $1 million to seven university teams to develop their innovative lunar dust mitigation solutions.

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Capabilities to Study Dark Regions on the Moon

NASA’s 2020 BIG Idea Challenge

During the 2020 BIG Idea Challenge, NASA asked Space Grant-affiliated universities to submit strong proposals for sample lunar payloads that can demonstrate technology systems needed for exploration and science in the Permanently Shadowed Regions (PSRs) in and near the Moon’s polar regions that have remained dark for billions of years.

Artist conception of technology designed to access, navigate, and explore surface and sub-surface areas on the Moon.

Marsboreal Greenhouse Design

NASA’s 2019 BIG Idea Challenge

The 2019 BIG Idea Challenge provided undergraduate and graduate students the opportunity to design, develop, and demonstrate innovative ideas for the installation and sustainable operation of a habitat-sized Mars greenhouse, with the primary purpose of food production. An efficient and safe greenhouse design could not only assist with Mars missions, but also long-term lunar missions with Artemis.

Artist’s rendering of the interior of a potential Mars greenhouse.

Solar Power Systems for Mars

NASA’s 2018 BIG Idea Challenge

The 2018 BIG Idea Challenge provided undergraduate and graduate students the opportunity to design, develop, and demonstrate concepts for a reliable operating power source that could be put in place on Mars ahead of the arrival of the first humans. The challenge sought concepts for unique designs, installation and sustainable operation of a large solar-power system. 

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In-Space Assembly of Spacecraft

NASA’s 2017 BIG Idea Challenge

The 2017 BIG Idea Challenge provided undergraduate and graduate students the opportunity to design, develop, and demonstrate modular concepts and systems that could provide the ability for in-space assembly of spacecraft – particularly tugs, propelled by solar electric propulsion (SEP) – that can transfer payloads for low-Earth orbit to a lunar distant retrograde orbit.

A solar electric propulsion thruster emits the blue hue of Xenon gas during testing. Vibrant blue light emanates in a circular shape from the dark grey thruster, which is mounted inside a vacuum chamber. The blue light then narrows into a plume as it moves farther away from the thruster, illuminating the otherwise darkened chamber.

Deployable Aeroshell Technology

NASA’s 2016 BIG Idea Challenge

NASA’s inaugural BIG Idea Challenge invited proposals for innovative ideas for generating lift using inflatable spacecraft heat shields or hypersonic inflatable aerodynamic decelerator (HIAD) technology. Interested teams of undergraduate and/or graduate students were asked to submit white papers describing their concepts outlining new approaches such as shape morphing and pneumatic actuation to dynamically alter the HIAD inflatable structure.

Artist’s rendering of a hypersonic inflatable aerodynamic decelerator technology concept.

Web Resources

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BIG Idea Challenge Website

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The Planning Process

Planners + Resources | Unit Plans (subject)  |  Unit Plans (grade) Big Ideas |  Concepts |  Curricular Competencies

* indicates new content that has been added since June 2020.

Unit Plans by Big Ideas

Big ideas by grade, kindergarten, arts education.

  • People connect to others and share ideas through the arts.

Social Studies

  • Stories and traditions about ourselves and our families reflect who we are and where we are from.
  • The motion of objects depends on their properties.

Applied Design, Skills and Technology

  • Skills can be developed through play.
  • Technologies are tools that extend human capabilities.
  • Designs grow out natural curiosity
  • Skills can be developed through play (2)
  • People connect to story through the arts
  • Engagement in the arts creates opportunity for inquiry through purposeful play

English Language Arts

  • Language and story can be a source of creativity and joy
  • Curiosity and wonder lead us to new discoveries about ourselves and the world around us
  • Objects and shapes have attributes that can be described, measured and compared (Math Gr 1-2)
  • Designs develop out of natural curiosity  (ADST 1-3)
  • Skills can be developed through play (ADST 1-3)
  • Living things have features and behaviours that help them survive in their environment
  • Our rights, roles, and responsibilities are important for building strong communities.
  • Inquiry through the arts creates opportunities for risk-taking
  • Living things have life cycles adapted to their environment
  • Water is essential to all living things
  • Local actions have global consequences, and global actions have local consequences.
  • Local actions have global consequences, and global actions have local consequences. (2)
  • Canada is made up of many diverse regions and communities.
  • Learning about indigenous peoples nurtures multicultural awareness and respect for diversity.

Applied Design, Skills and Technologies

  • Skills are developed through practice, effort, and action.
  • Texts can be understood from different perspectives.
  • Using language in creative and playful ways helps us understand how language works.
  • Using language in creative and playful ways helps us understand how language works. (2)

Mathematics

  • Developing computational fluency comes from a strong sense of number.
  • Number represents and describes quantity: Part of wholes can be represented by fractions and decimals.

Physical and Health Education

  • Daily physical activity enables us to practice skillful movement and helps us develop personal fitness.
  • Matter has mass, takes up space, and can change phase.
  • Living things sense and respond to their environment – Birds
  • Living things sense and respond to their environment – Farm
  • Living things sense and respond to their environment – Forest
  • Living things sense and respond to their environment – Pond
  • Interactions between First Peoples and Europeans lead to conflict and cooperation, which continues to shape Canada’s identity.
  • British Columbia followed a unique path in becoming a part of Canada.
  • The pursuit of valuable natural resources played a key role in changing the land, people and communities of Canada.
  • Canada’s policies and treatment of minority peoples have negative and positive legacies.
  • Canada’s policies and treatment of minority peoples have negative and positive legacies. (2)
  • Design can be responsive to identified needs.

  English Language Arts

  • Exploring and sharing multiple perspectives extends our thinking.

  Mathematics

  Physical and Health Education

  • Everyday material are often mixtures.
  • Multi-cellular organisms rely on internal systems to survive, reproduce, and interact with their environment. – Birds
  • Multi-cellular organisms rely on internal systems to survive, reproduce, and interact with their environment. – Farm  
  • Multi-cellular organisms rely on internal systems to survive, reproduce, and interact with their environment – Forest
  • Multi-cellular organisms rely on internal systems to survive, reproduce, and interact with their environment – Pond

  Social Studies

  • Systems of government vary in their respect for human rights and freedoms.
  • Computational fluency and flexibility with numbers extend to operations with integers and decimals.
  • Data from circle graphs can be used to illustrate proportion and to compare and interpret.
  • The constant ratio between the circumference and diameter of circles can be used to describe, measure and compare spatial relationships.
  • Linear relations can be represented in many connected ways to identify regularities and make generalizations.

Physical and Health Education

  • The electromagnetic force produces both electricity and magnetism.
  • Evolution by natural selection provides an explanation for the diversity and survival of living things.
  • Earth and its climate have changed over geological time.
  • Elements consist of one type of atom, and compounds consist of atoms of different elements chemically combined.
  • Number represents, describes, and compares the quantities of ratios, rates, and percents.
  • The theory of plate tectonics is the unifying theory that explains Earth’s geological processes.
  • Exploration, expansion, and colonization had varying consequences for different groups.
  • Exploration, expansion, and colonization had varying consequences for different groups. (2)
  • Contacts and conflicts between peoples stimulated significant cultural, social, political change.

Core French

  • Stories give us unique ways to interpret and share knowledge, thoughts, and feelings.
  • Disparities in power alter the balance of relationships between individuals and between societies.
  • Worldviews lead to different perspectives and ideas about developments in Canadian society.
  • Worldviews lead to different perspectives and ideas about developments in Canadian society. (2)

Comparative Cultures

  • Understanding the diversity and complexity of cultural expressions in one culture enhances our understanding of other cultures.
  • Interactions between belief systems, social organization, and language influence artistic expressions of culture.
  • Understanding the diversity and complexity of cultural expressions in one culture enhances our understanding of other cultures. (2)
  • Interactions between belief systems, social organization, and language influence artistic expressions of culture. (2)

BC First Peoples

  • The impact of contact and colonialism continues to affect the political, social, and economic lives of BC First Peoples.
  • The impact of contact and colonialism continues to affect the political, social, and economic lives of BC First Peoples. (2) 
  • The identities, worldviews, and language of BC First Peoples are renewed, sustained, and transformed through their connection to the land.
  • Cultural expressions convey the richness, diversity, and resiliency of BC First Peoples.

Download Complete lists of Big Ideas for Planning Purposes

  • Big Ideas by Grade – ALL GRADES
  • Big Ideas Kindergarten
  • Big Ideas Grade 1
  • Big Ideas Grade 2
  • Big Ideas Grade 3
  • Big Ideas Grade 4
  • Big Ideas Grade 5
  • Big Ideas Grade 6
  • Big Ideas Grade 7
  • Big Ideas Grade 8
  • Big Ideas Grade 9
  • Combined Grades Big Ideas – ALL GRADES
  • Combined Grades Big Ideas – K-1
  • Combined Grades Big Ideas – Grades 1-2
  • Combined Grades Big Ideas – Grades 2-3
  • Combined Grades Big Ideas – Grades 3-4
  • Combined Grades Big Ideas – Grades 4-5
  • Combined Grades Big Ideas – Grades 5-6
  • Combined Grades Big Ideas – Grades 6-7

Big Ideas by Subject

  • Skills can be developed through play.  (Grade 1-2)
  • Technologies are tools that extend human capabilities.  (Grade 1-2)
  • Designs grow out natural curiosity (Grade 1-2)
  • Skills can be developed through play (2) (Grade 1-2)
  • Skills are developed through practice, effort, and action. (Grade 4-5)
  • Design can be responsive to identified needs.  (Grade 6-7)
  • People connect to others and share ideas through the arts.  (Grade K-1)
  • People connect to story through the arts (Grade 1)
  • Engagement in the arts creates opportunity for inquiry through purposeful play (Grade 1)
  • Inquiry through the arts creates opportunities for risk-taking (Grade 2)
  • Creative expression is a means to explore and share one’s identity within a community. (Grade 4-5)
  • Engaging in creative expression and experiences expands people’s sense of identity and belonging. (Grade 4-5)
  • The impact of contact and colonialism continues to affect the political, social, and economic lives of BC First Peoples.  (Grade 12)
  • The identities, worldviews, and language of BC First Peoples are renewed, sustained, and transformed through their connection to the land. (Grade 12)
  • The impact of contact and colonialism continues to affect the political, social, and economic lives of BC First Peoples. (2) (Grade 12)
  • Cultural expressions convey the richness, diversity, and resiliency of BC First Peoples. (Grade 12)
  • Understanding the diversity and complexity of cultural expressions in one culture enhances our understanding of other cultures  (Grade 12)
  • Interactions between belief systems, social organization, and language influence artistic expressions of culture. (Grade 12)
  • Understanding the diversity and complexity of cultural expressions in one culture enhances our understanding of other cultures. (2) (Grade 12)
  • Interactions between belief systems, social organization, and language influence artistic expressions of culture. (2) (Grade 12)

Comparative World Religions

  • Comparing beliefs provides insights and understanding of diverse global cultures and peoples.
  • Comparing beliefs provides insights and understanding of diverse global cultures and peoples. (2)

Contemporary Indigenous Studies

  • Indigenous peoples are reclaiming mental, emotional, physical, and spiritual well-being despite the continuing effects of colonialism.
  • Indigenous peoples continue to advocate and assert rights to self-determination.
  • The identities, worldviews, and language of indigenous peoples are renewed, sustained, and transformed through the connection to the land.
  • Indigenous peoples continue to advocate and assert rights to self-determination. (2)
  • Stories give us unique ways to interpret and share knowledge, thoughts, and feelings.  (Grade 8-10)
  • Language and story can be a source of creativity and joy. (Grade 1-2)
  • Curiosity and wonder lead us to new discoveries about ourselves and the world around us. (Grade 1-2)
  • Texts can be understood from different perspectives .(Grade 4)
  • Using language in creative and playful ways helps us understand how language works. (Grade 4)
  • Using language in creative and playful ways helps us understand how language works. (2) (Grade 4-5)
  • Texts can be understood from different perspectives.  (Grade 4-7)
  • Texts can be understood from different perspectives.  (2) (Grade 4-7)
  • Exploring and sharing multiple perspectives extends our thinking.  (Grade 4-7)

Law Studies

  • Understanding legal rights and responsibilities allows citizens to participate more fully in society.
  • Understanding legal rights and responsibilities allows citizens to participate more fully in society. (2)
  • Laws can maintain the status quo and can also be a force for change.
  • Laws can maintain the status quo and can also be a force for change. (2)
  • A society’s laws and legal framework affects many aspects of people’s daily lives.
  • A society’s laws and legal framework affects many aspects of people’s daily lives. (2)
  • Designs develop out of natural curiosity   (ADST 1-3)
  • Developing computational fluency comes from a strong sense of number.  (Grade 4-7)
  • Number represents and describes quantity: Part of wholes can be represented by fractions and decimals. (Grade 4-7)
  • Computational fluency and flexibility with numbers extend to operations with integers and decimals. (Grade 7)
  • Data from circle graphs can be used to illustrate proportion and to compare and interpret.  (Grade 7)
  • The constant ratio between the circumference and diameter of circles can be used to describe, measure and compare spatial relationships.  (Grade 7)
  • Linear relations can be represented in many connected ways to identify regularities and make generalizations. (Grade 7)
  • Computational fluency and flexibility with numbers extend to operations with integers and decimals.  (Grade 7)
  • Number represents, describes, and compares the quantities of ratios, rates, and percents. (Grade 8)
  • Daily physical activity enables us to practice skillful movement and helps us develop personal fitness.  (Grade 4-7)
  • The motion of objects depends on their properties. (Grade K)
  • Living things have features and behaviours that help them survive in their environment. (Grade 1)
  • Living things have life cycles adapted to their environment. (Grade 2)
  • Water is essential to all living things. (Grade 2)
  • Matter has mass, takes up space, and can change phase.   (Grade 4)
  • Everyday materials are often mixtures. (Grade 6)
  • Multi-cellular organisms rely on internal systems to survive, reproduce, and interact with their environment.  (Grade 6)
  • Multi-cellular organisms rely on internal systems to survive, reproduce, and interact with their environment. (2) (Grade 6)
  • Multi-cellular organisms rely on internal systems to survive, reproduce, and interact with their environment (3) (Grade 6).
  • The electromagnetic force produces both electricity and magnetism. (Grade 7)
  • Earth and its climate have changed over geological time. (Grade 7)
  • Evolution by natural selection provides an explanation for the diversity and survival of living things.  (Grade 7)
  • Elements consist of one type of atom, and compounds consist of atoms of different elements chemically combined.  (Grade 7)
  • The theory of plate tectonics is the unifying theory that explains Earth’s geological processes. (Grade 8)
  • Living things sense and respond to their environment – Birds  (Grade 4)
  • Living things sense and respond to their environment – Farm (Grade 4)
  • Living things sense and respond to their environment – Forest (Grade 4)
  • Living things sense and respond to their environment – Pond (Grade 4)

Social Justice

  • The causes of social injustice are complex and have lasting impacts on society.
  • The causes of social injustice are complex and have lasting impacts on society. (2)
  • Social justice issues are interconnected.
  • Individual worldviews shape and inform the understanding of social justice issues.
  • Stories and traditions about ourselves and our families reflect who we are and where we are from. (Kindergarten)
  • Our rights, roles, and responsibilities are important for building strong communities. (Grade 1)
  • Local actions have global consequences, and global actions have local consequences.  (Grade 2)
  • Local actions have global consequences, and global actions have local consequences. (2) (Grade 2)
  • Canada is made up of many diverse regions and communities.  (Grade 2)
  • Learning about indigenous peoples nurtures multicultural awareness and respect for diversity. (Grade 3)
  • British Columbia followed a unique path in becoming a part of Canada.  (Grade 4)
  • The pursuit of valuable natural resources played a key role in changing the land, people and communities of Canada.  (Grade 4)
  • Interactions between First Peoples and Europeans lead to conflict and cooperation, which continues to shape Canada’s identity. (Grade 5)
  • Canada’s policies and treatment of minority peoples have negative and positive legacies. (Grade 5)
  • Canada’s policies and treatment of minority peoples have negative and positive legacies. (2) (Grade 5)
  • Systems of government vary in their respect for human rights and freedoms. (Grade 6)
  • Contacts and conflicts between peoples stimulated significant cultural, social, political change. (Grade 8)
  • Exploration, expansion, and colonization had varying consequences for different groups. (Grade 8)
  • Disparities in power alter the balance of relationships between individuals and between societies. (Grade 9)
  • Worldviews lead to different perspectives and ideas about developments in Canadian society. (Grade 10)
  • Worldviews lead to different perspectives and ideas about developments in Canadian society. (2) (Grade 10)

“Big Ideas are statements that are central to one’s understanding in an area of learning. A Big Idea is broad and abstract. It contains key concepts that generally are timeless and transferable to other situations. Big Ideas are the key concepts, principles, and theories that are used to organize knowledge within an area of learning. A Big Idea is a statement of an idea that is central to an area of learning or across disciplines and that links numerous understandings into a coherent whole.”

from The BC Ministry of Education’s New Curriculum

big ideas help

Homes & Gardens

Large garden ideas: 15 design savvy ways to transform a spacious plot

Posted: August 16, 2023 | Last updated: August 16, 2023

<p>                     Our large garden ideas are bursting with design tricks and inspiration – just what you need to whip your vast patch into shape. From simple planting tips to fill your outside space with year-round color and interest to nifty ways to help divide and cosy up a dull, empty plot, we can help you realize your vision and get the outdoor space you long for.                   </p>                                      <p>                     Forming a clear, overall plan for your garden layout is well worth the time and effort, but often tight budgets and other commitments mean putting them into action, all at once, is not always possible. But don’t despair, by just concentrating on one smaller area – maybe next to the house or a single aspect of your large garden ideas, you can gradually transform your space and enjoy the changes.                   </p>                                      <p>                     We’ve spoken to leading industry experts and experienced landscape designers to get their advice and top tips. Although no two projects are the same, great ideas are always transferable and these are just the ticket to transform your large garden ideas into somewhere truly special.                   </p>                                      <p>                     <em>BY JILL MORGAN</em>                   </p>

Looking for smart large garden ideas? Our selection will help you decide on the best plants, landscaping and lifestyle choices for your outside space

Our large garden ideas are bursting with design tricks and inspiration – just what you need to whip your vast patch into shape. From simple planting tips to fill your outside space with year-round color and interest to nifty ways to help divide and cosy up a dull, empty plot, we can help you realize your vision and get the outdoor space you long for.

Forming a clear, overall plan for your garden layout is well worth the time and effort, but often tight budgets and other commitments mean putting them into action, all at once, is not always possible. But don’t despair, by just concentrating on one smaller area – maybe next to the house or a single aspect of your large garden ideas, you can gradually transform your space and enjoy the changes.

We’ve spoken to leading industry experts and experienced landscape designers to get their advice and top tips. Although no two projects are the same, great ideas are always transferable and these are just the ticket to transform your large garden ideas into somewhere truly special.

BY JILL MORGAN

<p>                     Water features are the perfect way to bring light and a sense of space into any garden, and nothing can be more dramatic in a large, open plot. Rills and raised water features contrast sharply with smooth paving and dense areas of planting, as well as providing mesmerizing reflections too.                   </p>                                      <p>                     Sit back and watch scudding clouds overhead and lose yourself in the ripples created by the slightest breeze on the water’s surface. In this design, a large raised rectangular pool is framed by two rows of pleached hornbeams and links the greenhouse and kitchen garden with the central lawn. The fretwork sphere and tiered water feature are carefully lit from below to create stunning night-time features.                   </p>

1. Link areas with a raised reflective pool

Water features are the perfect way to bring light and a sense of space into any garden, and nothing can be more dramatic in a large, open plot. Rills and raised water features contrast sharply with smooth paving and dense areas of planting, as well as providing mesmerizing reflections too.

Sit back and watch scudding clouds overhead and lose yourself in the ripples created by the slightest breeze on the water’s surface. In this design, a large raised rectangular pool is framed by two rows of pleached hornbeams and links the greenhouse and kitchen garden with the central lawn. The fretwork sphere and tiered water feature are carefully lit from below to create stunning night-time features.

<p>                     Whether you need undercover space for entertaining, working out or just lounging, a sturdy and versatile shelter is a fantastic investment for your large garden ideas. Not only will it change how you use your garden, but it makes a dramatic focal point too.                   </p>                                      <p>                     Patio covers vary hugely from simple timber pergolas with canvas linings, to substantial, automated shelters. More expensive designs come with features such as rotating louvre slatted panels and retractable screens that form versatile covers and can be configured according to the weather conditions and the occasion.                   </p>                                      <p>                     You could even consider adding integrated outdoor lighting into the beams or roof blades – choose from cool or warm white or color changing LEDs, plus sound and heating.                   </p>

2. Go for a versatile garden shelter

Whether you need undercover space for entertaining, working out or just lounging, a sturdy and versatile shelter is a fantastic investment for your large garden ideas. Not only will it change how you use your garden, but it makes a dramatic focal point too.

Patio covers vary hugely from simple timber pergolas with canvas linings, to substantial, automated shelters. More expensive designs come with features such as rotating louvre slatted panels and retractable screens that form versatile covers and can be configured according to the weather conditions and the occasion.

You could even consider adding integrated outdoor lighting into the beams or roof blades – choose from cool or warm white or color changing LEDs, plus sound and heating.

<p>                     If you love plants and laid-back style, then take inspiration for your south-facing garden ideas from the dreamy prairie style of planting. Seas of swaying ornamental grasses and flowers, interwoven with pockets of color and texture form a beautiful, ever-changing scene that can be successfully scaled down from vast large gardens to a single border in smaller spaces.                   </p>

3. Try some prairie-style planting

Accentuate a large open site with some prairie style planting for your garden borders. Think of vast swathes of grasses and colorful perennials swaying in the breeze, providing an ever-changing display throughout the year.

The secret to making this way of planting work is to keep to a small palette of plants and repeat them at regular intervals. Plant them in drifts and ribbons, weaving them together to create a dense tapestry.

One place that offers plenty of inspiration is the Sussex Prairie Garden in England. 'We believe in an exuberance of spirit and this manifests itself in a mass planting of each variety of plant coupled with a mix of ornamental grasses to lift the levels and add sound, texture and spectacle,' explains creator Pauline McBride. 'Planting in this exuberant style means that visitors can immerse themselves in our welcoming borders as they walk through an ethereal wonderland.'

<p>                     Do your bit for wildlife gardens and create your new go-to spot, by building a pond. A magnet for birds, insects and mammals too, it’s amazing how quickly it will transform a featureless plot.                   </p>                                      <p>                     Designer Claudia de Yong has worked on a few ponds in her time and shares the following tips. 'The minute you introduce a water feature into a garden, whatever size, whatever style, you are immediately creating other dimensions. Water gently flowing over rocks and stone creates a soft, calming sound. Reflections of tree, plants and even buildings will as depth to your garden.'                   </p>                                      <p>                     Make the most of the site, by going for the biggest garden ponds you can – they always look smaller once they are full and planting has established. Native wildflowers and grasses will soften the edges and provide cover for wildlife, while a simple timber jetty is the perfect place to sit and gaze from.                   </p>

4. Establish a wildlife pond

Do your bit for wildlife gardens and create your new go-to spot, by building a pond. A magnet for birds, insects and mammals too, it’s amazing how quickly it will transform a featureless plot.

Designer Claudia de Yong has worked on a few ponds in her time and shares the following tips. 'The minute you introduce a water feature into a garden, whatever size, whatever style, you are immediately creating other dimensions. Water gently flowing over rocks and stone creates a soft, calming sound. Reflections of tree, plants and even buildings will as depth to your garden.'

Make the most of the site, by going for the biggest garden ponds you can – they always look smaller once they are full and planting has established. Native wildflowers and grasses will soften the edges and provide cover for wildlife, while a simple timber jetty is the perfect place to sit and gaze from.

<p>                     If you have a sizeable plot, think big. A few well-chosen large features will have more impact than cluttering the space with many, smaller features. Consider how and where to site sculptural pieces carefully. Do you want to position them as a dramatic centerpiece at the far end of a long, border-lined lawn or paved terrace, or would you prefer to go for an element of surprise, and tuck them around a hidden corner or separate garden ‘room’ with high hedging?                   </p>                                      <p>                     The style of artwork and choice of materials is a matter of personal taste. Contemporary pieces work beautifully in front of loose and airy, densely planted borders, while more intricate, traditional designs are set off perfectly by a dark, simple backdrop – think a clipped yew hedge or an ivy-covered garden wall.                   </p>                                      <p>                     'We’ve recently seen an increased demand for pieces that juxtapose dissimilar metals,' says the team at David Harber. 'For example, organic patinated bronze alongside the crisp, highly reflective mirrored finish of stainless steel or the warm, natural glow of gold.'                   </p>

5. Add drama with an eye-popping sculpture

If you have a sizeable plot, think big. A few well-chosen large features will have more impact than cluttering the space with many, smaller features. Consider how and where to site sculptural pieces carefully. Do you want to position them as a dramatic centerpiece at the far end of a long, border-lined lawn or paved terrace, or would you prefer to go for an element of surprise, and tuck them around a hidden corner or separate garden ‘room’ with high hedging?

The style of artwork and choice of materials is a matter of personal taste. Contemporary pieces work beautifully in front of loose and airy, densely planted borders, while more intricate, traditional designs are set off perfectly by a dark, simple backdrop – think a clipped yew hedge or an ivy-covered garden wall.

'We’ve recently seen an increased demand for pieces that juxtapose dissimilar metals,' says the team at David Harber. 'For example, organic patinated bronze alongside the crisp, highly reflective mirrored finish of stainless steel or the warm, natural glow of gold.'

<p>                     The pressure to use every inch of our homes recently has accelerated the trend for setting up an outdoor kitchen. If you have the space, why not make cooking in the open air a sociable occasion by setting up an adjacent lounge area.                   </p>                                      <p>                     'Our desire for a great outdoor space has evolved way beyond a portable barbecue and fold-away garden furniture and instead these are now required to be fully functional living spaces,' says Simon Burvill, founder of Gaze Burvill. 'With areas to relax, cook, entertain and dine, we can create distinct rooms to give a natural indoor-outdoor flow.'                   </p>                                      <p>                     Just as with an inside kitchen, ample storage and prep space is a must when considering how to design an outdoor kitchen. Go for a mix of drawers and cabinets, adding built-in fridges, wine coolers and ice-drawers where space and budget allows.                   </p>                                      <p>                     An outdoor sink, either plumbed into mains water or feeding off a concealed storage tank, will make every occasion easier and save endless return trips to the house. Upstands with shelving and hanging racks will ensure spices and cooking tools are easy to reach, and also provides a handy spot for growing herbs and edible flowers too.                   </p>

6. Devote space to an outdoor kitchen

The pressure to use every inch of our homes recently has accelerated the trend for setting up an outdoor kitchen. If you have the space, why not make cooking in the open air a sociable occasion by setting up an adjacent lounge area.

'Our desire for a great outdoor space has evolved way beyond a portable barbecue and fold-away garden furniture and instead these are now required to be fully functional living spaces,' says Simon Burvill, founder of Gaze Burvill. 'With areas to relax, cook, entertain and dine, we can create distinct rooms to give a natural indoor-outdoor flow.'

Just as with an inside kitchen, ample storage and prep space is a must when considering how to design an outdoor kitchen. Go for a mix of drawers and cabinets, adding built-in fridges, wine coolers and ice-drawers where space and budget allows.

An outdoor sink, either plumbed into mains water or feeding off a concealed storage tank, will make every occasion easier and save endless return trips to the house. Upstands with shelving and hanging racks will ensure spices and cooking tools are easy to reach, and also provides a handy spot for growing herbs and edible flowers too.

<p>                     Love wild swimming or just fancy a spot to dip your toes in the water, then why not go for a natural swimming pond for your backyard pool? Sympathetically designed to fit into the landscape, these pools can be planted up to form an enchanting garden feature as well as an idyllic place to bathe.                   </p>                                      <p>                     Stepping stones, timber jetties and pontoons can all be added into the design, as well as gentle sloping beaches, streams and plunge pools. Dependent on micro-organisms to clean the water, rather than chemicals, these pools will need to be planted up with a careful mix of aquatic plants to maintain the PH balance and prevent algae growth.                   </p>                                      <p>                     Specialists will design, construct and maintain your project, taking into account filtration and drainage issues, any planning issues and planting options. While wildlife, birds and insects will love to visit the pool, it’s best to discourage ducks and geese from taking up residence as they will affect the nutrient balance of the water.                   </p>

7. Create a natural swimming pond

Love wild swimming or just fancy a spot to dip your toes in the water, then why not go for a natural swimming pond for your backyard pool? Sympathetically designed to fit into the landscape, these pools can be planted up to form an enchanting garden feature as well as an idyllic place to bathe.

Stepping stones, timber jetties and pontoons can all be added into the design, as well as gentle sloping beaches, streams and plunge pools. Dependent on micro-organisms to clean the water, rather than chemicals, these pools will need to be planted up with a careful mix of aquatic plants to maintain the PH balance and prevent algae growth.

Specialists will design, construct and maintain your project, taking into account filtration and drainage issues, any planning issues and planting options. While wildlife, birds and insects will love to visit the pool, it’s best to discourage ducks and geese from taking up residence as they will affect the nutrient balance of the water.

<p>                     Fancy a simple but oh-so effective design? Then mix trees, grass and snaking garden paths. Perfect for creating a tranquil spot that's perfect for quiet contemplation or a fun spot for children to play, it’s a great way to make the most of large gardens.                   </p>                                      <p>                     Here, winter flowering cherry trees are dotted across a gently undulating grassy area. Curving turf paths, edged with simple pavers create sweeping clean lines that add movement and balance the slender trees.                   </p>                                      <p>                     'This is part of a very large garden and was originally just a flat bank situated quite a distance from the main house,' explains designer Jo Alderson. 'My client loves trees so we thought it would be fun to create a swirly maze for her grandchildren to discover and run around - together with visiting dogs! Throughout spring there are lots of bulbs popping up through the longer grass.'                   </p>

8. Use trees and paving to sculpt the land

Fancy a simple but oh-so effective design? Then mix trees, grass and snaking garden paths. Perfect for creating a tranquil spot that's perfect for quiet contemplation or a fun spot for children to play, it’s a great way to make the most of large gardens.

Here, winter flowering cherry trees are dotted across a gently undulating grassy area. Curving turf paths, edged with simple pavers create sweeping clean lines that add movement and balance the slender trees.

'This is part of a very large garden and was originally just a flat bank situated quite a distance from the main house,' explains designer Jo Alderson. 'My client loves trees so we thought it would be fun to create a swirly maze for her grandchildren to discover and run around - together with visiting dogs! Throughout spring there are lots of bulbs popping up through the longer grass.'

<p>                     Add character to large gardens by introducing a sweeping path and curvy retaining wall. The perfect design trick for dividing up sloping gardens into a series of more manageable terraces, it will also add a sense of horizontal movement and help to unify a large open space.                   </p>                                      <p>                     In this beautiful design, a snaking dry-stone wall and block paved path intertwine to create a cosy spot that's perfect for a secluded outdoor seating area. Surrounded by loose, textural planting it forms the main focal point of the garden. The beautiful, stacked stone wall also presents the ideal opportunity for a dramatic falling water feature.                   </p>

9. Introduce curves for added interest

Add character to large gardens by introducing a sweeping path and curvy retaining wall. The perfect design trick for dividing up sloping gardens into a series of more manageable terraces, it will also add a sense of horizontal movement and help to unify a large open space.

In this beautiful design, a snaking dry-stone wall and block paved path intertwine to create a cosy spot that's perfect for a secluded outdoor seating area. Surrounded by loose, textural planting it forms the main focal point of the garden. The beautiful, stacked stone wall also presents the ideal opportunity for a dramatic falling water feature.

<p>                     Make the most of your space by including a secluded garden retreat in your large garden. A shepherd's hut nestled behind a hedge or at the far end of the garden, amongst trees, can make the perfect spot for reading, an extra bedroom or for your garden office.                   </p>                                      <p>                     Traditional in shape and neat in size, these raised huts ooze rural style and charm. Fit them out with a wood burning stove, simple kitchen units and kettle, and they can be comfortably used all year-round. Go for a design that's well insulated and can be mains powered and you'll be comfortable outdoors, whatever the weather. Set it up with its own seating area, a log store and some fun fire pit ideas and you’ll have a home-from-home right on the doorstep.                   </p>                                      <p>                     Love the idea but need a more budget-friendly option? Don't discount your existing garden buildings as with some clever shed ideas, even your humble garden shed can become a tranquil outdoor hideaway.                   </p>

10. Include a secret hideaway

Make the most of your space by including a secluded garden retreat in your large garden. A shepherd's hut nestled behind a hedge or at the far end of the garden, amongst trees, can make the perfect spot for reading, an extra bedroom or for your garden office.

Traditional in shape and neat in size, these raised huts ooze rural style and charm. Fit them out with a wood burning stove, simple kitchen units and kettle, and they can be comfortably used all year-round. Go for a design that's well insulated and can be mains powered and you'll be comfortable outdoors, whatever the weather. Set it up with its own seating area, a log store and some fun fire pit ideas and you’ll have a home-from-home right on the doorstep.

Love the idea but need a more budget-friendly option? Don't discount your existing garden buildings as with some clever shed ideas, even your humble garden shed can become a tranquil outdoor hideaway.

<p>                     Paths don’t have to be paved, or even hard underfoot, and often the most enchanting are those that appear to be completely spontaneous. What could be more intriguing than a mown path through a wildflower meadow? Quick and easy to do, you can make the route as twisty or direct as you like. Be kind to your lawn mower by creating your path while the grass is low and repeating fortnightly. Alternatively, you may want to strim long grass first, before mowing neatly. Just check the route is free of wildlife before you start.                   </p>                                      <p>                     'This meadow area provided a lovely transition between manicured garden and arboretum,' says designer Rebecca Smith of her own garden. 'We cut the wildflower area once a year, in late summer when the weather is dry, using a strimmer. The cut plants are then left in place for up to a week, if the weather is dry, to allow the ripened seed to drop out onto the ground, before raking up all the cut stalks and composting them.'                   </p>

11. Cultivate a wild woodland area

Paths don’t have to be paved, or even hard underfoot, and often the most enchanting are those that appear to be completely spontaneous. What could be more intriguing than a mown path through a wildflower meadow? Quick and easy to do, you can make the route as twisty or direct as you like. Be kind to your lawn mower by creating your path while the grass is low and repeating fortnightly. Alternatively, you may want to strim long grass first, before mowing neatly. Just check the route is free of wildlife before you start.

'This meadow area provided a lovely transition between manicured garden and arboretum,' says designer Rebecca Smith of her own garden. 'We cut the wildflower area once a year, in late summer when the weather is dry, using a strimmer. The cut plants are then left in place for up to a week, if the weather is dry, to allow the ripened seed to drop out onto the ground, before raking up all the cut stalks and composting them.'

<p>                     Large garden ideas often call for a bold design, and it’s hard to beat a more formal approach for instant calm and elegance. Clean lines and symmetry always make a powerful statement, so look for opportunities to incorporate these into an overall plan.                   </p>                                      <p>                     Paved terraces, low retaining walls and sets of wide and shallow garden steps are all great ways to divide up a large space and add interest while retaining a sense of calm and tranquillity.                   </p>                                      <p>                     Pale blooms, lush green foliage and smooth, light grey paving also add to the timeless feel.                   </p>

12. Take a formal approach

Large garden ideas often call for a bold design, and it’s hard to beat a more formal approach for instant calm and elegance. Clean lines and symmetry always make a powerful statement, so look for opportunities to incorporate these into an overall plan.

Paved terraces, low retaining walls and sets of wide and shallow garden steps are all great ways to divide up a large space and add interest while retaining a sense of calm and tranquillity.

Pale blooms, lush green foliage and smooth, light grey paving also add to the timeless feel.

<p>                     An immaculate, rolling green lawn might be your pride and joy or even future dream feature for your large garden ideas, but how about using your lawn as a canvas for some ‘mow-art’.                   </p>                                      <p>                     For years, gardeners and groundsmen have been taking a pride in creating perfect grassy stripes or even checks for lawn decoration, but cylinder mower makers Allett have taken it further with its annual Creative Lawn Stripes competition.                   </p>                                      <p>                     Homeowners are encouraged to create imaginative designs using just their mowers and the results are inspiring. The secret to success is in a flat, well maintained lawn and a mower with front and back rollers and a sharp blade.                   </p>                                      <p>                     'The perfect height for perfect stripes is 20-30mm,' says Austin Jarrett, MD at Allett. 'The stripes are created by the reflection of the sun on the bent-over blades of grass. When mowing, make sure that the current stripe slightly overlaps the previous stripe, so that you do not have thin strips of uncut grass left between the stripes.'                   </p>

13. Add some wow to an extensive lawn

An immaculate, rolling green lawn might be your pride and joy or even future dream feature for your large garden ideas, but how about using your lawn as a canvas for some ‘mow-art’.

For years, gardeners and groundsmen have been taking a pride in creating perfect grassy stripes or even checks for lawn decoration, but cylinder mower makers Allett have taken it further with its annual Creative Lawn Stripes competition.

Homeowners are encouraged to create imaginative designs using just their mowers and the results are inspiring. The secret to success is in a flat, well maintained lawn and a mower with front and back rollers and a sharp blade.

'The perfect height for perfect stripes is 20-30mm,' says Austin Jarrett, MD at Allett. 'The stripes are created by the reflection of the sun on the bent-over blades of grass. When mowing, make sure that the current stripe slightly overlaps the previous stripe, so that you do not have thin strips of uncut grass left between the stripes.'

<p>                     Need to bring height and drama to your large garden? Then choose yourself a statement tree. Perfect for adding shape and structure, it will instantly help to divide up the space into different areas and create a more intimate and welcoming feel too.                   </p>                                      <p>                     Take time to research the best specimen for your patch and think carefully about your garden’s aspect and soil type too. Consider whether you prefer a deciduous or evergreen specimen and think about the shape and size of tree that will best suit your garden.                   </p>                                      <p>                     Look for varieties with standout qualities that particularly appeal to you – these could be dramatically colored or textured bark that is reflected in planting elsewhere in the garden, stunning spring blossom or spectacular, vibrant autumn foliage.                   </p>                                      <p>                     Maybe it’s the plant’s shape that will add interest – a multi-stemmed plant will fill out an empty space right away, lend a wild touch too, while a stately pine or walnut will add a touch of class.                   </p>                                      <p>                     We spoke to the team at tree specialists Barcham for their top recommendations:                   </p>                                      <p>                     <strong>- Liquidambar styraciflua 'Worplesdon'</strong>, a ‘maple-like’ tree with spectacular and long-lasting autumn color. The inner canopy turns buttercup yellow while the outer leaves change to a claret red.                   </p>                                      <p>                     <strong>- Sorbus aria Lutescens</strong>, the early spring foliage of this whitebeam emerge as a striking grey/silver/blue and the canopy has a graceful, rounded shape. Red orange berries shine out in autumn.                   </p>                                      <p>                     <strong>- Betula albosinensis Fascination</strong>, the gorgeous cinnamon colored peeling bark turns cream as it matures and has a glossy sheen too. The flame-shaped crown has a clean, architectural shape making it ideal for urban, modern gardens.                   </p>                                      <p>                     <strong>- Paper Mulberry</strong>, a lover of chalky soil, this tree is a magnet for pollinators in late summer thanks to its curious orange globe-like flowers. Perfect for creating shade, it has an architectural stem structure in winter.                   </p>

14. Plant a statement tree

Need to bring height and drama to your large garden? Then choose yourself a statement tree. Perfect for adding shape and structure, it will instantly help to divide up the space into different areas and create a more intimate and welcoming feel too.

Take time to research the best specimen for your patch and think carefully about your garden’s aspect and soil type too. Consider whether you prefer a deciduous or evergreen specimen and think about the shape and size of tree that will best suit your garden.

Look for varieties with standout qualities that particularly appeal to you – these could be dramatically colored or textured bark that is reflected in planting elsewhere in the garden, stunning spring blossom or spectacular, vibrant autumn foliage.

Maybe it’s the plant’s shape that will add interest – a multi-stemmed plant will fill out an empty space right away, lend a wild touch too, while a stately pine or walnut will add a touch of class.

We spoke to the team at tree specialists Barcham for their top recommendations:

- Liquidambar styraciflua 'Worplesdon' , a ‘maple-like’ tree with spectacular and long-lasting autumn color. The inner canopy turns buttercup yellow while the outer leaves change to a claret red.

- Sorbus aria Lutescens , the early spring foliage of this whitebeam emerge as a striking grey/silver/blue and the canopy has a graceful, rounded shape. Red orange berries shine out in autumn.

- Betula albosinensis Fascination , the gorgeous cinnamon colored peeling bark turns cream as it matures and has a glossy sheen too. The flame-shaped crown has a clean, architectural shape making it ideal for urban, modern gardens.

- Paper Mulberry , a lover of chalky soil, this tree is a magnet for pollinators in late summer thanks to its curious orange globe-like flowers. Perfect for creating shade, it has an architectural stem structure in winter.

<p>                     Indulge your romantic side and add a historic feature to your garden that will get everyone talking. Popularised in the 18th century at the height of English Landscape design, follies were architectural buildings – usually built in a semi ruinous state – added for decoration and intrigue.                   </p>                                      <p>                     Positioned at the end of a vista, next to a lake to create a stunning reflection or perched high on a hill, these constructions were unique but often inspired by Gothic, Greek or Roman architecture. Local materials and salvaged architectural finds were often incorporated, alongside personalized details such as carved initials over doorways and arches or family crests.                   </p>                                      <p>                     While also eclectic in style, many of the follies are built in cast or reconstituted stone, meticulously finished to create a weathered look, and reclaimed bricks. Choose from freestanding walls featuring arched doorways and mullioned windows or historically inspired facades for summer houses and hot tub enclosures. Stone-pillared pergolas and temple-style porticos are a great choice, if you fancy making a grander impression.                   </p>

15. Have some fun with a folly

Indulge your romantic side and add a historic feature to your garden that will get everyone talking. Popularised in the 18th century at the height of English Landscape design, follies were architectural buildings – usually built in a semi ruinous state – added for decoration and intrigue.

Positioned at the end of a vista, next to a lake to create a stunning reflection or perched high on a hill, these constructions were unique but often inspired by Gothic, Greek or Roman architecture. Local materials and salvaged architectural finds were often incorporated, alongside personalized details such as carved initials over doorways and arches or family crests.

While also eclectic in style, many of the follies are built in cast or reconstituted stone, meticulously finished to create a weathered look, and reclaimed bricks. Choose from freestanding walls featuring arched doorways and mullioned windows or historically inspired facades for summer houses and hot tub enclosures. Stone-pillared pergolas and temple-style porticos are a great choice, if you fancy making a grander impression.

<p>                     Creating a series of garden ‘rooms’ or smaller zones is a great way to add interest and make tackling large gardens seem less intimidating. Stone walls, hedges, and fretwork screens all work well as stylish garden dividers.                   </p>                                      <p>                     Dense areas of tall planting work well and will help you to focus your garden design and available budget into manageable phases. Try ornamental grasses such as Calamagrostis 'Karl Foerster', Molinia Breeze  and Miscanthus sinensis 'Flamingo'.                   </p>                                      <p>                     Think about the different ways you want to use the garden too. An adventure play area, room for growing fruit and vegetables, a sunken lounge area with fire pit for entertaining or a sheltered spot for chilling out with a book or podcast can all be accommodated and can have a dedicated spot too.                   </p>                                      <p>                     The secret to successful large garden ideas though is to have a masterplan to ensure the space fits together as a whole. Final details don’t have to be set from the outset and, of course, plans can and will evolve, but this approach really helps to unify the overall design.                   </p>

How do you make a large garden cozy?

Creating a series of garden ‘rooms’ or smaller zones is a great way to add interest and make tackling large gardens seem less intimidating. Stone walls, hedges, and fretwork screens all work well as stylish garden dividers.

Dense areas of tall planting work well and will help you to focus your garden design and available budget into manageable phases. Try ornamental grasses such as Calamagrostis 'Karl Foerster', Molinia Breeze  and Miscanthus sinensis 'Flamingo'.

Think about the different ways you want to use the garden too. An adventure play area, room for growing fruit and vegetables, a sunken lounge area with fire pit for entertaining or a sheltered spot for chilling out with a book or podcast can all be accommodated and can have a dedicated spot too.

The secret to successful large garden ideas though is to have a masterplan to ensure the space fits together as a whole. Final details don’t have to be set from the outset and, of course, plans can and will evolve, but this approach really helps to unify the overall design.

<p>                     'In a large garden, the spatial arrangements should be set out to enrich the experience of interconnecting gardens with smooth transitions between areas,' says landscape designer Adrienne Hendy-Curzon. 'A multi-seasonal design approach will allow the merits of each season to be championed too.                   </p>                                      <p>                     'A large garden also provides an opportunity to design for future proofing with fundamental improvements of rain harvesting and water storage for the long term, and scope for rich biodiversity and sustainability within the site.'                   </p>

How can I make a large garden more interesting?

'In a large garden, the spatial arrangements should be set out to enrich the experience of interconnecting gardens with smooth transitions between areas,' says landscape designer Adrienne Hendy-Curzon. 'A multi-seasonal design approach will allow the merits of each season to be championed too.

'A large garden also provides an opportunity to design for future proofing with fundamental improvements of rain harvesting and water storage for the long term, and scope for rich biodiversity and sustainability within the site.'

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Keeping a Mortgage After 65: A ‘No Brainer’ or a Big Risk?

Fueled by once-low rates, more older Americans have mortgage debt, according to new research. But the downsides can be significant, some experts say.

Donna and Gary Jacobs, wearing jeans and winter coats, walk down a tree-lined path with a castle behind them.

By Martha C. White

Conventional wisdom dictates that retiring with debt — especially a debt as large and significant as a mortgage — is financially dicey at best and potentially ruinous at worst.

That’s not how Brian Lindmeier sees it. “It just doesn’t make any sense at all to pay off the house,” he said.

Mr. Lindmeier, 80, a retired purchasing and inventory manager, and his wife, Cindy, who retired from the local public school system, refinanced their home in Orange, Calif., at the end of 2020. They rolled over their balance into a new 30-year loan and slashed their interest rate in half to a rate below 3 percent. Mr. Lindmeier called the move a “no brainer.”

“The money I’d have to take out of my savings or out of my investments is yielding higher interest than the interest I’m paying on the loan,” he said.

For a growing number of older Americans, signing up for a mortgage that is likely to outlive them makes good economic sense. A significant percentage of homeowners have fixed-rate mortgages with historically low rates. Roughly six of 10 mortgage borrowers in the third quarter of last year held loans with interest rates of less than 4 percent, according to the online real estate brokerage Redfin. Nearly a quarter had rates of less than 3 percent.

A campaign of rate increases by the Federal Reserve, which is intended to tamp down inflation, has driven yields that investors can get on ultrasafe instruments like certificates of deposit to 5 percent or higher.

Even those who have spent years saving with the intention of paying off their mortgages with a lump sum at retirement are now finding themselves recalculating. Some are determining that those funds would be better deployed by earning returns on other investments or helping them meet their cash flow needs for everyday expenses.

Eric Zittel, chief lending officer at Financial Partners Credit Union in Downey, Calif., said a number of his members, including Mr. Lindmeier, are keeping their mortgages — and their cash.

“They’re realizing they can get a 4.5 percent to 5 percent rate just for a C.D. When you do the math, it makes a lot more sense for them to keep those funds.”

A number of financial advisers and retirement planners argue that the imperative to pay off a mortgage before retirement is an outdated axiom in the current economic climate.

“While paying off a debt feels like a very conservative, secure move, trading your liquidity for a paid-off mortgage is quite risky,” said Evan Beach, president of Exit 59 Advisory, a wealth management firm focusing on retirement-income planning in Alexandria, Va. “You’re giving up money in your pocket that you may actually need for something else.”

Gary Jacobs, a client of Mr. Beach’s and a retired federal employee, and his wife, Donna, a retired nurse, refinanced the mortgage on their home in Chevy Chase, Md., at the end of 2021 when mortgage rates were at a historic trough.

“Timing is everything, and we timed it just right this time,” Mr. Jacobs, 79, said. Refinancing into a new 30-year mortgage at a rate roughly half of their previous interest rate lowered the couple’s monthly payment by around $300.

“Although we could have, we didn’t feel like drawing down on our cash reserves in order to pay the mortgage off,” Mr. Jacobs said, adding that paying off the mortgage would have taken about half of their savings. “We’re conservative in the sense of wanting to be prepared for eventualities where we might need the cash.”

This dynamic is one factor driving historically large percentages of older Americans to carry mortgage debt into their senior years, according to a new report from the Joint Center for Housing Studies of Harvard University. In 2022, researchers found that just over 40 percent of homeowners older than 64 had a mortgage, a jump from roughly 25 percent a generation ago.

Ultralow mortgage rates were a big driver of the increase, said Jennifer Molinsky, project director of the center’s housing and aging society program. “We do think that, for some people, there is a calculated financial decision that they’d prefer to keep their mortgage, even if they could pay it off, and invest it elsewhere,” she said.

But Ms. Molinsky expressed concern that the increase came in tandem with an overall rising debt load among seniors. “There’s a trend among all older adults that there’s a higher level of debt across the board,” she said.

The downside of having a mortgage

Retirees on fixed incomes may struggle to manage higher-interest and variable-rate debt like outstanding credit card balances. In a worst-case scenario, if a health crisis or the death of a spouse destabilizes their life or their finances, older Americans could be at risk of losing their homes.

“For a lower-income senior, homeownership can sometimes become challenging, because when people enter their retirement years, they often see a decrease in income,” said Lori Trawinski, director of finance and employment for the AARP Public Policy Institute.

While the recent run-up in home prices has given homeowners more equity on paper, this can pose a challenge for those on fixed incomes since those higher valuations can lead to higher property taxes and insurance premiums.

Some experts in elder finance and policy point out that because a mortgage is almost always the biggest component of a homeowner’s monthly expenses, homeowners in their 50s and 60s have less resilience to absorb a financial hit like an unexpected job loss or caregiving demands.

“Housing is the biggest chunk of that budget for everybody, so it’s undoubtedly more expensive on a month-to-month basis to have a mortgage than to have a home that’s paid off,” said Beth Truesdale, a research fellow at the W.E. Upjohn Institute for Employment Research.

While people might intend to remain employed until they are able to draw Social Security, Ms. Truesdale said, her research indicates that only about half of American workers remain employed throughout their 50s. This suggests that an income-reducing event is more common than many people expect. While the drop in labor force participation is more pronounced among women and less-educated workers, the employment rate drops by about 20 percentage points among all demographics for people in their 50s.

“Even for people who start out with the advantages, there’s no guarantee they can work as long as they want to,” Ms. Truesdale said.

For those who own their homes free and clear, the Joint Center for Housing Studies found that older Americans often struggle to tap the equity locked up in their homes. And those homes might not be as valuable as their owners believe. Ms. Trawinski of the AARP said longtime homeowners might be content living with, for instance, outdated kitchens or bathrooms.

“It often happens that people will not do those kinds of upgrades,” she said. Older homeowners might also have mobility limitations or other physical challenges that make maintenance and upkeep of a property more challenging.

Lower-income senior homeowners, who are more likely to be people of color, are also more liable to struggle to pay for necessary repairs and upgrades. “There’s less ability to invest in that property and maintain it over time,” Ms. Molinsky of the center for housing studies said. “People need to maintain the value of that asset if they want to use that equity later in life,” but, she added, maintenance can entail significant costs.

The effect that housing costs can have on the average household budget can prompt some people to view a mortgage as a risky obligation to carry into retirement — in some cases, whether that concern is warranted or not, said David Frisch, founder of Frisch Financial Group in Melville, N.Y.

“In addition to the financial calculations, it’s also psychological in terms of risk,” he said, adding that even when the math suggests that maintaining a mortgage would cost less than paying it off, some homeowners’ intense aversion to debt influences their choices. “Some people don’t want that mortgage payment hanging over their head even though they’re earning more” by keeping that cash in C.D.s or Treasury securities, he said.

Some financial planners embrace a less-debt-is-better philosophy, as well. Jamie Cox, managing partner of Harris Financial Group in Richmond, Va., said a homeowner’s psychological approach to debt plays a role in his reluctance to encourage a client to hold onto a mortgage.

During the financial crisis, Mr. Cox said, his clients with paid-off mortgages were more sanguine about the drop in their portfolios because they didn’t have that obligation hanging over their heads. “They’re better investors because they’re not afraid of losing their homes,” he said.

Figuring out what’s best for you

No single decision will work for everyone, so financial planners suggest that homeowners at or near retirement consider the specifics of their mortgage terms, cost of living and risk tolerance, along with the following points:

If you took advantage of historically low rates to refinance, it’s possible that you could earn a higher yield by keeping money earmarked for a mortgage payoff in safe investments like C.D.s or Treasuries.

Financial advisers warn against paying off a mortgage if doing so would leave you with little or no emergency savings. Advisers typically suggest keeping an emergency fund of between three and six months’ worth of living expenses in cash or similarly liquid instruments.

Your personal risk tolerance matters. Saving a couple hundred dollars a month shouldn’t come at the price of your peace of mind.

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10 Big Ideas Math Features that Help Promote Productive Math Discussions

  • May 14 2020
  • Big Ideas Learning Consultants

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Big Ideas Math consultants share their favorite program features that help teachers encourage students to have productive math discussions.

Over the past few months, remote learning has altered the way we approach many aspects of our teaching. And even though our physical classrooms have changed significantly, our discussions with our students should not. Earlier this week, Sophie Murphy outlined some tips for how to have meaningful and productive math discussions . We reached out to our team of experts to share their favorite Big Ideas Math features to start those discussions, and how to use them in your remote learning classrooms.

1. Success Criteria – Grade K-12, Teaching Edition

Success-Criteria

Modeling Real Life Grade 7 Chapter 8 Learning Target and Success Criteria

The Success Criteria , which are included at the beginning of each chapter and Section in the Teaching Edition, (both print and digital), are very helpful in the promotion of productive math discussion in the math classroom. Success Criteria are the measures by which students and teachers can determine how well students have met the Learning Target of the chapter. They can be useful in helping students to take ownership in their individual learning and being able to express their understanding of what they have learned. Teachers can use these “I can” statements as discussion points or prompts to encourage students to speak about what they know and to determine their confidence factor. Teachers can then use what students express to informally assess student progress. They can then determine how to proceed, whether it be to continue moving forward, pause to reteach, or provide intervention assistance to those in need.

- Tim Taykowski

2. Red Question Marks – Grade K-12, Teaching Edition

Red-Question-Marks-in-Dig-In

Red Question Marks Found in the Teaching Edition of Modeling Real Life 5th Grade

I find the Red Question Marks in the Teaching Edition to be helpful for promoting discussion. They are great prompts for eliciting student thinking. Sometimes they challenge students to think deeper or help students connect what they are learning to prior knowledge or real-life experiences. They don’t have to be used as a script. I recommend that teachers take a look at them prior to teaching the lesson in class so they can think about how they might put the question in their own words or edit it to better align with the current interests or academic background of their class. Sometimes a good question can divide a class! To further promote discussion, you can take this opportunity to set up a mock debate:

  • Have students get into groups based on the answer they agree.
  • Give them a little time to come up with evidence.
  • Have them present their arguments.

- Sophia Montiel

3. Try Its and Monitoring Progress – Grade 6-12, Student Edition

Try-it

6th Grade Modeling Real Life Try It

The Try Its in the Middle School Student Edition and the Monitoring Progress in the High School Student Edition teach students how to uncover the different layers of understanding. Learners realize there is a difference between comfortably following along with the teacher and working out a problem independently from scratch. Students take ownership of their own learning when they test their understanding of the concepts found in the stepped-out examples. By working the preceding examples as a class, students gain the necessary exposure to the appropriate concepts and skills. Then, by completing the Try Its or Monitoring Progress immediately afterwards, students test their level of understanding and reinforce the correct procedure. 

Teachers get continual feedback of students' understanding after every example. Teachers rely on this data to find the ideal pace and determine if extra examples are needed or if the class can skip an example and move on to the next. The scaffolded Try-Its and Monitoring Progress reach all levels of learners right where they are, and the additional exercises ensure that students reinforce sound problem-solving technique.

- Erin Cockrell

4. Performance Tasks – Grade 6-12, Assessment Book

Performance-Task

Performance Tasks For Algebra 1 Chapter 9

I was always amazed at my students’ curiosity, especially once I learned how to tie that curiosity into math discussions. When I used Big Ideas Math in my classroom, the Performance Tasks helped make sure that every unit had at least one place where we could have productive discussions. Because the tasks are real-world applications; they allowed my students to see math in action, which is always helpful to promote meaningful mathematical discussions and solidify their understanding of the underlying math. They quickly became one of my students’ favorite activities.

Since the Performance Tasks can be found in the “Featured Chapter Resources” section of the main dashboard, these were easy to access. I used these as mini projects to close out a chapter and would always have some sort of group activity that allowed students to share their work. I would often use gallery walks because they are structured and can be easily timed to make sure that I did not spend too much time on presentations.

- Matt Stoddard

5. Closures – Grade K-12, Teaching Edition

Closures

Closures found in Grade 4 of Big Ideas Math: Modeling Real Life

Closures, located in the Teaching Edition at the end of every lesson, can help students organize the information in a meaningful context in their minds. This helps students better understand what they learned and provides a way that they can apply it to the world around them. Summarizing and making that connection will also help students take ownership of their learning targets for that particular lesson. Laurie’s Notes provide instruction for a closure, but the teacher should prepare before the lesson to modify/plan for individual student needs in the classroom. The teacher should prepare the closure to meet the current academic needs in the classroom. The teacher can choose to conduct the closure in small groups, partners, or as a whole group to promote engagement. 

- Margaret Rebman

6. Explore and Grow or Explorations – Grade K-12, Student Edition

Exploration

Example of an Exploration found in 8th Grade Big Ideas Math: Modeling Real Life

The explorations have really helped increase “math talk” with my students. The explorations are found at the beginning of each lesson, in both the Teaching Edition and Student Edition. In addition, they can be accessed digitally through the Dynamic Student Edition and the resources tab on the teacher dashboard. No matter how you decide to access them, you will quickly see that the exploration tasks are carefully designed to be appropriate, relevant, and challenging to all students. They also naturally generate curiosity and encourage questioning within students, which is the springboard for math discussions. The explorations can be repeated for emphasis, and even adjusted, with Laurie’s Notes, according to the instructional level of your students. To get the most from this embedded resource, I suggest having students complete them daily and own 90% of the work. This means that the teacher should behave as a facilitator that encourages and challenges thinking. Once the explorations are complete, reserve time to process and discuss findings and learnings.

- Angela Gray

Explore-and-Grow

Explore and Grow for 3rd Grade Big Ideas Math: Modeling Real Life

The Explore and Grow, or Explorations, are designed to develop conceptual understanding are to be completed with a partner or group. This allows students to use each other’s prior knowledge and problem-solving skills as they work through the productive struggle of these tasks. Through this process the students will need to have meaningful math conversations between themselves, which allows teachers to gain insight into the students understanding of the concept. During this time, teachers may need to prompt students to elicit their thinking, therefore encouraging further discussion. The observations the teacher is making during this time will help to guide the instruction that will follow. 

- Amanda Shelley

Having students work in pairs to complete the Explorations or Explore and Grows at the start of each lesson is a quick and easy way to promote discussion among students. The questions and activities in the Explorations and Explore and Grows have students draw on their own ideas and prior knowledge to work through a problem, so all students have something they can contribute. They often include models and manipulatives to support students and help them connect ideas. In the Explorations there are guiding questions for students. You can have students discuss these questions with their partners and then share ideas as a class. You can encourage deeper discussion by having students question each other and justify their solutions to the class.

- Erin Ross

7. Cross-Curricular Connections – Grade K-5, Teaching Edition

Cross-Curriculuar

Cross-Curricular Connections give examples of how to apply math in other subjects.

I love the Cross-Curricular Connections that Laurie Boswell has in each section of every chapter. It promotes class discussion at any grade level, and it constantly reminds students that math is connected to EVERYTHING. You can find these activities under Connect and Extend Learning at the end of every section. You’ll find that Laurie provides you with suggested details on how to implement every cross-curricular activity. These cross-curricular activities allow your students to have an additional modeling real life experience while emphasizing what’s been taught in that particular section.

- Jennifer Marcum

8. Dig-Ins – Grade K-5, Teaching Edition

Dig-Ins

Big Ideas Math: Modeling Real Life 2nd Grade Dig In

Dig-Ins, located inside the Teaching Edition both in print and online, promote discussion by giving students a task and encouraging them to work with a partner or small group. They discuss how they would solve and share their ideas with their peers. In some instances, they may disagree in which they would have to provide evidence.

- Janay Foster

9. STEAM Videos – Grade 3-12, Student Dynamic E-book

STEAM-Videos

STEAM Videos are included within the Big Ideas Math Dynamic Classroom

STEAM Videos, located in the Student Dynamic E-Book as well as the Resources section online, provide a great starting point for student discourse. There is an incredibly wide range of topics such as sports, architecture, and science that all focus on how important math is in real-world situations. Teachers can play them at the beginning of class time as a bellringer to initiate thought and conversation around the lesson at hand or students can watch them on their own for entertainment and to promote thinking about mathematics in a new way.

10. Math Games – Grade K-12, Online

Game-Library

List of interactive and printable games found in the Big Ideas Math Dynamic Classroom

One resource that I think would be best beneficial for teachers to use for student engagement in conversation would be the math games! Math games are a phenomenal way to differentiate instruction and to truly test the skills of each learner. Seeing students may be overwhelmed with many changes they've experienced since COVID-19, math games would be a great way to lighten their mood and assess them informally on the curriculum. The math games can be found in the online platform in the resource section. The math games promote productive math discussion because they are able to help break down any anxiety that students may face, and get down to the realistic understanding and conceptual framework that students should know regarding particular standards found within the math games. When the students know how to be successful at the game, then they understand the curriculum. The math games can be the teacher's assurance that their students have succeeded in the content.

I would suggest the teacher use math games at the ends of explaining the curriculum and towards the end of a practice section with students. They can assign math games for a project, review before a quiz, and for extra practice. Math games would be great for revisiting specific standards that students may struggle with, as well as making sure that students are proficient and have mastered other standards.

- India White

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  5. Big Ideas: Keeping the Expert at the Center

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    Here is a quick example of a basic plan to help learners ask the right questions, generate the needed guiding activities to answer the questions. Tools: bubble.us, FreeMind, XMind. Photo Essay - Grab those phones, cameras, etc and take a walk around the community or school and take pictures of issues and concerns.

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  15. Khan Academy Aligned to Big Ideas Math Algebra 1

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  27. Live Chat Tutor

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