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## Arithmetic and Number Concepts

## Fourth Grade (Grade 4) Problem Solving Strategies Questions

- 2,175 + 8,259 = 10,434
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- 10,434 - 2,175 = 8,259
- 8,000 + 2,000 = 10,000
- $5 for each of the first 10 pages
- $1 for each remaining page
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- 7,821 - 4,567 = ?
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- The Easter bunny delivers 8 eggs to the Martin family.
- There are 4 people in the Davolio family.
- 6 eggs are delivered to the Burke family.
- How many total eggs do the Martin and Burke families receive?
- If she is playing singles or doubles.
- How many cans of tennis balls bought.
- Whether she won or lost the match.
- How many cans of tennis balls the store had.
- 160 - 8 = 152
- 160 + 8 = 168
- 160 + 16 = 176
- 160 - 16 = 144
- Draw 4 tallies on one side. Draw 0 tallies on the other. Add.

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## Classroom Q&A

In this EdWeek blog, an experiment in knowledge-gathering, Ferlazzo will address readers’ questions on classroom management, ELL instruction, lesson planning, and other issues facing teachers. Send your questions to [email protected]. Read more from this blog.

## Four Teacher-Recommended Instructional Strategies for Math

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(This is the first post in a two-part series.)

The new question-of-the-week is:

What is the single most effective instructional strategy you have used to teach math?

This post is part of a longer series of questions and answers inviting educators from various disciplines to share their “single most effective instructional strategy.”

Two weeks ago, educators shared their recommendations when it came to teaching writing.

Last month , it was about teaching English-language learners.

There are many more to come!

Today, Cindy Garcia, Danielle Ngo, Patrick Brown, and Andrea Clark share their favorite math instructional strategies.

## ‘Concrete Representational Abstract’

Cindy Garcia has been a bilingual educator for 14 years and is currently a district instructional specialist for PK-6 bilingual/ESL mathematics. She is active on Twitter @CindyGarciaTX and on her blog:

The single most effective strategy that I have used to teach mathematics is the Concrete Representational Abstract (CRA) approach.

During the concrete step, students use physical materials (real-life objects or models) to explore a concept. Using physical materials allows the students to see and touch abstract concepts such as place value. Students are able to manipulate these materials and make sense of what works and what does not work. For example, students can represent 102, 120, and 201 with base 10 blocks and count each model to see the difference of the value of the digit 2 in each number.

During the representational step, students use pictures, images, or virtual manipulatives to represent concrete materials and complete math tasks. Students are making connections and gaining a deeper understanding of the concept by creating or drawing representations.

During the abstract step, students are now primarily using numbers and symbols. Students working at the abstract stage have a solid understanding of the concept.

The CRA approach is appropriate and applicable to all grade levels. It is not about the age of the student but rather the concept being taught. In 3rd grade, it is beneficial to students to have them use base 10 blocks to create an open-area model, then draw an open-area model, and finally use the multiplication algorithm. In algebra, it is STILL beneficial to practice using algebra tiles to multiply polynomials using an open-area model.

The CRA approach provides students P-12 to have multiple opportunities to explore concepts and make connections with prior concepts. Some teachers try to start teaching a concept at the abstract level, for example, the standard algorithm for multiplication. However, they soon find out that students have difficulty remembering the steps, don’t regroup, or don’t line up digits correctly. One of the main reasons is that students don’t understand this shortcut and they have not had the concrete & representational experiences to see how the shortcuts in the standard algorithm work.

## ‘Encouraging Discourse’

Danielle Ngo is a 3rd grade teacher and Lower School math coordinator at The Windward School . She has been a teacher for 10 years and works primarily with students who have language-based learning disabilities:

Growing up, so many of us were taught that there is one right answer to every math problem, and that there is one efficient way to arrive at that conclusion. The impetus to return to this framework when teaching math is a tempting one and one I’ve found myself having to fight actively against during my own classroom instruction. In my experience, the most effective way to counter this impulse is to mindfully increase the discourse present during my math lessons. Encouraging discourse benefits our students in several ways, all of which solidify crucial math concepts and sharpen higher-order thinking and reasoning skills:

Distributes math authority in the classroom: Allowing discourse between students—not just between the students and their teacher—establishes a classroom environment in which all contributions are respected and valued. Not only does this type of environment encourage students to advocate for themselves, to ask clarifying questions, and to assess their understanding of material, it also incentivizes students to actively engage in lessons by giving them agency and ownership over their knowledge. Learning becomes a collaborative effort, one in which each student can and should participate.

Promotes a deeper understanding of mathematical concepts: While the rote memorization of a process allows many students to pass their tests, this superficial grasp of math skills does not build a solid foundation for more complex concepts. Through the requisite explanation and justification of their thought processes, discourse pushes students to move beyond an understanding of math as a set of procedural tasks. Rather, rich classroom discussion gives students the freedom to explore the “why’s and how’s” of math—to engage with the concepts at hand, think critically about them, and connect new topics to previous knowledge. These connections allow students to develop a meaningful understanding of mathematical concepts and to use prior knowledge to solve unfamiliar problems.

Develops mathematical-language skills: Students internalize vocabulary words—both their definitions and correct usage—through repeated exposures to the words in meaningful contexts. Appropriately facilitated classroom discourse provides the perfect opportunity for students to practice using new vocabulary terms, as well as to restate definitions in their own words. Additionally, since many math concepts build on prior knowledge, classroom discussions allow students to revisit vocabulary words; use them in multiple, varied contexts; and thus keep the terms current.

## ‘Explore-Before-Explain’

Patrick Brown is the executive director of STEM and CTE for the Fort Zumwalt school district,in Missouri, an experienced educator, and a noted author :

The current COVID-19 pandemic is a sobering reminder that we are educating today’s students for a world that is increasingly complex and unpredictable. The sequence that we use in mathematics education can be pivotal in developing students’ understanding and ability to apply ideas to their lives.

An explore-before-explain mindset to mathematics teaching means situating learning in real-life situations and problems and using those circumstances as a context for learning. Explore-before-explain teaching is all about creating conceptual coherence for learners and students’ experiences must occur before explanations and practice-type activities.

Distance learning reaffirmed these ideas when I was faced with the challenge of teaching area and perimeter for the first-time to a 3 rd grade learner. I quickly realized that rather than viewing area and perimeter as topics to be explained and then practiced, situating learning in problem-solving scenarios and using household items as manipulatives can illustrate ideas and derive the mathematical formulas and relationships.

Using Lego bricks, we quickly transformed equations and word problems into problem-solving situations that could be built. Student Lego constructions were used as evidence for comparing and contrasting physically how area and perimeter are similar and different as well as mathematical ways to calculate these concepts (e.g., students quickly learned by using Legos that perimeter is the distance around a shape while area is the total shape of an object). Thus, situating learning and having students use data as evidence for mathematical understanding have been critical for motivating and engaging students in distance learning environments.

Using an explore-before-explain sequence of mathematics instruction helps transform traditional mathematics lessons into activities that promote the development of deeper conceptual understanding and transfer learning.

## A ‘Whiteboard Wall’

Andrea Clark is a grade 5-7 math and language arts teacher in Austin, Texas. She has a master’s in STEM education and has been teaching for over 10 years:

If you want to increase motivation, persistence, and participation in your math classroom, I recommend a whiteboard wall. Or some reusable dry erase flipcharts to hang on the wall. Or some dry erase paint. Anything to get your students standing up and working on math together on a nonpermanent surface.

The idea of using “vertical nonpermanent surfaces” in the math classroom comes from Peter Liljedahl’s work with the best conditions for encouraging and supporting problem-solving in the math classroom. He found that students who worked on whiteboards (nonpermanent surfaces) started writing much sooner than students who worked on paper. He also found that students who worked on whiteboards discussed more, participated more, and persisted for longer than students working on paper. Working on a vertical whiteboard (hung on the wall) increased all of these factors, even compared with working on horizontal whiteboards.

Adding additional whiteboard space for my students to write on the walls has changed my math classroom (I have a few moveable whiteboard walls covered in dry erase paint as well as one wall with large whiteboards from end to end). My students spent less time sitting down, more time collaborating, and more time doing high-quality math. They were more willing to take risks, even willing to erase everything they had done and start over if necessary. They were able to solve problems that were complex and challenging, covering the whiteboards with their thinking and drawing.

And my students loved it. They were excited to work together on the whiteboards. They were excited to come to math and work through difficult problems together. They moved around the room, talking to other groups and sharing ideas. The fact that the boards were on the wall meant that everyone could see what other groups were doing. I could see where every group was just by looking around the room. I could see who needed help and who needed more time to work through something. But my students could see everything, too. They could get ideas from classmates outside of their group, using others’ ideas to get them through a disagreement or a sticking point. It made formally presenting their ideas easier, too; everyone could just turn and look at the board of the students who were sharing.

I loved ending the math class with whiteboards covered in writing. It reminded me of all of the thinking and talking and collaborating that had just happened. And that was a good feeling at the end of the day. Use nonpermanent vertical surfaces and watch your math class come alive.

Thanks to Cindy, Danielle, Patrick, and Andrea for their contributions!

Please feel free to leave a comment with your reactions to the topic or directly to anything that has been said in this post.

Consider contributing a question to be answered in a future post. You can send one to me at [email protected] . When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.

You can also contact me on Twitter at @Larryferlazzo .

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## 4th Grade Logic and Problem Solving Worksheets

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## 10 Strategies for Problem Solving in Math

Jessica Kaminski

8 minutes read

June 19, 2022

Kids often get stuck when it comes to problem solving. They become confused when you offer them word problems or include an unknown variable like x in their math question. In such cases, teachers have to guide kids through this problem-solving maze, which is why this article covers the strategies for problem solving in math and the ways your students can leverage them.

## What Are Problem Solving Strategies in Math?

To solve an issue, one must have a reliable strategy. Strategies for problem solving in math refer to methods of approaching math questions to ensure accurate results and increased efficiency. Such strategies simplify math for kids with no experience in problem solving and those already familiar with it.

There are various ways to implement problem solving strategies in math, and each method is different. While none is foolproof, they can improve your student’s problem-solving skills, especially with exercises and examples. The keyword here is practice — the more problems students solve, the more strategies and methods they pick up.

## Strategies for Problem Solving in Math

Even if a student is not a math whiz, appropriate strategies for problem-solving in math can help them find solutions. Students may solve math issues in many ways, but here are ten math strategies for problem solving with high success rates. Depending on usage and preference, the strategies give kids renewed confidence as they work through difficulties.

## Understand the Problem

Before solving a math problem, kids need to know and understand their nature. They should identify if the question is a fraction problem , a word problem, a quadratic equation, etc. An excellent way to boost their understanding is to look for keywords in the problem, revisit other similar questions, or check online. This step keeps the student on track.

Math for Kids

## Guess and Check

The guess and check approach is one of the time-intensive strategies for problem solving in math. Students are to keep guessing until they find the proper answer.

After assuming a solution, kids need to put it back into the math problem to determine its accuracy. The procedure may seem laborious, but it often uncovers patterns in a child’s thought process.

## Work It Out

When kids are working on a math problem, please encourage them to write down every step. This strategy is a self-monitoring method for math students since it demands that they first understand the problem. If they immediately start solving the problem, they risk making mistakes.

Using this strategy, students will keep track of their ideas and correct mistakes before arriving at a final answer. Even after working out their math problems in the supplementary sheet, a child may still ask you to explain the processes. This confirmation stage etches the steps they took to solve the problem in their minds.

## Work Backwards

There are times when math problems may be best solved by looking at them differently. Kids need to understand that recreating math problems will be handy for project management and engineering careers.

Using the “Work Backwards” strategy, students anticipate challenges in real-world situations and prepare for them. They can start with the final result and reverse engineer it to arrive at the initial problem.

A math problem that may seem confusing to kids can generally become simpler once you represent it visually. Having kids visualize and act out the math problem are some of the most effective math strategies for problem solving.

Drawing a picture or making tally marks on a sheet of working-out paper is a visualization option. You could also model the process on the whiteboard and give students a marker to doodle before writing down the solution.

## Find a Pattern

Pattern recognition strategies help kids understand math fundamentals and remember formulas. The best way to uncover patterns in a math problem is to teach pupils to extract and list relevant details. They can use the strategy when learning shapes and repetitive concepts, which makes the approach one of the most effective elementary math strategies for problem solving.

Using this method, students will recognize similar information and find the missing details. Over time, this approach will help students solve math problems faster.

One of the best problem solving strategies for math word problems is asking oneself, “what are some possible solutions to this issue?” It helps you consider the question more carefully, think outside the box, and avoid tunnel vision when facing challenges. So, encourage kids to muse over math problems and not settle for the first answer that enters their minds.

## Draw a Picture or Diagram

Like visualization, creation of a diagram of a math problem will help kids figure out the best ways to approach it. Use shapes or numbers to represent the forms to keep things basic. Depending on the situation, patterns and graphs may also be valuable, and you can encourage kids to use dots or letters to represent the items.

Diagrams are even beneficial in many non-geometrical situations. After studying, students can create sketches of the concepts they read about for later revision. The approach will help kids determine what kind of math problem they are dealing with and the steps needed whenever they encounter a similar idea.

## Trial and error method

Trial and error approach may be one of the most common strategies for solving math problems. However, the efficiency of this strategy depends on its application. If students blindly try solving math questions without specific formulas or directions, the chances of success will be low.

On the other hand, if they start by making a list of possible solutions based on preset guidelines and then attempting each one, they increase their odds of finding the correct answer. So, don’t be quick to discourage kids from using the trial and error strategy.

## Review answers with peers

Strategies for problem solving in math that involve reviewing solutions with peers are enjoyable. If students come up with different answers to the same question, encourage them to share their thought processes with the rest of the class.

You could also have a session with the class to compare children’s working techniques. This way, students can discover loopholes in their ideas and make the necessary adjustments.

Check out the Printable Math Worksheets for Your Kids!

Many strategies for problem solving in math influence students’ speed and efficiency in tests. That is why they need to learn the most reliable approaches. By following the problem solving strategies for math listed in this article, students will have better experiences dealing with math problems.

Jessica is a a seasoned math tutor with over a decade of experience in the field. With a BSc and Master's degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly . She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.

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## Skills kids need going into fourth grade

## By Amanda Morin

## At a glance

In preparation for fourth grade, third graders focus on using language and writing in all subjects.

Most kids who are ready for fourth grade understand why and how multiplication works.

Fourth graders have to support their statements about a text with facts and details.

## Skills to get ready for grade 4: English language arts and literacy

Rising fourth graders are also expected to know how to:

- Read many types of stories and describe what happened, how the characters were affected, and what lessons they learned
- Answer questions about reading material that covers history, social studies, and science; also use information in illustrations, maps, and charts to help answer questions
- Give a class presentation on a topic using facts, details, and specific vocabulary
- Participate in discussions by speaking clearly, listening, sharing opinions, building on other people’s ideas, and asking questions
- Use dialogue and description to write about what a character is thinking and feeling
- Gather information from online sources in addition to books and articles; use that information to write research papers

## Skills to get ready for grade 4: Mathematics

- Explain what multiplication and division are
- Know the times tables up to 12 and multiply numbers by 10
- Use addition, subtraction, multiplication, and division to solve word problems involving more than one step
- Understand the concept of area and how it relates to multiplication
- Understand and identify fractions as numbers that can be placed on a number line; compare two fractions (like knowing that 2/3 is bigger than 3/5)
- Express whole numbers as fractions and recognize fractions that are whole numbers (like knowing that 8/2 is the same as 4)
- Measure weights and volumes
- Read charts and graphs and show data as a graph or chart

## How to help your rising fourth grader

- Practice word problems with more than one step or operation.
- Talk about the characters and ideas in books you read together.
- Expose your child to informational text like charts, brochures, and newspapers.
- Role-play social situations .
- Use multisensory techniques to build reading skills .
- Try multisensory techniques to build math skills , too.

## Key takeaways

In fourth grade, kids are expected to understand many types of stories and write research papers.

Consider talking to the teacher if your child is having trouble keeping up with schoolwork.

There are lots of ways to help your child prepare for fourth grade at home.

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## 4th Grade Math Word Problems: Strategies, Ideas and Examples for Teachers

## Characteristics

- Understand: What are you being asked to find out? Students need to identify the outcome of the problem and keep this in mind as they are working towards a solution.
- Plan: What are you going to have to do to solve this problem? Will you need to guess and check? What operation(s) are involved? Will you draw a picture to help you? Can you make an estimate?
- Solve: If the plan is sound, then this is the stage where you put it into action
- Check: Look at your answer. Does it answer the question? Is it a reasonable answer? Is there a way to check and see if your answer is correct?

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## 4th grade math skills: Find out what you need to know for your student

## Addition, subtraction, multiplication & division

Quickly and accurately, add and subtract multi-digit whole numbers up to 1 million (1,000,000).

Understand a prime number as having only one factor pair: one and itself.

## Parenting Guides 4th grade math tips: Here's how to help your student

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## How to Master Math: Fractions

Add and subtract fractions with the same denominator (bottom number).

Add and subtract mixed numbers with the same denominators.

Multiply fraction by whole number

Solve word problems involving multiplication of fractions by a whole number.

Write fractions with denominators of 10 or 100 as decimals.

Comparing fractions and decimals

## Measurement & data

Solve word problems involving addition, subtraction, multiplication, and division of:

- units or intervals of time (seconds, minutes, hours)
- units of money (using decimal notation – for example: .25, .05, $2.35)
- units of mass (grams, kilograms)
- units of weight (ounces, pound)
- units of volume (milliliters, liters)
- units of distance/length (inches, feet, yards, miles, centimeters, meters, kilometers)

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## How to Master Math: Geometry

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For tips to help your fourth-grader in math class, check out our fourth grade math tips page .

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This practice guide provides five recommendation s for improving students' mathematical problem solving in grades 4 through 8. This guide is geared toward teachers, math coaches, other educators, and curriculum developers who want to improve the mathematical problem solving of students. 1. Prepare problems and use them in whole-class instruction.

Assist students in monitoring and reflecting on the problem-solving process. 1. Provide students with a list of prompts to help them monitor and reflect during the problem-solving process. 2. Model how to monitor and reflect on the problem-solving process. 3. Use student thinking about a problem to develop students' ability to monitor and ...

Step 1: Understanding the problem We are given in the problem that there are 25 chickens and cows. All together there are 76 feet. Chickens have 2 feet and cows have 4 feet. We are trying to determine how many cows and how many chickens Mr. Jones has on his farm. Step 2: Devise a plan Going to use Guess and test along with making a tab

Grade 4 Problem Solving Strategies 4989 + 2788 = ( 4900 + 2700) + ( 89 + 88) = ( 4900 + 2700) + ( 89 + 88 + 2 - 2) = ( 4900 + 2700) + ( 89 + ( 88 + 2) - 2) = ( 4900 + 2700) + ( 89 + 90 - 2) = ( 4900 + 2700) + ( 179 - 2) = ( 4900 + 2700) + ( 177 ) = ( 4900 + 2700 + 300 - 300) + 177 = ( 4900 + ( 2700 + 300) - 300) + 177 = ( 4900 + 3000 - 300) + 177

Four teachers share their favorite strategies for math instruction, including the Concrete Representational Abstract approach. ... Andrea Clark is a grade 5-7 math and language arts teacher in ...

Browse our printable 4th Grade Logic and Problem Solving Worksheets resources for your classroom. Download free today! ... Math in Science: Exploring Range, Median, and Mode. ... This math daily warm up worksheet for grades 4 to 6 features problem-solving strategies with math problems. For this… Subjects: Mathematics. Logic and Problem ...

1:1 Online Math Tutoring Let's start learning Math! Guess and Check The guess and check approach is one of the time-intensive strategies for problem solving in math. Students are to keep guessing until they find the proper answer. After assuming a solution, kids need to put it back into the math problem to determine its accuracy.

Multiply by 1-digit numbers 0/1300 Mastery points Comparing with multiplication Multiplication by 10s, 100s, and 1000s Multi-digit multiplication: place value and area models Estimate products Multiply with partial products Multiply by 2-digit numbers 0/500 Mastery points

This centers set covers multiplication and division for fourth grade standards. The focus of these centers is strategies and problem solving. There are 10 total centers. (CC and TEKS) Every center has an answer key included so students can easily check their work. Fill your fourth grade math centers/rotations with these activities!

Internet Activities. This 4th grade math activity will help your students review 2-digit multiplication strategies (area model, partial products, and the traditional algorithm) along with mental math and word problems. Boom Cards have been the most valuable tool in preparing my students for regular chapter tests and end of the year state testing!

In fourth grade, students begin to calculate the area of shapes and use different problem-solving strategies to solve word problems. To work on these skill areas, they're expected to be able to: Explain what multiplication and division are Know the times tables up to 12 and multiply numbers by 10

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (See Appendix A, Table 2.) [4-OA2]

The purpose of this research was to investigate studentsâ€™ problem solving strategies (Posamentier & Krulik, 1998) in a problem solving- mathematics classroom, using an open approach as a teaching approach and composed of four phases: 1) posing open-ended problems, 2) studentsâ€™ self learning, 3) whole class discussion, and 4 ...

Examples. A one-step problem may be as simples as, "Jack has $4.25 and Kayla has $3.80. How much money do they have altogether?". This straightforward problem merely requires the students to add the two amounts of money together. At the beginning of fourth grade, this would be an appropriate example of 4th grade math word problems.

By Parent Toolkit Staff. In fourth grade, students focus most on using all four operations - addition, subtraction, multiplication, and division - to solve multi-step word problems involving multi ...

The learning program has to enable students to develop new mathematical knowledge through problem-solving, solve mathematics and other problems, implement and adjust various strategies available to solve problems, and monitor and reflect the process of solving mathematical problems (NCTM, 2000).

About This Chapter. Help your 4th grade students catch up on multiplication strategies and mental math with this chapter. As a learning aid for the classroom and home, our lesson materials provide ...