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Classroom Q&A

With larry ferlazzo.

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.



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 .

Education Week has published a collection of posts from this blog, along with new material, in an e-book form. It’s titled Classroom Management Q&As: Expert Strategies for Teaching .

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10 Strategies for Problem Solving in Math

Jessica Kaminski

8 minutes read

June 19, 2022

strategies for problem solving in math

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

math problem solving strategies 4th grade science

By Amanda Morin

math problem solving strategies 4th grade science

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.

Getting ready for fourth grade involves focusing on using language and writing in all subjects. Math skills include using more than one step or operation to solve a problem.

To see if your child is ready for fourth grade, take a look at your state’s academic standards . Not all states use the same standards, but many of them have similar expectations for students. Here are some of the key skills kids are expected to master by the end of third grade in preparation for fourth grade.

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

To prepare for fourth grade, students are exposed to a variety of reading material, including fiction, nonfiction, charts, and maps. They’re expected to understand these new materials and write about what they’ve read . As writers, kids are expected to start organizing information and ideas more effectively and support their statements or observations with facts and details.

Rising fourth graders are also expected to know how to:

Is your child struggling with reading? Learn ways to help your child build phonological awareness in grade school, along with other ways to improve reading skills at home .

Skills to get ready for grade 4: Mathematics

By the end of third grade, children need to be familiar with fractions and start to understand the “whys” of multiplication and division. 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:

See how learning and thinking differences can affect math skills . And explore a list of questions to ask about the school’s math instruction .

How to help your rising fourth grader

Kids learn at different rates. Don’t worry if your child hasn’t mastered all of these skills before starting fourth grade. But if your child is having trouble with many of these skills, you may want to consider talking with the teacher . Together you can come up with a plan to figure out what’s making learning harder.

Read about fourth-grade learning challenges for kids who learn and think differently. And explore ways to help your child prepare for fourth grade at home. Here are some ideas:

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.

Tell us what interests you

About the author.

Amanda Morin is the author of “The Everything Parent’s Guide to Special Education” and the former director of thought leadership at Understood. As an expert and writer, she helped build Understood from its earliest days. 

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Problem Solving

What Is Problem Solving? Problem solving is finding an answer to a question. How to Problem Solve: Read the problem carefully. Decide on an operation to use to solve the problem. Solve the problem. Check your work and make sure that your answer makes sense. Read More...

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

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


Solving word problems takes skill, attention to detail, and a good problem solving strategy. Fourth grade math word problems usually

involve one of the basic math operations - addition, subtraction, multiplication, or division. It is not uncommon to see two operation types in one problem, but generally speaking there is often only one operation involved. The word problems themselves require either a one or two step calculation to correctly solve the question, and they are characterized by real world scenarios familiar to a 4th grade student.

4th Grade Math Word Problems: 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. A more advanced one-step problem would be, “A friend tells you that they will be 405 weeks old on their next birthday. How old is that in years?”

Two-step word problems require more effort. For instance, “Michael ate 12 cookies, while his sister ate 9 cookies. If mom baked 56 cookies, how many are left?” Again this would be a word problem students may encounter at the beginning of 4th grade. More taxing problems could include the likes of, “A sign before a bridge says ‘weight limit 2 Tons.’ The pickup truck weighs 1,675 lb, and has a bag of sand that weighs 400 lb in the back. The driver weighs 175 lb. Should he drive the truck across the bridge?”

There are many different strategies for solving this type of problem, but the one that I have had the most success with is a four-step problem solving strategy.

A good place to find examples of 4th grade math word problems is the Primary Resources website . Here you will find a selection of free PDF, Word, and SMART Notebook files to download. It is an English site, so the equivalent US grade level is Year 5, but feel free to move up and down a grade to suit the abilities of your children. SMART Board users should also check out the resources on the SMART Exchange website . It has a selection of problems and teaching strategies for download. Abcteach.com also has another reasonably good selection of word problems that you can print out. If copyright allows, you can also run some of these PDFs through a free converter like www.pdftoword.com and then you will be free to edit any of the numbers to suit your needs.


Word problems are relatively easy to differentiate by just changing the numbers in the story - larger numbers for the more gifted children, and smaller numbers for your less able students. You can also add or remove steps. One step problems are less work, and easier to solve, than two-step problems, so save those for your lower ability students, and add steps to challenge your gifted and talented children .

4th grade math word problems may seem like a chore to some students, but practice and perseverance is the keys to success. For more information on what is taught in 4th Grade Math, read 4th Grade Skills: What Every 4th Grader Needs to Know .

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

math problem solving strategies 4th grade science

In fourth grade , students focus most on using all four operations - addition, subtraction, multiplication, and division - to solve multi-step word problems involving multi-digit numbers. Fourth-grade math extends their understanding of fractions, including equal (equivalent) fractions and ordering fractions. They add and subtract fractions with the same denominator (bottom number), multiply fractions by whole numbers and understand relationships between fractions and decimals.

Addition, subtraction, multiplication & division

Multi-digit whole numbers

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

Understand factors – whole numbers (numbers without fractions) that can be multiplied together to get another number. Understand that one number can have several factor pairs – for example, 3 and 4 are factors of 12 (3 x 4 = 12), and so are 2 and 6 (2 x 6 = 12), and 1 and 12 (1 x 12 = 12).

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

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

Relationship to place value

Read, write, and compare multi-digit whole numbers, understanding that the value of a digit is ten times what it would be in the place to its right – for example, seven is 10 times greater than 0.7. Use understanding of place value to round multi-digit whole numbers to any place.

Multiply a number of up to four digits by any one-digit number and multiply two two-digit numbers. Divide a number of up to four digits by any one-digit number, including problems with remainders. Explain and illustrate using equations and visual rectangular models.

Two hundred fifty doughnuts are divided evenly among six classrooms, How many doughnuts will each classroom receive, and how many doughnuts are left over for the principal?

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parenting-guides 4th Grade Parenting Guides

Word problems

Solve multi-step word problems with whole numbers, using addition, subtraction, multiplication, and division problems with remainders. Use mental math and estimation strategies (such as rounding) to check how reasonable an answer is. Write equations for these problems with a letter standing for the unknown quantity.

A rectangular field has a perimeter of 400 yards. The field has a length of 125 yards and a width of w yards. Find w. 400 = 125 + 125 + w + w.

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How to Master Math: Fractions

Breaking down fractions

Break fractions down into smaller fractions that have the same denominator (bottom number) in various ways.

3/4 = 1/4 + 1/4 + 1/4

3/4 = 1/4 + 2/4

Adding and subtracting

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

5/8 + 2/8 = 7/8

7/8 - 5/8 = 2/8

Working With mixed numbers

Add and subtract mixed numbers with the same denominators.

1 1/6 + 2 4/6 = 3 5/6

Equivalent fractions

Using visual fraction models – number lines, fraction bars (see example below), understand how fractions can be equal (equivalent) even when the number and size of the parts (the numerators and denominators) are different. Recognize and create equal (equivalent) fractions – for example: 2⁄4 = 1⁄2 (or 2⁄4 = 1⁄4 + 1⁄4).

Numerators and denominators

Compare two fractions with different numerators (top numbers) and different denominators (bottom numbers) by changing one or both fractions so that they both have the same denominator. For example, in comparing 3⁄8 and 4⁄16, use visual fraction models to understand that 4⁄16 is the same as 2⁄8.

3/8 > 2/8 so 3/8 > 4/16

Comparing numerators

Understand that in comparing two fractions with the same denominator, the larger fraction is the one with the larger numerator.

Multiply fraction by whole number

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

Mary wants to make bows for six friends. Each bow requires 5⁄8 of a yard of ribbon. How many yards of ribbon does Mary need?

Fractions as decimals

Write fractions with denominators of 10 or 100 as decimals.

Write 4/10 as 0.4

Write 0.83 as 83/100

Comparing fractions and decimals

Compare numbers written as fractions and numbers written as decimals, using the symbols > (greater than), = (equal to), and < (less than). Use visual models such as fraction bars or number lines to explain and justify the answer.

Measurement & data

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

Practice converting larger units to smaller units by multiplying. For example, three hours = 3×60 = 180 minutes.

Emma studied for one hour. Ethan studied for 15 minutes. What is the difference in the number of minutes they studied? Emma's study session was how many times longer than Ethan's?

Understand perimeter as the measurement around something, and area as the measurement of the flat surface inside the perimeter of something. Find perimeter and area to solve real-world cost problems.

Juan wants to carpet his bedroom. His bedroom is two yards wide and five yards long. The carpeting costs $7 per square yard. How much will Juan’s new carpet cost? Explain or illustrate how you solved this problem.

Juan decides to put a decorative border high all the way around his room near the top of the walls. The border costs $3 per yard. How much will the border cost? Explain or illustrate how you solved this problem.

Tip: Use math in house projects

Encourage your child to use his math skills for projects around the house. If you’re wallpapering or carpeting, for example, have him calculate wall or floor areas and figure out the total cost of various materials.

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How to Master Math: Geometry

Lines and angles

Draw and identify different types of lines and angles, including line segments, rays, parallel lines, perpendicular lines, and right angles. Use the presence or absence of these lines or angles to categorize or group (classify) two-dimensional shapes or figures such as rectangles, parallelograms, trapezoids, and triangles.

Tip: Keep an eye out for math concepts

Encourage your child to spot examples of some of the math concepts he is learning about. See how many right angles or right triangles he can spot. Or have him look for parallel lines, such as train tracks or pillars in a building.

Lines of symmetry

Understand line of symmetry: a line across a two-dimensional figure such that the figure can be folded along the line into identical matching parts. Identify the most common symmetrical shapes: circles, squares, rectangles, ovals, equilateral triangles (three equal sides), isosceles triangles (two equal sides), hexagons, and octagons.

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

TODAY's Parenting Guides resources were developed by NBC News Learn with the help of subject-matter experts, and align with the Common Core State Standards.

Parent Toolkit is a one-stop resource for parents produced by NBC News Learn.


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