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## Unit 1: Place value

Unit 2: addition, subtraction, and estimation, unit 3: multiply by 1-digit numbers, unit 4: multiply by 2-digit numbers, unit 5: division, unit 6: factors, multiples and patterns, unit 7: equivalent fractions and comparing fractions, unit 8: add and subtract fractions, unit 9: multiply fractions, unit 10: understand decimals, unit 11: plane figures, unit 12: measuring angles, unit 13: area and perimeter, unit 14: units of measurement, course challenge.

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

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.

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?

## 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.

## 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

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.

## 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.

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.

## Characteristics

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.

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.

## Differentiation

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 .

Printable & online resources for educators

You are browsing Grade 4 questions. View questions in All Grades .

## Arithmetic and Number Concepts

Function and algebra concepts, geometry and measurement, mathematical process, logical thinking, problem solving strategies, statistics and probability concepts.

You can create printable tests and worksheets from these Grade 4 Problem Solving Strategies questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

## 10 Strategies for Problem Solving in Math

Jessica Kaminski

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.

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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## March 24, 2021 3-5-operations-and-algebraic-thinking , k-2-operations-and-algebraic-thinking , Math

Word problem solving strategies for students in grades k–4 [free templates], by: jeff todd.

Math problem solving strategies should begin as early as Kindergarten or Grade One! As nonfiction reading has seen a stronger emphasis in recent years, we can think of word problems as part of the genre of nonfiction. The downloads for today’s post include several templates or graphic organizers to help students make the connection between word problems and equations that represent those problems.

As a math teacher, I have heard many times that “we are all teachers of reading,” and this post will show how the two areas relate, both math and reading, as students create representations to help them move from words to equation and vice versa. Plus, grab my downloadable templates for multiple representations below! By using these templates to design lessons, you are able to address many of the Standards for Mathematical Practice that undergird math word problem solving strategies.

Manipulative and visual representation of math word problems are closely related. These representations are the math problem solving strategies that students can employ. I hope you’ll bear with me as I give a bit of the history of what I have learned about teaching students using manipulatives and representations. In the 1960s, Jerome Bruner coined the terms enactive, iconic, and symbolic to describe how students progress from using manipulatives, to making drawings based on the manipulatives, to using numbers and symbols alone. Today, we might call these steps concrete, representational (semi-concrete), and abstract. Singapore Math uses the terms concrete, pictorial, and abstract. These three sets of terms all refer to the same core strategy of using manipulatives with mastery to show a mathematical idea, then having students represent that idea using paper and pencil (re-presenting it), and, finally, using only numbers and symbols to represent it.

I would encourage you to have students first work with manipulatives such as teddy bear counters, little cubes, or even beans. These help to show the relationships between the situation students are reading about in a word problem. It is best to have them use the template to represent their idea using a ten frame, number bond, array or area model, and tape diagram (semi-concrete, pictorial or iconic representations). Finally, they will understand the meaning of the equation (abstract or symbolic representation) when they write it.

## Math Word Problem Solving Strategies for Students

If you are looking for math word problem strategies in Kindergarten through Grade 4, you will find the downloadable templates below very helpful. By using the templates, you can give students strategies to read word problems and create representations to solve them, or even give them a representation and have them create word problems. Use these downloadable templates to give students math problem solving strategies involving addition, subtraction , multiplication, and division. Print them and use them today in your class!

In the earliest grades, students are only expected to add. A typical word problem might be, “Chris has three oranges and two apples. How many pieces of fruit does Chris have all together?” Students can model the problem using cubes of different colors. The downloadable template has a spot for the question, then students can make a drawing based on their manipulatives. The key semi-abstract representations for these students are ten frames and number bonds. Particularly with number bonds, students are having to think about parts and totals. Finally, students write an addition sentence.

There are two templates available for adding . The first has one ten frame targeted for Kindergarten where students only add within ten. The second has two ten frames targeting first grade, where students add within twenty. Advanced students could be pushed to represent their addition sentences using a number line, but that is not included with this download.

As students progress through Grade 1 and into Grade 2, they are learning about the relationship between addition and subtraction. Conceptually, this is different from early work with just adding. Strategies for solving addition word problems with two addends can be formulaic. The two numbers in the word problem must be added, but when students encounter word problems with a missing part, they must have strategies and representations to think about parts and wholes.

On the template for adding and subtracting , you will find number bonds and a tape diagram. Each template has a frame with two number bonds, one with the “whole” x-ed out, the other with one of the “parts” x-ed out. Students need to read the problem and decide whether it is a missing-part or a missing-whole type problem. This is where we need to tie in the reading with the math. Similarly, students should complete the tape diagram using the part and whole ideas, but this time using a “?” or a letter as a variable to represent the unknown.

Finally, students should write at least one addition or subtraction sentence to represent the problem using a “?” or variable for the unknown. Then, they can write the number sentence showing the “solution” in place of the question mark or variable. Advanced students could be pushed to represent their number sentence using a number line, but that is not included with this download.

## Grade 3 and 4—Multiplying & Dividing

Building on work in second grade, Grade 3 and Grade 4 students need to adopt strategies for solving word problems that involve multiplication and division. These problems require different representations than the strategies for math word problems involving addition and subtraction.

The downloadable template for Grades 3 and 4 include a space for an array model, an area model and a tape diagram. Just to be clear, students can represent multiplication and division word problems using any of these three representations:

You can see that this series of abstract representations of multiplication and division move from the more concrete (semi-abstract) versions where you can count dots or squares, to more abstract versions where students move away from counting to finding solutions. This also aids students in the beginning use of variables to represent unknowns, as they can label missing parts of the area or array models with a letter.

In the last box of the downloadable template, students are asked to write the equation using a variable or question mark for the unknown and then to “solve” it. By solving, I mean not using algebraic steps (i.e., divide both sides by three), but instead just to write “x = 7” in the case of the example immediately above. Students could use any form of reasoning, including going back to using physical counters and dividing them into equal groups.

## How The Standards For Math Practice Relate To Using The Templates

I want to share some thoughts about how these downloadable templates can be used to develop students’ strategies to solve math word problems and tap into the Standards for Mathematical Practice (SMPs).

SMP 1: Make sense of problems and persevere in solving them.

When students are asked to make a diagram, they must be clear about what parts and wholes are. Giving them representations such as number bonds, area and array models, or tape diagrams helps them make sense of the problems and the relationships of the elements that they find when reading the word problem.

SMP 2: Reason abstractly and quantitatively.

When students create a representation such as in Download 4, (3 boxes of “x” equal to 21), this is an abstract representation. It doesn’t say anything about what the problem is about. When students read a word problem involving quantities (three toys that cost \$21 total) and make the tape diagram they move from quantities to abstractions. Another way to use these templates is to complete the tape diagram (or array or area model) and ask students to fill in the other boxes. In other words, students will create their own word problems from the tape diagram. They start with the abstract representation and come up with a quantitative idea (this problem could be 21 apples and three people or 21 chocolates and three boxes, etc).

SMP 4: Model with mathematics.

These kinds of models, such as area models and tape diagrams, if introduced early, will help students when they use area models in upper grades to model more complex problems.

SMP 7: Look for and make use of structure.

Reading word problems and then making representations using the templates will help students look for keywords and how they relate to the structure of parts and wholes, rows and columns, factors, totals, and divisors. Seeing the common underlying structures using number bonds, ten frames, area and array models, and tape diagrams helps to reinforce common underlying structures that appear in various word problems.

Download and use my free templates to help students make connections between word problems and equations that represent those problems. When you do this, you will engage students in the use of the Standards for Mathematical Practice outlined above, giving them ways to picture word problems in their heads and create representations that show the relationships of the quantities involved.

Ideas, Inspiration, and Giveaways for Teachers

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## Check Out These 50 Fourth Grade Math Word Problems of the Day

Mr. Smith’s class collected coins in a big jar for 6 months.

Opening your daily math lesson with a Fourth Grade Math Word Problem of the Day is an excellent way to set the stage for learning! Incorporate them at the start of your math block to build confidence, critical thinking skills, and a learning community. Students will get used to reading for meaning, while also identifying key information. Encourage students to write out equations and draw pictures to explain their thinking, since this helps them see the light when they are stuck!

Topics in these fourth grade math word problems cover patterns & place value, addition/subtraction, multiplication, division, fractions, decimals, measurement, and comparisons. If you’d like even more math word problems, we publish them daily on our kid-friendly site: the Daily Classroom Hub . Make sure to bookmark the link!

Want this entire set of word problems in one easy document? Get your free PowerPoint bundle by submitting your email here . All you need to do is post one of the problems on your whiteboard or projector screen. Then let kids take it from there.

## 50 Fourth Grade Math Word Problems

1. jill wrote the number 730,918. she challenged jane to rearrange the digits to create the highest possible number. what number did jane make.

## 35. 150 kids signed up for the summer soccer league. There are going to be ten teams, and the Dragons are one of the teams. Each team has 3 coaches and they want an equal number of players on each team. How many players should be on the Dragons?

36. the wonderful widget company produces 480 widgets every day. they have 6 widget making machines running every day, with each machine making equal amounts of widgets. the company runs six days a week. how many widgets does each machine make.

## Enjoying these fourth grade math word problems? Check out our fourth grade hub for even more resources.

Get a PPT version of these word problems.

## 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 - Strategies to Multiply by One-Digit Numbers

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## Four Teacher-Recommended Instructional Strategies for Math

• Share article

(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!

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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## 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:

• 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

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:

• 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

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

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.

• 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.

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## Why are effective Math strategies so important for students?

Getting students excited about math problems, top 9 math strategies for engaging lessons.

• How teachers can refine math strategies

Math is an essential life skill. You use problem-solving every day. The math strategies you teach are needed, but many students have a difficult time making that connection between math and life.

Math isn’t just done with a pencil and paper. It’s not just solving word problems in a textbook. As an educator, you need fresh ways for math skills to stick while also keeping your students engaged.

In this article, we’re sharing 9 engaging math strategies to boost your students’ learning . Show your students how fun math can be, and let’s freshen up those lesson plans!

Unlike other subjects, math builds on itself. You can’t successfully move forward without a strong understanding of previous materials. And this makes math instruction difficult.

To succeed in math, students need to do more than memorize formulas or drill times tables. They need to develop a full understanding of what their math lessons mean , and how they translate into the real world. To reach that level of understanding, you need a variety of teaching strategies.

Conceptual understanding doesn’t just happen at the whiteboard. But it can be achieved by incorporating fun math activities into your lessons, including

• Hands-on practice
• Collaborative projects
• Gamified or game-based learning

Repetition and homework are important. But for these lessons to really stick, your students need to find the excitement and wonder in math.

Creating excitement around math can be an uphill battle. But it’s one you and your students can win!

Math is a challenging subject — both to teach and to learn. But it’s also one of the most rewarding. Finding the right mix of fun and learning can bring a lot of excitement to the classroom.

Think about what your students already love doing. Video games? Legos? Use these passions to create exciting math lesson plans your students can relate to.

Hands-on math practice can engage students that have disconnected from math. Putting away the pencils and textbooks and moving students out of their desks can re-energize your classroom.

If you’re teaching elementary or middle school math, find ways for your students to work together. Kids this age crave peer interaction. So don’t fight it — provide it!

Play a variety of math games or puzzles . Give them a chance to problem-solve together. Build real-world skills in the classroom while also boosting student confidence.

And be sure to celebrate all the wins! It is easy to get bogged down with instruction and testing. But even the smallest accomplishments are worth celebrating. And these rewarding moments will keep your students motivated and pushing forward.

Keep reading to uncover all of our top math strategies for keeping your students excited about math.

## 1. Explicit instruction

You can’t always jump straight into the fun. Explicit instruction still provides the best foundation for the activities to come.

Set up your lesson for the day at the whiteboard, along with materials to demonstrate the coming activities. Make sure to also focus on any new vocabulary and concepts.

Tip: don't stay here for too long. Once the lesson is introduced, move on to the next fun strategy for the day!

## 2. Conceptual understanding

Helping your students understand the concept behind the lesson is crucial, but not always easy. Even your highest performing students may only be following a pattern to solve problems, without grasping the “why.”

Visual aids and math manipulatives are some of your best tools to increase conceptual understanding. Math is not a two dimensional subject. Even the best drawing of a cone isn’t going to provide the same experience as holding one. Find ways to let your students examine math from all sides.

Math manipulatives don’t need to be anything fancy. Basic wooden blocks, magnets, molding clay and other toys can create great hands-on lessons. No need to invest in expensive or hard-to-find materials.

Math word problems are also a great time to break out a full-fledged demo. Hot Wheels cars can demonstrate velocity and acceleration. A tape measure is an interactive way to teach area and volume. These materials give your students a chance to bring math off the page and into real life.

## 3. Using concepts in Math vocabulary

There’s more than one way to say something. And the more ways you can describe a mathematical concept, the better. Subtraction can also be described as taking away or removing. Memorizing multiplication facts is useful, but seeing these numbers used to calculate area gives them new meaning.

Some math words are going to be unfamiliar. So to help students get comfortable with these concepts, demonstrate and label math ideas throughout your classroom . Understanding comes more easily when students are surrounded by new ideas.

For example, create a division corner in your station rotations , with blocks to demonstrate the concept of one number going into another. Use baskets and labels to have students separate the blocks into each part of the division problem: dividend, divisor, quotient and remainder.

Give students time to explore, and teach them big ideas with both academic and everyday terms. Demystify math and watch their confidence build!

## 4. Cooperative learning strategies

When students work together, it benefits everyone. More advanced students can lead, helping them solidify their knowledge. And they may have just the right words to describe an idea to others who are struggling.

It is rare in real-life situations for big problems to be solved alone. Cooperative learning allows students to view a problem from various angles. This can lead to more flexible, out-of-the-box thinking.

After reviewing a word problem together as a class, ask small student groups to create their own problems. What is something they care about that they can solve with these skills? Involve them as much as possible in both the planning and solving. Encourage each student to think about what they bring to the group. There’s no better preparation for the future than learning to work as a team.

## 5. Meaningful and frequent homework

When it comes to homework, it pays to think outside of textbooks and worksheets. Repetition is important, but how can you keep it fun?

Create more meaningful homework by including games in your curriculum plans. Encourage board game play or encourage families to play quiz-style games at home to improve critical thinking, problem solving and basic math skills.

Sometimes you need homework that doesn’t put extra work onto the parents. The end of the day is already full for many families. To encourage practice and give parents a break, assign game-based options like Prodigy Math Game for homework.

With Prodigy, students can enjoy a fun, video game experience that helps them stay excited and motivated to keep learning. They’ll practice math skills, while their parents have time to fix dinner. Plus, you’ll get progress reports that can help you plan future instruction . Win-win-win!

Set an Assessment through your Prodigy teacher account today to reinforce what you’re teaching in class and differentiate for student needs.

## 6. Puzzle pieces math instruction

Some kids excel at math. But others pull back and may rarely participate. That lack of confidence is hard to break through. How can you get your reluctant students to join in?

Try giving each student a piece of the puzzle. When you’re presenting your class with a problem, this creates necessary collaboration to get to the solution.

Each student is given a piece of information needed to solve the problem. A number, a unit of measurement, or direction — break your problem into as many pieces as possible.

If you have a large class, break down three or more problems at a time. The first task: find the other students who are working on your problem (try color-coding or using symbols to distinguish each problem’s parts). Then watch the learning happen as everyone plays their own important role.

## 7. Verbalize math problems

There’s little time to slow down in the classroom. Instruction has to move fast to keep up with the expected standards. And students feel that, too.

When possible, try to set aside some time to ask about your students’ math struggles. Make sure they know that they can come to you when they get stuck. Keep the conversation open to their questions as much as possible.

One great way to encourage questions is to address common troubles students have encountered in the past. Where have your past classes struggled? Point these out during your explicit instruction, and let your students know this is a tricky area.

It’s always encouraging to know you’re not alone in finding something difficult. This also leaves the door open for questions, leading to more discovery and greater understanding.

## 8. Reflection time

Providing time to reflect gives the brain a chance to process the work completed. This can be done after both group and individual activities.

## Group Reflection

After a collaborative activity, save some time for the group to discuss the project . Encourage them to ask:

• What worked?
• What didn’t work?
• Did I learn a new approach?
• What could we have done differently?
• Did someone share something I had never thought of before?

These questions encourage critical thinking. They also show the value of working together with others to solve a problem. Everyone has different ways of approaching a problem, and they’re all valuable.

## Individual Reflection

One way to make math more approachable is to show how often math is used. Journaling math encounters can be a great way for students to see that math is all around.

Ask them to add a little bit to their journal every day, even just a line or two. Where did they encounter math outside of class? Or what have they learned in class that has helped them at home?

Math skills easily transfer outside of the classroom. Help them see how much they have grown, both in terms of academics and social emotional learning .

## 9. Making Math facts fun

As a teacher, you know math is anything but boring. But transferring that passion to your students is a tricky task. So how can you make learning math facts fun?

Play games! Math games are great classroom activities. Here are a few examples:

• Design and play a board game.
• Build structures and judge durability.
• Divide into groups for a quiz or game show.
• Get kids moving and measure speed or distance jumped.

Even repetitive tasks can be fun with the right tools. That’s why engaging games are a great way to help students build essential math skills. When students play Prodigy Math Game , for example, they learn curriculum-aligned math facts without things like worksheets or flashcards. This can help them become excited to play and learn!

## How teachers can refine Math strategies

Sometimes trying something new can make a huge difference for your students. But don’t stress and try to change too much at once.

You know your classroom and students best. Pick a couple of your favorite strategies above and try them out.

If you're looking to freshen up your math instruction, sign up for a free Prodigy teacher account. Your students can jump right into the magic of the Prodigy Math Game, and you’ll start seeing data on their progress right away!

## Math Problem Solving Strategies

In these lessons, we will learn some math problem solving strategies for example, Verbal Model (or Logical Reasoning), Algebraic Model, Block Model (or Singapore Math), Guess & Check Model and Find a Pattern Model.

Related Pages Solving Word Problems Using Block Models Heuristic Approach to Problem-Solving Algebra Lessons

## Problem Solving Strategies

The strategies used in solving word problems:

• What do you know?
• What do you need to know?
• Draw a diagram/picture

Solution Strategies Label Variables Verbal Model or Logical Reasoning Algebraic Model - Translate Verbal Model to Algebraic Model Solve and Check.

## Solving Word Problems

Step 1: Identify (What is being asked?) Step 2: Strategize Step 3: Write the equation(s) Step 4: Answer the question Step 5: Check

## Problem Solving Strategy: Guess And Check

Using the guess and check problem solving strategy to help solve math word problems.

Example: Jamie spent \$40 for an outfit. She paid for the items using \$10, \$5 and \$1 bills. If she gave the clerk 10 bills in all, how many of each bill did she use?

## Problem Solving : Make A Table And Look For A Pattern

• Identify - What is the question?
• Plan - What strategy will I use to solve the problem?
• Solve - Carry out your plan.
• Verify - Does my answer make sense?

Example: Marcus ran a lemonade stand for 5 days. On the first day, he made \$5. Every day after that he made \$2 more than the previous day. How much money did Marcus made in all after 5 days?

## Find A Pattern Model (Intermediate)

In this lesson, we will look at some intermediate examples of Find a Pattern method of problem-solving strategy.

Example: The figure shows a series of rectangles where each rectangle is bounded by 10 dots. a) How many dots are required for 7 rectangles? b) If the figure has 73 dots, how many rectangles would there be?

a) The number of dots required for 7 rectangles is 52.

b) If the figure has 73 dots, there would be 10 rectangles.

Example: Each triangle in the figure below has 3 dots. Study the pattern and find the number of dots for 7 layers of triangles.

The number of dots for 7 layers of triangles is 36.

Example: The table below shows numbers placed into groups I, II, III, IV, V and VI. In which groups would the following numbers belong? a) 25 b) 46 c) 269

Solution: The pattern is: The remainder when the number is divided by 6 determines the group. a) 25 ÷ 6 = 4 remainder 1 (Group I) b) 46 ÷ 6 = 7 remainder 4 (Group IV) c) 269 ÷ 6 = 44 remainder 5 (Group V)

Example: The following figures were formed using matchsticks.

a) Based on the above series of figures, complete the table below.

b) How many triangles are there if the figure in the series has 9 squares?

c) How many matchsticks would be used in the figure in the series with 11 squares?

b) The pattern is +2 for each additional square.   18 + 2 = 20   If the figure in the series has 9 squares, there would be 20 triangles.

c) The pattern is + 7 for each additional square   61 + (3 x 7) = 82   If the figure in the series has 11 squares, there would be 82 matchsticks.

Example: Seven ex-schoolmates had a gathering. Each one of them shook hands with all others once. How many handshakes were there?

Total = 6 + 5 + 4 + 3 + 2 + 1 = 21 handshakes.

The following video shows more examples of using problem solving strategies and models. Question 1: Approximate your average speed given some information Question 2: The table shows the number of seats in each of the first four rows in an auditorium. The remaining ten rows follow the same pattern. Find the number of seats in the last row. Question 3: You are hanging three pictures in the wall of your home that is 16 feet wide. The width of your pictures are 2, 3 and 4 feet. You want space between your pictures to be the same and the space to the left and right to be 6 inches more than between the pictures. How would you place the pictures?

## The following are some other examples of problem solving strategies.

Explore it/Act it/Try it (EAT) Method (Basic) Explore it/Act it/Try it (EAT) Method (Intermediate) Explore it/Act it/Try it (EAT) Method (Advanced)

Finding A Pattern (Basic) Finding A Pattern (Intermediate) Finding A Pattern (Advanced)

## Enable Teachers

Enabling parents and professionals to become better teachers.

## 4th Grade Math IEP Goal Bank Based On The Common Core Standards

Math goals are often tricky to line up with the Common Core Standards (which aren’t endorsed by the department of Ed anymore but are still used by almost every curriculum). Meeting a low skill level to an upper grade level can take a lot of thought. Hopefully these examples can give you some new ideas, get you thinking about new ways to track, and if they are written well, they should lead you to progress monitoring.

A question I hear a lot is: How can I use standards that are often too advanced for grade level students, to guide my students who are below grade level? My first thought is to take only the meat of the standards. Many textbooks create math problems that are “interpretations” of the standards. However, when you get to the meat of the standard, there is one or two key skills that students can learn. It’s okay if students can’t do every aspect of the standard. If they can access the basic skill, or one aspect of the content, that is still grade level content AND is differentiating.

There’s a common misconception that if a student receives a goal on grade level, that they no longer need services. This is not true if the IEP goals are creating a way to access grade level standards through differentiating and narrowing down content. I am always a proponent of getting students in special education as much grade level content as possible. So to wrap this up, look for narrowing down the standards to a specific skill that can be taught. Talk with general education teachers to help guide you to which skills are most important. And of course, look at their testing to see which skill areas they are deficient in. Sometimes I write a goal that is skill specific and then another that is grade specific (but still under their area of weakness). Other times, I write them together.

## Operations And Algebraic Thinking

Use the four operations with whole numbers to solve problems.

These standards and example goals, would all be working on skills around actual computation. So if a student is struggling in computations, I would try to tie into one grade level of these standards.

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. CCSS.MATH.CONTENT.4.OA.A.1

Complex Example: Student will be able to take a product in a single digit multiplication problem, and then use the multiplier and multiplicand to make statements about the product being so many times larger. Student will master this goal when they can verbally say the product is ___ times larger across 5 equations, with an average accuracy rate of 70%, across 10 trials.

Complex Example : Using a check list with steps to remember, Student will be able to interpret a single digit multiplication statement that a product is a specific times as many as the multiplier. Student will show mastery when they solve this across 3 statements, with an average accuracy rate of 80% across 10 trials.

Simple Example: Using a visual representation of a single digit multiplication equation, Student will be able to say the product is ___ times larger than ____, across 3 equations, with an average accuracy rate of 75% across 4 consecutive trials.

Simple Example: Student will be able to solve a multiplication problem with digits 1-5 and then say the multiplication sentence using correct vocabulary with on 3 multiplication problems, with 80% accuracy across 10 trials.

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. CCSS.MATH.CONTENT.4.OA.A.2

Note: see definition of multiplicative comparison here .

Complex Example: Using a calculator, Student will be able to write a multiplication equation from a single digit multiplicative comparison, on 2 equations, with an average accuracy rate of 70% across 10 trials.

Simple Example: Given a multiplication chart, Student will be able to write a multiplication equation from single digit sentence using “twice as many” across 2 equations, and 10 total trials, with at least 80% accuracy. (consider doing a few other goals on three times, four times, etc.)

Simple Example: Given a multiplication problem from 1-10, Student will be able to draw a picture of two times as many, on 2 equations per trial, across 10 total trials with an average accuracy rate of 80%.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. CCSS.MATH.CONTENT.4.OA.A.3

Note: This would be a great standard to create a goal and then benchmarks that include writing an equation with a missing quantity, check their work, or use estimation strategies.

Complex Example: Using a graphic organizer, Student will be able to write an equation with a missing variable from a 4th grade level division or multiplication problem, with an average accuracy rate of 90% across 10 trials.

Complex Example: Student will be able to use estimation strategies to check their answer on two digit multiplication and division problems.

Simple Example: Using a graphic organizer, student will be able to solve 3 double digit multiplication word problems, with an average accuracy rate of 75% across 10 trials.

## Gain familiarity with factors and multiples

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. CCSS.MATH.CONTENT.4.OA.B.4

Complex Example: Student will be able to use multiple addition or subtraction to find the factors of numbers 1-100, on 3 numbers at a time, across 10 trials with an average accuracy rate of 80%.

Simple Example: Given 5 numbers that are a multiple and factors, Student will be able to identify which number is a multiple and which numbers are factors. Student will master this goal when they can identify 3 sets of multiples, with 90% accuracy across 10 trials.

## Generate and analyze patterns

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.  For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way . CCSS.MATH.CONTENT.4.OA.C.5

Complex Example: Student will be able skip count by 5, 6, and 7’s with an average accuracy rate of 70% across 10 trials.

Simple Example: Student will be able to use a number line to count by 2’s across 10 trials with a 90% accuracy rate.

## Number & Operations in Base Ten

Generalize place value understanding for multi-digit whole numbers.

These standards and example goals are all related to understanding numbers and counting. If a student is showing a weak understanding with “mathematical thinking” or “processes” these goals would be under those umbrella terms. (Also, when determining goals, you only need data to show that a student needs a goal. If you give them a test that shows these specific skills are a weakness, that is good enough.)

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.  For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division . CCSS.MATH.CONTENT.4.NBT.A.1

Complex Example: Student will be able to divide by multiples of 10 up to 1,000 on 5 sample problems per trial, across 10 trials, with an average accuracy rate of 70%.

Complex Example: Student will be able to multiply by multiples of 10 up to 1,000 on 3 sample problems per trials, across 10 trials, with an average accuracy rate of 90%.

Simple(er) Example: Student will be able to able to write the place value of 4 sample numbers (that could be between 1-1,000) in base ten numerals (450 is 400 + 50) across 10 trials with an average accuracy rate of 90%.

Simple Example: Student will be able to identify the place value of 5 numbers (from 1-100,000) with an average accuracy rate of 70% across 10 trials.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. CCSS.MATH.CONTENT.4.NBT.A.2

Note: For this standard, and with most students, I would break it up into a few different goals. You could just benchmarks if you wanted to. You could put these examples together or use all of them.

Complex Example: Student will be able to write the place value of 2 sample numbers (between 1-1,000,000) in base ten numerals and then determine which is larger or equal to each other across 20 trials with an average accuracy rate 90%.

Simple Example: Student will be able to look at two numbers written as a base ten numeral (1-1,000), and determine if the number is greater, less, or equal, across 20 trials with an average accuracy rate of 90%.

Simple Example: Student will be able to compare two numbers (1-1,000) and determine if they are greater, less, or equal across 20 trials with an average accuracy rate of 80%.

Use place value understanding to round multi-digit whole numbers to any place. CCSS.MATH.CONTENT.4.NBT.A.3

Complex Example: Student will be able to round 5, 4-digit numbers to the nearest thousand or hundred, across 10 trials with an average accuracy rate of 80%.

Simple Example: Student will be able to determine if 3, two digit numbers are closer to lower or upper multiple of ten (26 is closer to 30), across 20 trials with an average accuracy rate of 70%.

## Use place value understanding and properties of operations to perform multi-digit arithmetic.

These standards go back to computing goals, but could also be used under mathematical concepts.

Fluently add and subtract multi-digit whole numbers using the standard algorithm. CCSS.MATH.CONTENT.4.NBT.B.4

Example: Student will be able to add 3, 4 digit numbers (or less) with an average accuracy rate of 80% across 10 trials.

Example: Using graph paper to help organize numbers, Student will be able to add 2, 2 digit by 2 digit numbers with an average accuracy rate of 70% across 15 trials.

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. CCSS.MATH.CONTENT.4.NBT.B.5

Example: Using a multiplication chart, Student will be able to multiply 2, four digit by one digit, with an average accuracy rate of 80% across 10 trials.

Example: Student will be able to draw a picture to show 10, two digit multiplication problems, with 80% accuracy across 3 consecutive trials.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. CCSS.MATH.CONTENT.4.NBT.B.6

Example: Student will be able to use a multiplication chart to help them divide four-digit dividends and one-digit divisors across 10 trials with an average accuracy rate of 90%.

Example: Student will be able to use a calculator to find the correct answer to a multi-digit division problem, with 100% across 3 consecutive trials.

## Numbers and Operations – Fractions

Extend understanding of fraction equivalence and ordering.

Explain why a fraction  a / b  is equivalent to a fraction ( n  ×  a )/( n  ×  b ) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. CCSS.MATH.CONTENT.4.NF.A.1

Complex Example: Student will be able to draw 3 picture of two equivalent fractions pairs, with an average accuracy rate of 80% across 10 trials.

Complex Example: Student will be able to use multiplication to find an equivalent fraction with 90% accuracy across 5 consecutive trials.

Simple Example: Student will be able to use a manipulative to show two equivalent fractions with 90% accuracy across 3 consecutive trials.

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. CCSS.MATH.CONTENT.4.NF.A.2

Complex Example: Using a calculator, Student will be able to find a common denominator between two fractions, across 10 trials, with 5 fractions per trial, with an average accuracy rate of 90%.

Complex Example: Using a calculator, Student will be able to find a common denominator, then determine which fraction is greater or lesser, across 5 trials, with 2 fractions per trial, having an average accuracy rate of 70%.

Simple Example: Student will be able to compare two fractions with the same denominator across 5 trials with an average accuracy rate of 90%.

## Build fractions from unit fractions

Understand a fraction  a / b  with  a  > 1 as a sum of fractions 1/ b . CCSS.MATH.CONTENT.4.NF.B.3.A Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. CCSS.MATH.CONTENT.4.NF.B.3.B Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.  Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8 . CCSS.MATH.CONTENT.4.NF.B.3.C Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. CCSS.MATH.CONTENT.4.NF.B.3.D Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. CCSS.MATH.CONTENT.4.NF.B.3

Complex Example: Student will be able to solve a fraction addition or subtraction word problem (with the same denominator), and create a picture of the two fractions, with 80% accuracy across 10 trials.

Simple Example: Student will be able to use fraction manipulatives to show how many equal pieces are in a fraction, with 100% accuracy across 3 consecutive trials.

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. CCSS.MATH.CONTENT.4.NF.B.4

Complex Example: Student will be able to determine the operation being used in a word problem, and then multiply a fraction by a whole number, with 80% accuracy across 10 trials.

Simple Example: Student will be able to use manipulative to solve a multiplication problem of a fraction and whole number, with 70% accuracy across 15 trials.

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. 2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100 . CCSS.MATH.CONTENT.4.NF.C.5

Example: Student will be able to change a fraction with a denominator 10, to an equivalent fraction with denominator 100, across 10 trials with an average accuracy rate of 75%.

Use decimal notation for fractions with denominators 10 or 100.  For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram . CCSS.MATH.CONTENT.4.NF.C.6

Example: Student will be able to change a fraction with denominator 100 into a decimal with 80% across 20 trials.

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. CCSS.MATH.CONTENT.4.NF.C.7

Example: Student will be able to compare two, two-digit decimals, across 5 questions, with 80% accuracy across 10 trials.

## Measurement and Data

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.  For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), … CCSS.MATH.CONTENT.4.MD.A.1

Example: Student will be able to multiply to find out the equivalent units in km, m, and cm. Student will mastery this when they can do this 5 times, across 5 trials, with 70% accuracy.

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. CCSS.MATH.CONTENT.4.MD.A.2

Complex Example: Student will set up a fraction multiplication problem using distances across 10 trials with 70% accuracy.

Apply the area and perimeter formulas for rectangles in real world and mathematical problems.  For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor . CCSS.MATH.CONTENT.4.MD.A.3

Complex Example: Student will be able to use fraction multiplication rules to solve a missing unit problem with 90% accuracy across 10 trials.

Complex Example: Student will be able to use a set up a fraction problem with a missing unit with 70% accuracy across 10 trials.

## Represent and interpret data

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.  For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection . CCSS.MATH.CONTENT.4.MD.B.4

Example: Student will be able to read a line plot and answer 3 literal questions about the data with 100% accuracy across 3 consecutive trials.

## Geometric measurement: understand concepts of angle and measure angles AND Geometry

For these goals, I would only use them as needed. If a student is all caught up in other areas, it may be time to consider if they need a math goal. However, there is always an outlier case. Or if a student is in a classroom where they are never in the general education classroom, they may have a goal for this.

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#### IMAGES

1. Math Problem Solving Worksheets For 4th Grade

2. ️ Math problem solving rubric 4th grade. Math problem solving problems

3. 😎 Problem solving math grade 4. 4th Grade Math Problems. 2019-02-01

4. 😊 Problem solving grade 4. 4th grade word problem worksheets. 2019-01-16

5. Math Problem Solving

6. 😍 Math problem solving for 4th grade. 4th grade math problems solving

#### VIDEO

1. 1st Grade Video 18: Solving Problems Part 2

2. Math grade 4 Fractions a Story problem #shorts ماث رابعة ابتدائي المنهج الجديد الترم الثاني الكسور

3. Problem Solving Strategies

4. How to solve addition and subtraction of fractions? Full Explanation. Class 4 and 5

5. "The Formula for Finding the Area of a Triangle: Understanding the Basics and Applications" #shorts

6. Can you solve this 5th-grade math problem?

Add and subtract fractions. 0/1600 Mastery points. Decomposing fractions Adding and subtracting fractions with like denominators Adding and subtracting fractions: word problems Mixed numbers. Adding and subtracting mixed numbers Adding and subtracting mixed numbers word problems Fractions with denominators of 10 and 100 Line plots with fractions.

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....

3. Module 1: Problem Solving Strategies

Example 1: 1, 4, 7, 10, 13… Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19. Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4. 4 + 5 = 9 9 + 7 = 16 So the next number would be 16 +9 = 25 25 + 11 = 36

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

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.

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

6. 10 Strategies for Problem Solving in Math

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.

7. Word Problem Solving Strategies for Students in Grades K-4 [Free Templates]

SMP 1: Make sense of problems and persevere in solving them SMP 2: Reason abstractly and quantitatively SMP 4: Model with mathematics SMP 7: Look for and make use of structure Manipulative and visual representation of math word problems are closely related. These representations are the math problem solving strategies that students can employ.

8. Check Out These 50 Fourth Grade Math Word Problems of the Day

How many total legs were there? 17. Donna picks 5 apples every minute in the orchard. How many apples does she pick in 20 minutes? 18. Morris the magician pulled 2 doves out of his hat, twice as many rabbits as doves, and 4 times as many mice as rabbits. How many animals did he pull out of his hat? 19. Tina is making pizzas for 15 guests.

9. Problem Solving. Fourth Grade Math Worksheets and Study Guides

Use the four operations with whole numbers to solve problems. 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]

10. 4th Grade Problem Solving Strategies

1. Timmy drank 2 quarts of water yesterday. He drank twice as much water today as he drank yesterday. How many cups of water did Timmy drink in the two days? 2. Lisa recorded a 2-hour television show. When she watched it, she skipped the commercials. It took her 84 minutes to watch the show.

11. Best Practices for Math Teaching

Explore these strategies that include key elements of evidence-based math instruction: Representing numbers Counting with manipulatives Place value with straw bundles Place value with disks Building fact fluency Fraction number lines Dividing fractions with fractions strips How can families support this at home? Common Core math standards.

12. 4th Grade Math Strategies Teaching Resources

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!

13. Improving Mathematical Problem Solving in Grades 4 Through 8

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.

14. PDF Improving Mathematical Problem Solving in Grades 4 Through 8

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 ...

15. Four Teacher-Recommended Instructional Strategies for Math

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,...

16. Skills Kids Need Going Into Fourth Grade

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 ...

17. Top 9 Math Strategies for Successful Learning (2021 and Beyond)

Math isn't just done with a pencil and paper. It's not just solving word problems in a textbook. As an educator, you need fresh ways for math skills to stick while also keeping your students engaged. In this article, we're sharing 9 engaging math strategies to boost your students' learning.

18. Math Problem Solving Strategies

2. 1. The following video shows more examples of using problem solving strategies and models. Question 1: Approximate your average speed given some information. Question 2: The table shows the number of seats in each of the first four rows in an auditorium. The remaining ten rows follow the same pattern. Find the number of seats in the last row.

19. 4th Grade Math IEP Goal Bank Based On The Common Core Standards

Simple Example: Using a graphic organizer, student will be able to solve 3 double digit multiplication word problems, with an average accuracy rate of 75% across 10 trials. Gain familiarity with factors and multiples B.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors.

20. Ch 6 : 4th Grade Math: Multiplication Strategies & Mental Math