Wondering how to teach 4th grade math? Begin with much-needed background concepts, work from concrete to abstract, and scaffold from simple to complex applications. Then they’ll get it.

*This post was written for anyone who works with 4th grade math students – student teachers, new and experienced teachers, instructional aides, tutors, and parents.*

Estimated reading time: 23 minutes

## Table of contents

## Introduction

Most teachers change grades, but not me. I spent more than 35 years in one grade. That gave me plenty of time to figure out how to teach 4th grade math.

During my career, I was required to use a wide variety of math programs. Some focused on repetition of skills. Others explored concepts. A few used inquiry. Many blended the approaches. But all had holes. And none of them met every child’s needs.

What did I learn? The most powerful instructional platforms are **teachers**. Only they can ascertain each child’s needs. Only they can try multiple ways to convey a concept so that everyone gets it. You know what I’m talking about. It’s not in a book.

I’ve decided to use this blog post to explain what worked for me. I won’t clutter the text with images. Instead, you can use the linked words to read more and see the pictures. Buttons will take you to supporting resources in my TPT store.

## Begin 4th Grade Math with Whole Numbers

This is it. Kids’ last chance to truly understand whole numbers. Therefore, 4th grade math teachers must find out who’s got it and who doesn’t. Then they need to take action. By the end of the year, everyone must be proficient at working with multi-digit whole numbers.

### First, Find Out What They Know About Whole Numbers and Operations

To ensure mastery, the year should begin with a pretest of whole numbers and operations. The teacher needs to know what each kid can do.

In my class, I asked kids to answer twenty questions, one for each of these deconstructed concepts:

- writing a multi-digit number in standard form
- writing a multi-digit number in words
- writing a multi-digit number in expanded form
- comparing a multi-digit number with <, >, and =
- rounding to the nearest ten, hundred, and thousand
- adding without regrouping
- adding with regrouping
- subtracting without regrouping
- subtracting with regrouping
- subtracting across zeros
- multiplying a one-digit number by another one-digit number
- multiplying a two-digit number by a one-digit number
- multiplying a three-digit number by a one-digit number
- multiplying a four-digit number by a one-digit number
- multiplying two two-digit numbers
- dividing a one-digit number by a one-digit number
- dividing a two-digit number by a one-digit number without a remainder
- dividing a two-digit number by a one-digit number with a remainder
- dividing a three-digit number by a one-digit number with regrouping
- dividing a four-digit number by a one-digit number with regrouping

Sometimes, I presented these problems as task cards. Other times, I gave them as a test. And now they’re also available in a self-grading digital format.

When I checked their answers, I had a pretty good idea of who knew what.

Obviously, some skills (like subtracting across zeros and multiplying two two-digit numbers) were a disaster. When all or most kids missed a specific question, I knew I’d teach that concept to everyone. For other skills, however, I met with small remedial groups.

In any case, this assessment provided starting points for how to teach 4th grade math for the rest of the year.

### Bring on the Math Facts

During the first week of school, I told my class, “My goal is for each and every one of you to know your math facts (2s through 9s) by the end of the first quarter.” If you teach fourth grade, you’ll know that’s a tall order. But this process *really works*!

For each student, start with a multiplication chart. First, test them to find out which facts they already know. (I prefer questioning them face-to-face, but you can also use a timed test.) Second, color the facts they passed on their chart. After this, keep all students’ charts on your desk.

At this point, I liked to give my students a pep talk. I’d say, “Did you know that there are only 36 facts to memorize? Hmm, most of you already know your twos and threes – and even your fives. That leaves only 16. How many people can memorize 16 facts?” Of course, most hands would shoot up.

Next, each child worked on one set of facts independently. For example, if they’d already passed twos and threes, they’d start with fours. We used a specific sequence to learn each set:

- Skip count to find the multiples for the number (e.g., 4, 8, 12, 16, 20, 24, 28, 32, 36.)
- Write them on a sheet of paper or personal white board.
- Using a small object (like an eraser), whisper the sequence of multiples while tossing the object from hand to hand. Repeat until you no longer need to look at the numbers to recite them.
- Use a set of flash cards – for only that set of multiples – to test yourself. Pull out the ones you know right away and focus only on those that give you trouble. Take them home and practice overnight.
- See the teacher to be tested (orally) on that set of facts.
- Color more numbers on the facts chart and get started on the next set.

If you think about it, a child could pass all their facts in less than two weeks or sooner. Because – hey, they’re only working on facts they don’t know.

As my students tackled their facts, two other things happened in the math classroom: (1) instruction of other concepts as usual and (2) math facts baseball. Twice a week, my students took four quizzes over basic math facts (addition, subtraction, multiplication, and division.) For the first three weeks, they had three minutes for each 36-problem quiz. Then we moved to two minutes. After checking their work, kids ran the bases: one 100% score got them to first; two was a double; three, a triple; and four, a home run.

### Spend Time with Multi-Digit Whole Numbers

For the most part, my incoming 4th grade math students lacked understanding (and skills) related to numeration. Without that, what’s the point of starting anything else? So my first unit always addressed place value.

#### The Value of a Digit

Kids began by building whole numbers. Using a place value chart and number cards, they arranged numbers in the write places and added zeros. This activity let them practice identifying place values by name and prepared them to write numbers in standard form.

Then they moved digits to the left. Again, they added zero as a place holder. These simple actions established that a digit in the place to the left is ten times greater. (To reinforce this we always sang, “To the left, to the left, everything’s ten times in the place to the left.” Thanks, Beyoncé.)

Once the conceptual groundwork was laid, kids multiplied and divided by 10, 100, and 1000 to further establish patterns.

#### Reading Big Numbers Out Loud

Next, my 4th grade math students focused on the periods of three numbers found in multi-digit numbers. You know, like the millions, thousands, and ones. After they understood that, they could easily read any number. They just read what was between the commas and said the period name after it. For example, 12,047,129 would be read as *twelve million, forty-seven thousand, one hundred twenty-nine. *Oh yeah. No *ands*. That word is only used at a decimal point.

#### Writing Numbers in Standard Form and Words

The obvious follow-up to reading large numbers was writing them. Using processes learned in their value of a digit lessons, they wrote the numerals, added zeros as placeholders, and voila – they could write multi-digit numbers.

Writing in words was a little harder. My students needed some tips. For example, you must add a comma after the period name and a hyphen between two-digit numbers after twenty. And spelling word names always got them. Instead of stressing about it, I simply created a spelling test of number words.

#### Writing Numbers in Expanded Form

Although this skill seems easy, my 4th grade math students had a bad habit. Whenever they encountered a one-word number like *nineteen*, they kept the two digits together. So 5,019 = 5,000 + 19. To break this habit, I used place value charts. After writing the standard form in the first row, they simply dropped each non-zero whole number down to a separate row. Then, you guessed it, they added zeros as placeholders. Then they could see that in expanded form 5,019 = 5,000 + 10 + 9.

#### Rounding

As you probably already know, this highly conceptual skill gave kids trouble. Sure, they could use the “number next door” trick. But they really didn’t understand.

Enter number lines. When rounding by ten, they first counted by tens to find the multiples less and greater than the number. For example, 253 comes between 250 and 260. Then they wrote those numbers on the farthest ends of a number line broken into ten segments. Next, they marked the number at the correct position and looked to see which it was closer to.

My students struggled with this process. Of course, it would have been easier to just let them use the trick. However, I found that the struggle strengthened their overall number sense. And that’s important.

#### Comparing and Ordering

Fortunately, this was easy for my 4th grade math students. Instead of instruction, we played games (and you can too!) First, kids roll a set of dice. Then they write numbers that can be made of those digits, order them, and compare two of them. We began with just three dice, but soon kids wanted to roll more. That was fine with me. After all, they were making sense of bigger and bigger numbers.

### Work with Factors and Multiples

After place value, I like to teach factors and multiples. In my mind, all of these things – place value, factors and multiples, even multiplication facts patterns – are necessary to build number sense early in the year. You can think of them as the foundation for more complex operations.

#### Using Arrays

Sure, my 4th grade math students had already experienced arrays in their primary classes. But this year they would explore all factor pairs for a number. From these arrays, they could also tell if a number was prime, composite, and/or square (and I mean truly square.)

It’s easy to do. Just give kids a number and ask them to draw all possible arrays. If it has only one array, it’s prime. Multiple arrays make it composite. And if one of them is square, it’s also a square number. Furthermore, you can give them two related numbers (like 12 and 24) and ask them to find similarities. Soon you’ll be talking about common factors. What a great way to get ready for fractions!

#### Exploring Factor Pairs

One of our 4th grade math standards says that kids should be able to generate all factor pairs for numbers up to 100. Therefore, in the end, I wanted them to complete a worksheet that asked them to do just that.

Unfortunately, they weren’t ready. So I made 100 cards with T-charts. Each had a different number at the top. Then I passed them out (giving some of the easier numbers to my less-ready students.) Each child wrote a factor on one side of the T-chart and its pair on the other.

As a grand finale, I made a huge Venn diagram using hula hoops. Each child categorized their number as prime, composite, and/or square. (Of course, no numbers could be found at the intersections of all categories, and the prime category did not intersect with the other two.)

Alas, many of my students were still not ready to list all factors for numbers to 100. Therefore, we moved on to prime factorization. After that, we practiced with a number of the day.

(I hope you noticed that I didn’t give up on my goal. Instead, I added more activities and pushed the assessment back.)

#### Decomposing Numbers Through Prime Factorization

Okay, I’ll admit it. I’m a math geek at heart. My 4th grade math students didn’t really need prime factorization, but it provided a good way to boost number sense. Additionally, it gave kids more experience with factors and multiples.

I decided to try two methods: factor trees and the ladder method. Surprisingly, most kids really liked both processes, which was a win for student engagement.

#### Practicing with a Number of the Day

Like I said, my students just weren’t ready to list the factors of numbers to 100. So I moved on to the next unit of study in 4th grade math. However, as a bell ringer, I gave them a number of the day. They found the number’s prime factorization; listed its factors; identified it as even, odd, prime, composite, and/or square; and listed a few multiples. Not only did this brief activity improve fluency with factors, but it was also great for math vocabulary.

After ten numbers of the day, guess what? They were ready to list factors of numbers to 100 – and meet the standard!

### Move to Multiplication and Division of Multi-Digit Whole Numbers

Now that the foundation was laid, it was time to address long multiplication and division.

For both, I generally used my math textbook. However, after being burned a few times, I learned to follow the advice of my university professors: (1) build on earlier concepts and (2) work from concrete to abstract.

#### Building on What They Already Know

Now my kids would use everything I’d already taught in fourth grade math:

- Their understanding of place value helped them understand how to tackle first one digit and then the other.
- Working with arrays made area models easier.
- They could round to estimate the product or quotient.
- All that work with factors provided more fluency when dividing.
- And those multiplication facts? Well, I need say no more.

#### Working from Concrete to Abstract

Area models offer beautiful conceptual pictures of multi-digit operations. And I agree that they’re the best place to start. However, not all kids are ready to understand them. Furthermore, drawing them takes time. Although I did use area models in my classroom, I moved away from them quickly.

Next, we used place value (and a little algebra) to show how to break down a problem. For example, 18 x 6 = (10 + 8) x 6 = (10 x 6) + (8 x 6). Of course, it doesn’t have to be written algebraically, but kids need to know what’s behind any strategy you’re teaching.

Finally, it was time to teach strategies. Partial products? Great starting point. Algorithms? Okay. Lattice method. Sure. Long or short division? Both, please. I often used multiple methods – because everyone’s brain is wired differently.

My only suggestions are (1) don’t jump from one method to another too quickly, (2) if one method is working, you probably shouldn’t rock the boat with another, (3) let kids solve problems with the method that works best for them, and (4) use graph paper (because kids’ numbers tend to run together terribly.)

## Next, Study Measurement in Fourth Grade Math

### Front-Loading Customary and Metric Units of Measurement

About six weeks before customary and metric measurement, my class began a daily activity called Estimation Station. First, I assigned a date and unit of measurement to each child. On the assigned date, the student brought something from home, set up an estimation sheet, and invited classmates to take a stab at it. For example, a student assigned to milliliters might bring a small vase.

Since the winner(s) got to pick from my classroom prize box, engagement was at an all-time high. More importantly, kids got a much-needed introduction to purposes and relative sizes of units of measurement.

### Measuring Perimeter and Area

At some time in the distant past, my class began using Perry the ant to help them remember the difference between perimeter and area. Perry, you see, walks around the side of an area. It stuck.

Perimeter and area fit well just after factors and multiples. This topic re-establishes when to add and when to multiply. It also reinforces the area model for multiplication.

To practice, my students used differentiated worksheets with real-life pictorial problems. Their packet began with simple rectangles. Then they moved to problems involving adding or subtracting. For example, to figure the area of a wall, kids would subtract the area of a window.

### Exploring Customary and Metric Units of Measurement

Measuring customary lengths gets kids ready for fractions; measuring metric lengths prepares them for decimals. Furthermore, converting measures reinforces fluency of multiplication and division. That’s why it’s a perfect fit here – after whole number operations, but before fractions and decimals.

#### Customary Measurement

Estimation Station gives kids a feel for units of measurement. Afterward, they’re ready for some hands-on measurement experience. In 4th grade math, that means measuring to the nearest eighth of an inch. Unfortunately, it’s not as easy as it sounds.

In my class, we began by folding a strip of paper in half (and labeling 1/2.) Then we folded it in in half again (and labeled 1/4, 2/4, and 3/4.) Finally, we folded it one more time (and labeled 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, and 7/8). This simple but profound activity packed a lot of power. Not only did it show them how a ruler is organized, but it also introduced equivalent fractions.

After this, kids needed practice. Before using actual rulers, I set them loose with the Ruler Game. This online game lets students practice measuring to the nearest eighth over and over in a short time. Therefore, mastery (with a little help from the teacher) occurs quickly.

In addition to measuring, 4th grade math students must convert. What a nightmare. Fortunately, the CCSS has suggested conversion tables for this age group. Basically, kids just skip count to create a table (e.g., 1 foot = 12 inches, 2 feet = 24 inches, etc.) Then they refer to it when solving problems. Brilliant.

My class worked on units of length, capacity, and weight. For each, they began with even measures. Then they moved on to mixed measures and story problems.

#### Metric Measurement

For metric measurement, we followed a similar format: measuring in centimeters and millimeters, equivalencies, and conversions. What a great way to prepare for decimals!

In addition, I learned how to teach 4th grade math within my science curriculum. When choosing activities, I looked for labs that required use of rulers, graduated cylinders, and balance scales.

## By Now, Kids Are Ready for Fractions and Decimals

### Fractions

Figuring out how to teach 4th grade math isn’t always easy. But like I said before, it works best when you begin with something concrete. Therefore, we began fractions with manipulatives. Then kids worked with pictures. They named parts of a whole, parts of a set, and on a number line.

Next, they created area models and other pictures to illustrate fractions of their own. By splitting these in different ways, they explored equivalent fractions. In time, they began to recognize relationships between the numerator and denominator: a ratio.

Finally, we moved away from pictures and toward abstract representations: fractions written with numbers. Our focus shifted to the value of each fraction. Specifically, kids explored whether a fraction was closer to zero, one-half, or one.

#### Ordering and Finding Equivalent Fractions

One of my favorite activities involved fractions written on cards. We began with a stack of cards to eighths: 0, 0/8, 0/4, 0, 2, 1/8, 2/8, 1/4, 3/8, 4/8, 2/4, 1/2, 5/8, 6/8, 3/4, 7/8, 8/8, 4/4, 2/2, and 1. Kids sequenced the cards horizontally on a desk or table and arranged equivalent fractions vertically. Once they got that, I slowly added fractions with other denominators (such as twelfths, sixteenths, twenty-fourths, and even tenths.) We kept the cards on the side table, and when they finished their math lesson, they would grab the deck and practice. Seeing a group of kids down on the floor working with these cards was a common (and welcome!) occurrence.

Sure, we eventually generated equivalent fractions by multiplying by one (or 2/2, 3/3, etc.) Additionally, we divided by one to find the simplest form. But I feel certain that sequencing fractions and their equivalents *before learning this* this caused the growth of many new connections in students’ brains.

As a 4th grade math teacher, it’s important to make them think. Don’t just give them a strategy. I can’t emphasize this enough.

#### Adding and Subtracting Fractions

In most cases, 4th grade students must only add like fractions. Obviously, this is an easy process for them. As always, we moved from concrete to abstract. First, we used manipulatives. Second, pictures. And finally, numbers. Although it’s tempting to tackle adding and subtracting mixed numbers, I advise against it (unless your standards require it.) Why? Keeping the denominators the same for one entire year makes that concept so clear. Plenty of time for murky waters next year.

#### Finding the Fraction of a Whole Number

When I first began teaching (about a million years ago), our math workbook included a wonderful page. On it, kids needed to find the fraction of a set of items. So, for example, given a set of eight cowboy hats, they might be asked to color 1/4 of the group green, 1/2 of the group red, and 1/8 of the group yellow. Well, one out of every four is two, one out of every two is four, and one out of every eight is one. I don’t know how you feel about this, but for me, it’s profound. This is how my 4th grade math class began their journey in finding the fraction of a whole number.

Of course, from this, kids could see that we first divide by the denominator and then multiply by the numerator. Bingo! (But again, don’t teach a trick without first figuring out what’s behind it.)

### Decimals

Decimals express numbers in place values less than one. Now it’s time to tie them to fractions and place value.

Before coming to 4th grade, students had experience with money. That helps. Then when we explored centimeters and millimeters, they understood even better.

After the struggle with fractions, I always found decimals to be refreshingly easy. 1/10 = 0.1, and 1/100 = 0.01. 0.1 x 10 = 1, so the Beyoncé rule (everything’s ten times in the place to the left) still applies. Furthermore, 0.01 x 10 = 0.1.

Fortunately, this unit simply sets the stage for all the decimals in fifth grade. Enjoy this brief introduction!

## After All of That, Geometry Is the Easiest Part of Fourth Grade Math

Let’s face it, numeration and operations of whole numbers and fractions get a little heavy. But the geometry strand of fourth grade math brings opportunities for hands-on fun.

(This unit also introduces lots of math vocabulary. I suggest using a word wall and/or giving vocabulary quizzes.)

### Our 3-D World

One of my favorite math lessons involved the three dimensions: length, width, and height. I talked and drew. My students took notes and drew along with me. So enjoyable.

First, I would explain that a point has no dimension. Instead, it’s a location, or point of reference. Second, we’d explore figures with one dimension: line segments, rays, and lines. Third, we’d jump into basic two-dimensional (or planar) shapes, such as triangles, quadrilaterals, pentagons, circles. (This provided a good chance to introduce the term polygon.) Finally (why not), we’d explore 3-D shapes – and draw them: pyramids (polygon connected to a point), prisms (polygon connected to a congruent polygon), cylinders, and spheres.

Afterward, kids explored the three-dimensional shapes we discussed. On a worksheet, they told how many vertices, straight edges, curved edges, flat sides, and curved sides each of these possessed:

- triangular pyramid
- triangular prism
- rectangular pyramid
- rectangular prism
- cube
- cone
- cylinder
- sphere

Early in my career, my students could use a Kleenex box to actually touch and count attributes of a rectangular solid and a ball for a sphere. But soon I broke down and purchased a set of geometric solids.

### Parallel, Perpendicular, Etc.

Fortunately, kids have manipulatives to explore lines right in their desks: pencils. As you explain parallel, perpendicular, intersecting (and, of course, skew), don’t be afraid to discuss abstract planes in your classroom. Moving the pencils all around will drive your point home. (No pun intended.) Don’t forget to show how a line or ray that is not touching but on the same plane will continue on to intersect another line, ray, or segment.

### Polygons

In addition to classifying polygons by number of sides, my class dove into classification by angles and lengths of sides:

- Triangles can be classified by angle (acute, right, and obtuse) and by side (equilateral, isosceles, and scalene.) Furthermore, if you rip the corners off of any paper triangle and arrange them with the vertices touching, they will form a straight edge. That’s because the angles in a triangle add up to 180 degrees.
- Quadrilaterals fall into six basic categories: parallelogram, square, rectangle, rhombus, trapezoid, and kite. Furthermore, the sum of the angles in a quadrilateral is 360 degrees. (When you tear off the corners, they fit together perfectly.)

Once again, manipulatives provide the best experiences. I found plastic polygon shapes in old math kits, and my students classified them.

### Symmetry

Many activities use pictures to teach bilateral symmetry, but I began with polygons. To me, it was the perfect extension of our previous activities.

I opened with a discrepant event. First, I explained symmetry as the ability to fold something and make its sides match. Next, holding a rectangular sheet of paper in front of me, I asked, “How many lines of symmetry does this paper have?” Of course, they said four. So I folded it in half vertically. One. Then horizontally. Two. Then on the diagonal. What? Wait. That doesn’t work!

After that, we tried a square. Yep. Four lines of symmetry.

As kids explored the number of lines of symmetry for polygons, they found a pattern. Only regular polygons (which have congruent sides and angles) have the same number of sides and lines of symmetry.

In my classroom, my students used Miras, or Reflective GeoMirrors. To establish a line of symmetry, they set the Mira on the figure. If the position was a line of symmetry, they could look through the Mira and find that the two sides matched. If Miras aren’t in your budget, you can have kids cut out polygons and fold instead.

### Angles

Bring out the protractors! In fourth grade math, kids learn the terms right, obtuse (ob-TOOOOOSE, or greater than 90 degrees), and acute (a cute little angle, less than 90 degrees). They also learn to measure angles.

Thank goodness for clear protractors and digital projectors. To teach this skill, I modeled it a lot. First, line up the protractor with one ray. (Seriously, kids have trouble with this.) And don’t forget to center the angle’s vertex. Then see where the other ray meets the protractor. If the angle is obtuse, use the bigger number. If it’s acute, use the smaller. And then there’s the part about whether they should count up or down for the ticks. Not an easy task to teach!

Next, my students tried it on their own. Using just three angles, I could easily ascertain who got it and who didn’t. Once again, some kids moved to the side table while others completed more tasks.

## How to Teach 4th Grade Math (IMHO)

If you think about it, 4th grade math teachers’ main job is to establish mastery of whole numbers – place value, multiplication, and division. It’s hard work, and it takes a long time. But it’s worth it.

Then we teach customary and metric measurement. Measuring with a ruler introduces fractions and decimals. Converting units of measurement reinforces multiplication and division skills.

Next, we work on fractions and decimals. Although our job is simply to introduce, some concepts, like ordering and finding equivalent fractions, take some real brain power.

Finally, we get the fun job of introducing the 3-D world through geometry. Our students explore polygons, find lines of symmetry, and learn to use a protractor.

Once again, here’s my take on how to [successfully] teach 4th grade math concepts:

- Provide thorough background knowledge and understanding.
- Begin with concrete experiences, then move to abstract.
- Scaffold from simple to complex.
- Keep working with each child until they establish mastery.

## Tentative Schedule

**First Quarter **(Work math facts into schedule during the first nine weeks.)

- Place Value
- Factors and Multiples

**Second Quarter** (Schedule estimation station.)

- Multiplying Multi-Digit Whole Numbers
- Dividing Multi-Digit Whole Numbers

**Third Quarter**

- Measurement
- Fractions

**Fourth Quarter**

- Decimals
- Geometry

## About the Author

Brenda Kovich taught fourth grade for 35 years. During that time, she was named teacher of the year in two school districts and earned National Board Certification as a Middle Childhood Generalist. Additionally, she served on state and local math curriculum committees (which helped her figure out how to teach 4th grade math even better.) Currently, Brenda supports upper elementary teachers through blogging, creating instructional materials, and occasionally returning to the classroom to cover maternity leaves.