Most lessons are designed with multiple ways to represent each math topic. Please teach all the methods even though you may prefer one method over another. By providing multiple representations, students are given the opportunity to compare and contrast. Strategies that engage students in comparative thinking had the greatest effect on student achievement, leading to an average percentile gain of 45 points. More recently, Marzano's research in The Art and Science of Teaching (2007) reconfirmed that asking students to identify similarities and differences through comparative analysis leads to eye-opening gains in student achievement.

The design of each three-part lesson:

Teacher Notes (about 30 minutes)

Teaches the teacher how to understand the content
Demonstrates each of the multiple representations that students will learn
Is not a replacement for students taking their own notes

Teacher can use the examples in the Teacher Notes and work through them with the students.
Students should copy their own notes and do practice problems in their own journal

Class practice (about 10-15 minutes)

Give a limited amount of time to do the class practice. Students are not necessarily expected to finish the entire set of practice problems.
In general, only give students 10 - 15 minutes to work on the class practice problems.
When the class practice has multiple columns of problems, tell students to do the left column of problems first, then the word problems, then the right column of problems.
As students are working on the class practice, the teacher should wander around the classroom noting problems that were difficult for the whole class.
After the 10-15 minutes of practice, discuss the problems that students thought were tough.

Homework

This is a near exact copy of the class practice
students are expected to complete the entire homework set of problems

Every lesson is designed to be a one-day lesson taking about 45 minutes. It is strongly recommended that teachers preface every lesson with a 10- to 15-minute number talk. Here is a resource for implementing number talks in your classroom:

www.dailynumbertalk.info

What Common Core standards are in this unit?

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

4.NF.3b: 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.

4.NF.3c: 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.

A thought about fractions…

Fractions are a bit of a mystery to students. This unit attempts to demystify fractions by employing some very deliberate publishing designs.

Number lines

Students will be required to draw numerous number lines throughout the unit. The purpose of this is to provide students will tons of experience making fractions thereby developing number sense with relations to fractions. Teachers are encouraged to all students to share their techniques for accurately dividing up lines into the required number of partitions. For example, to cut a line into sixths, a student might cut it in half and then cut each half into thirds. Similarly, another student might draw sixths by cutting a line into thirds and then each third in half.

Area model

Students will also be expected to draw lots of area models to represent fractions. In general, students will use only vertical lines to cut a rectangle into fractions.

However, for larger denominators students are welcome to use horizontal lines as well.

Why so many methods? Isn’t one way good enough?

The short answer is NO. As a book review of Harvey Silver’s book Compare & Contrast puts it:

Comparative thinking is one of our first and most natural forms of thought. When we are infants, one of the first differences we must identify is that between mother and other. Without the ability to make comparisons—to set one object or idea against another and take note of similarities and differences—much of what we call learning would quite literally be impossible.

In other words, your students will learn fractions better if they regularly have opportunities to compare and contrast the various ways of modeling fraction problems.

Nearly all the figures in this module of lessons have been hand drawn. While we could have used computer generated graphics, we deliberately chose to use hand drawn figures to send students a subtle (or not so subtle) message that fractions are not mysterious. In fact, anyone can drawn fractions.

Additional notes will show up here...

LESSON 1: Using models to add simple fractions

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

In this lesson we will introduce to students two models for adding simple fractions with common denominators: number line and area model. To be sure, there are other models that can also be used (sets, circles, etc.), but we will limit ourselves to just the number line and area models at this time.

Number line

Remember that adding whole numbers can be modeled on a number line. For example, 3+2 can be modeled as follows:

We can also switch the order of the addends and still see that their sum is 5. This means addition is commutative.

In the same way that whole numbers can be modeled on the number line, fractions can also be modeled on the number line.

To show on the number line, we draw a number line from 0 to 1 and cut it into eight equal parts because the denominator is 8. Then we draw a “hop” of three-eighths followed by a hop of two-eighths. Since we end up on , we know that

Example 2: Show on the number line.

Teachers should give students plenty of opportunities to practicing partitioning the number line into the required number of parts (whatever the denominator says). This helps students develop a deeper understanding of fractions.

Area model

Example 3: Use an area model to show .

Since both fractions have 8 as the denominator, we will draw two equal-sized rectangles and cut each of them into eight pieces. The first rectangle has three parts shaded and the second rectangle has two parts shaded. Combining those shaded parts together gives us 5 shaded parts out of 8 total.

Example 4: Use an area model to show .

CLASS PRACTICE (10 - 15 minutes)

Students should do their personal best to complete the class practice problems within the allotted 10 to 15 minutes. For some classes or for some students, it may be appropriate to modify the assignment by specifying which problems they work on first.

LESSON 1 CLASS PRACTICE - Using models to add simple fractions

Draw a number line, cut it into the number of parts indicated by the denominator, and then show the “hops”. The first one has been done for you.

Write the addition problem being modeled on the following number line.

Use the two rectangles to model the two fractions being added. Use the third rectangle to show the sum. The first one has been done for you.

Write the addition problem being modeled with the following rectangles.

LESSON 1 HOMEWORK - Using models to add simple fractions

Draw a number line, cut it into the number of parts indicated by the denominator, and then show the “hops”. The first one has be done for you.

Write the addition problem being modeled on the following number line.

Use the two rectangles to model the two fractions being added. Use the third rectangle to show the sum. The first one has been done for you.

Write the addition problem being modeled with the following rectangles.

LESSON 2: Adding simple fractions with like denominators

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

In this lesson we will continue adding simple fractions, however, now students will record their thinking numerically, rather than using models.

It is very likely students will have noticed the pattern for adding fractions with like denominators. If not, help students recognize the rule: “To add fractions with like denominators, add the numerators and record the sum on top of the original denominator.”

Example 1:

To add these fractions, first we notice that they indeed have a common denominator. Now we are free to add the numerators and write the sum over 12, the denominator.

Example 2: Add . Simplify the final answer if needed.

In this problem, we see that the sum is . However, is a fraction that can be written in the simpler form of .

Here is a second method for simplifying .

It is usually best practice to write the final answer in simplest form.

Example 3:

Example 4:

CLASS PRACTICE (10 - 15 minutes)

LESSON 2 CLASS PRACTICE - Adding simple fractions with like denominators

Find each sum. Simplify if possible.

A side of an equilateral triangle is inches long. What is the perimeter of this triangle?

Rob and Nancy are working on a project. Rob completes of it on Monday and of it on Tuesday. Nancy completes of it on Wednesday and of it on Thursday. Is the project finished yet? Explain.

Samantha jogged of a mile, which is mile less than Jessica jogged. How far did Jessica jog?

LESSON 2 HOMEWORK - Adding simple fractions with like denominators

Find each sum. Simplify if possible.

A side of an equilateral triangle is inches long. What is the perimeter of this triangle?

Rob and Nancy are weaving bracelets. So far Rob’s bracelet is inch long and Nancy’s bracelet is inch long. What is the total length they have eaved so far?

Charlotte and Duane are reading the same book. Charlotte has read of the book. Duane has read of the book more than Charlotte. What fraction of the book has Duane read?

LESSON 3: Using models to subtract simple fractions

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

Just as we did with adding fractions, we will use two models for showing subtraction of fractions: number line and area model. Indeed, there are several other models we could use, but for the purposes of this module, we will only focus on the two.

Example 1:

To model this problem with a number line we begin by drawing a number line from 0 to 1 and cutting it into ten equal intervals, since the denominator is 10. Then we start at the location of and move backwards 4 intervals because we are subtracting . Since we end up at , the answer is .

We can solve the same problem using the area model by drawing a rectangle and then cutting it into 10 equal pieces. Then we shade in 7 of those pieces to represent . Finally we cross off 4 of those pieces to represent the subtraction.

Example 2:

This problem represents one additional level of complexity because after subtracting we will need to simplify the fraction to get our final answer.

Another way to show how to simplify the fraction:

Example 3:

This problem is different from the previous two problems because it involves a fraction larger than one. Subtracting is modeled the same way.

CLASS PRACTICE (10 - 15 minutes)

LESSON 3 CLASS PRACTICE - Using models to subtract simple fractions

Draw a number line, cut it into the number of parts indicated by the denominator, and then show the “hops”. The first one has be done for you.

Use one or more rectangles to draw the first fraction. Then use X’s to show the subtraction.

Ribbon A is inch long. Ribbon B is inch long. How much longer is Ribbon A than Ribbon B? Use either the number line or the area model to show your thinking.

Charlotte has of a pound of flour. After making some pancakes, Charlotte has pound of flour left over. How much flour did Charlotte use for the pancakes?

Peavey is a poodle and has of a cup of dog food in her bowl. After she eats of a cup of food, how much food is still in her bowl?

LESSON 3 HOMEWORK - Using models to subtract simple fractions

Draw a number line, cut it into the number of parts indicated by the denominator, and then show the “hops”. The first one has be done for you.

Use one or more rectangles to draw the first fraction. Then use X’s to show the subtraction.

Ribbon A is inch long which is inch longer than Ribbon B. How long is Ribbon B? Use either the number line or the area model to show your thinking.

Grace is going to school which is mile away. After jogging some distance, Grace walks the final mile to school. How far did Grace jog?

Donevan has of bag of fertilizer. After he uses of the bag on the first garden, how much fertilizer is left over for the second garden?

LESSON 4: Subtracting simple fractions with like denominators

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

In this lesson we will continue subtracting simple fractions, however, now students will record their thinking numerically, rather than using models.

It is very likely students will have noticed the pattern for subtracting fractions with like denominators. If not, help students recognize the rule: “To subtract fractions with like denominators, subtract the numerators and record the difference on top of the original denominator.”

Example 1:

The first thing is to notice that we have common denominators. Now we can simply subtract the numerators and write the difference on top of 12, since that is the denominator.

Example 2:

In this problem, we see that the difference is . However, is a fraction that can be written in the simpler form of .

Here is a second method for simplifying .

It is usually best practice to write the final answer in simplest form.

Example 3:

Example 4:

CLASS PRACTICE (10 - 15 minutes)

LESSON 4 CLASS PRACTICE - Subtracting simple fractions with like denominators

Find each difference. Simplify if possible.

A single length of rope meter long is cut into two pieces. If one piece is meter long, how long is the second piece of rope?

Jadon has pencil that is foot long. After sharpening his pencil, it is now foot long. How much shorter is the pencil now?

Mikey and Jessica have eaten a total of pounds of french fries. If Mikey ate pound of french fries, how much did Jessica eat?

LESSON 4 HOMEWORK - Subtracting simple fractions with like denominators

Find each difference. Simplify if possible.

Duane is walking on a path that is mile long. So far he has walked miles. How much further does he have to go?

Christina has a bag of jelly beans that weighs of a pound. After eating some of the jelly beans the bag now weighs of a pound. How much did Christina eat?

Mike and Erika have shoveled a total of tons of dirt. If Mike shoveled ton of dirt, how much did Erika shovel?

LESSON 5: Using models to add mixed numbers

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

When we see a mixed number such as , it is understood that the whole number is being added to the fraction. So, if we wanted to, we could write it as . We will use this fact to help us understand how to add mixed numbers.

Example 1: Add

We can model this on the number line by drawing an extended number line and cutting each whole interval into five parts since the denominator is 5. Then starting at we continue up the number line an additional . The answer is , since that is where we end up.

We can also model this problem using the area model as shown here.

Example 2: Add

We can model this on the number line by drawing an extended number line and cutting each whole interval into eight parts since the denominator is 8. Then starting at we continue up the number line an additional . The answer is , since that is where we end up.

We can also model this problem using the area model as shown here.

It is best practice to simplify the final answer if possible, so the answer in simplest form is .

NOTE: In this lesson (and all future lessons) we will interchangeably use two different methods for simplifying a fraction: the factoring method and the division method. Here is a quick reminder of the two methods.

Simplifying by factoring

Simplifying by division

Example 3: Add

Number line:

Area model:

Example 4: Add

Number line:

Area model:

CLASS PRACTICE (10 - 15 minutes)

LESSON 5 CLASS PRACTICE - Using models to add mixed numbers

Use a number line to model each addition problem. Simplify the final answer if possible.

Use the area model to solve each addition problem. Simplify the final answer if possible.

Allan jogged miles. Evan jogged mile further than Allan. How far did Evan jog?

Charlotte is knitting a scarf. On Monday she knitted inches and on Tuesday she knitted inches. How far has she knitted in all?

A length of rope has been cut into two smaller pieces. One is feet long and the other is feet long. How long was the original length of rope?

LESSON 5 HOMEWORK - Using models to add mixed numbers

Use a number line to model each addition problem. Simplify the final answer if possible.

Use the area model to solve each addition problem. Simplify the final answer if possible.

Ernie and Vince are eating pizza. Ernie ate pieces of pizza. Vince ate more pieces than Ernie. How much pizza did Ernie and Vince eat in all?

Ginny is making dresses. On Monday she sewed dresses and on Tuesday she sewed dresses. How many dresses did she sew in all?

A length of rope has been cut into two smaller pieces. The shorter piece is meters long and the longer piece is meter longer than the shorter piece. How long was the original length of rope?

LESSON 6: Adding mixed numbers with like denominators

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

In this lesson we will continue adding mixed numbers with like denominators, however, now students will record their thinking numerically, rather than using models.

Example 1:

To add these mixed number we first decompose each number into its component parts. The we add the whole numbers together and the fractions together. Doing so, we see the sum is . Since the fraction is already in simplest form, it is also our final answer.

Example 2:

After adding the whole numbers together and the fractions together we get . However, we see that this fraction is not in simplest form, so we need to simplify it to .

Example 3:

This problem is different from the previous ones because adding the fractions gives us an improper fraction which needs to be simplified.

Example 4:

This problem represents the highest level of complexity since the sum results in an improper fraction that also needs to be simplified.

CLASS PRACTICE (10 - 15 minutes)

LESSON 6 CLASS PRACTICE - Adding mixed numbers with like denominators

Find each sum. Simplify if possible.

A side of an equilateral triangle is inches long. What is the perimeter of this triangle?

Grace is using flour to make a batch of pancakes. After using cups of flour to make the first batch of pancakes, she has cups of flour left over. How much flour did Grace have at the start?

Samantha jogged kilometers, which is kilometer less than Jessica jogged. How far did Jessica jog?

LESSON 6 HOMEWORK - Adding mixed numbers with like denominators

Find each sum. Simplify if possible.

Jordan has two dogs: Peavey and Puffy. Peavey weighs kilograms. Puffy weighs kilograms more than Peavey. How much does Puffy weigh?

Donevan is walking to school which is a certain distance away. After walking kilometers, he still has kilometers to go. What is the total distance Donevan will be walking?

Charlotte has eaten pieces of pizza, which is pieces less than Duane has eaten. How many pieces of pizza has Duane eaten?

LESSON 7: Using a model to subtract a fraction from a whole number

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

Suppose we wanted to subtract . We can model this problem using either the number line or the area model.

To use a number line for modeling this problem, we begin by drawing a number line from 0 to 2 and partitioning each whole interval into 5 parts. We cut each whole interval into 5 parts because the fraction being subtracted has the denominator of 5.

Then start at 2 and move backwards three fifths. This places us at . So,

Using the area model is similar to the number line. We begin by drawing two rectangles and partition one of those rectangles into fifths. After crossing off three of the fifths, we are left with . So,

Numerically, we would solve this problem as

Example 2: Subtract . Use the number line, area model, and show the mathematics.

Example 3: Let’s reason how to solve using mental math.

We know each whole number can be partitioned into eighths. If one of the whole numbers has five eighths removed, there will be three eighths remaining. So the answer is .

Here is how we might write it numerically.

Let’s confirm our answer by using the area model.

CLASS PRACTICE (10 - 15 minutes)

LESSON 7 CLASS PRACTICE - Using a model to subtract a fraction from a whole number

Solve using the number line or the area model. Then show the solution numerically. The first problem has been solved for you already.

Problem	Number line	Area model

Debi has 3 candy bars. She eats of one candy bar. How much does she have left over?

John is going to school, which is 2 miles away. He jogs the first ¾ of a mile and walks the rest. How far does John walk?

Duane has incorrectly solved . Find his mistake and circle it. Use a number line or area model to explain how to fix his mistake.

LESSON 7 HOMEWORK - Using a model to subtract a fraction from a whole number

Solve using the number line or the area model. Then show the solution numerically.

Problem	Number line	Area model

Jim has 2 liters of soda. He drinks of one liter. How much soda does he have left over?

Margaret has 3 yards of ribbon. She uses of a yard of ribbon on a dress she is making. How much ribbon does Margaret have left over?

Dale has 5 bags of fertilizer for his garden. He spreads the fertilizer and has of a bag left over. How much fertilizer did Dale use?

LESSON 8: Subtracting a simple fraction from a whole number

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

In this lesson we will continue to subtract a simple fraction from a whole number, however, now students will show their thinking numerically rather than with a model.

Example 1: Suppose we wanted to subtract .

Whether we used the number line or the area model, we need to partition at least one of the whole numbers into fifths in order to subtract.

Numerically, we would record our thinking as follows…

	The two wholes are separated into one whole and five fifths. This then allows us to subtract .
An alternate way of recording our thinking is to convert the entire two wholes into 10 fifths. Then we can subtract.

Example 2: Subtract .

Example 3: Subtract .

Example 4: Subtract .

To show our thinking on this problem numerically, we imagine cutting all the whole intervals into four parts since the denominator is 4. Then we can subtract.

An alternate way to show our thinking is to convert all the whole numbers into fourths and then subtract.

If students are more comfortable subtracting using the models, it is acceptable to allow them continued use of the models rather than forcing them to use strictly numbers. In time, students will naturally transition away from the models.

Here is a source to create as many additional practice worksheets as needed:

http://www.worksheetworks.com/math/fractions/subtraction-skills/from-wholes.html

CLASS PRACTICE (10 - 15 minutes)

LESSON 8 CLASS PRACTICE - Subtracting a simple fraction from a whole number

Solve each problem numerically. You may use a number line or area model to verify your solution.

Jonas has 3 cupcakes and eats of a cupcake. How many cupcakes does he have left?

Donevan lives 2 miles away from school. He jogs the first miles and then walks the rest. How far does Donevan walk?

Susie has 5 cups of flour and uses of a cup of flour for a cookie recipe. How much flour does Susie have left over?

LESSON 8 HOMEWORK - Subtracting a simple fraction from a whole number

Solve each problem numerically. You may use a number line or area model to verify your solution.

Jeremy has 3 sticks of salt water taffy and eats of a stick. How many sticks of taffy does Jeremy have left?

Darion has an empty 3-gallon container. After pouring in of a gallon of water into the cooler, how much more water will the container hold?

Maria has 4 cups of sugar and uses some of the sugar for a brownie recipe. Now she has cup of sugar left over. How much sugar did Maria use for the brownie recipe?

LESSON 9: Using models to subtract a fraction from a mixed number

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

In the previous lesson we subtracted a fraction from a whole number. In this lesson we will use a model to subtract a fraction from a mixed number.

Example 1:

First, let’s find the answer to this problem using a number line. Starting at and then going backwards , we end up at , which is the answer.

Another way to find this answer is to use an area model and decompose the second fraction.

Area model

Numerically

Draw the model

Here is the problem

Cross off ⅕ so far.

Decompose ⅘ into ⅕ and ⅗. Then subtract ⅕.

Decompose one of the wholes into fifths.

So this...

becomes...

Now we can cross off the remaining ⅗.

We can now subtract ⅗.

Instead of decomposing the second fraction, we could have drawn a model where we decompose the first number instead.

Area model

Numerically

Draw the model

Here is the problem

Decompose one of the wholes into fifths. Instead of there is now .

Decompose the first number into 2 and , which then becomes .

Now cross off ⅘ .

Now subtract.

Let’s do a little practice with these two methods using the area model.

Example 2: Draw an area model to subtract by decomposing the second fraction.

Area model	Numerically

Example 3: Draw an area model to subtract by decomposing the first number.

Area model	Numerically

LESSON 9 CLASS PRACTICE - Using models to subtract a fraction from a mixed number

LESSON 9 HOMEWORK - Using models to subtract a fraction from a mixed number

LESSON 10: Subtracting a simple fraction from a mixed number

Common Core Standard

4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

TEACHER NOTES

LESSON 10 CLASS PRACTICE - Subtracting a simple fraction from a mixed number

LESSON 10 HOMEWORK - Subtracting a simple fraction from a mixed number

LESSON 11: Using models to subtract mixed numbers

Common Core Standard

TEACHER NOTES

In this lesson we will focus on subtracting mixed numbers with like denominators such as . We will use models (number line and area) to develop an understanding of subtracting mixed numbers.

Example 1:

When using the number line to model this problem, there are two ways to find the answer: the going backwards method and the counting up method.

Going backwards:

With this method we start at and then go backwards on the number line by . The answer is because that is where we end up on the number line.

Counting up:

With this method we start at and measure how much we have to count up to get to . Since we have to count up , that is the answer.

We can also use the area model by drawing the representation of and then crossing off enough pieces to represent . Since there aren’t enough fractional pieces to cross off , we need to cut one of the wholes into fifths. The answer is because that is how much is left.

Example 2:

Going backwards:

With this method we start at and then go backwards on the number line by . The answer is because that is where we end up on the number line. Now we simplify the answer to .

This is what it looks like numerically:

Counting up:

With this method we start at and measure how much we have to count up to get to . Since we have to count up , that is the answer. Now we simplify the answer to .

This is what it looks like numerically:

For the area model, we draw a representation of and then cross off one whole. However, since we do not have enough fractional pieces to cross off , we will partition one of the wholes into twelfths in order to cross off . There are remaining which can be written in the simpler form of .

This is what it looks like numerically:

Example 3:

Going backwards:

Counting up:

Area model:

Draw and then cross off one whole. Since we only have 11 fourteenths and we need to cross off 13 fourteenths, we will decompose one of the wholes into fourteenths. This makes 4 wholes and 25 fourteenths. Now we can cross off and we are left with which simplifies to .

This is what it would look like numerically.

CLASS PRACTICE (10 - 15 minutes)

LESSON 11 CLASS PRACTICE - Using models to subtract mixed numbers

Subtract using either the number line model or the area model.

Problem	Number line or area model

Grace is finger knitting a scarf. She starts with yards of yarn and after making the scarf there is yards of yarn left over. How much yarn did Grace use to make the scarf?

Duane jogs for miles and then he walks for miles. How much further did Duane walk than jog?

Jane has liters of water. After drinking liter of water, how much water does Jane have left?

LESSON 11 HOMEWORK - Using models to subtract mixed numbers

Subtract using either the number line model or the area model.

Problem	Number line or area model

Donevan is driving his car. He starts with gallons of gas and after driving there is now gallons of gas in the tank. How much gas did Donevan use during his drive?

Tank A has gallons of water in it. Tank B has gallons of water in it. How much more water does Tank A have compared to Tank B?

Cliff has meters of welding tape. After using meters of welding tape for a project, how much tape does Cliff have left?

LESSON 12: Subtracting mixed numbers with like denominators

Common Core Standard

TEACHER NOTES

LESSON 12 CLASS PRACTICE - Subtracting mixed numbers with like denominators

LESSON 12 HOMEWORK - Subtracting mixed numbers with like denominators

page of 1Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.