learning together about building on informal ... · © 2015 national council of teachers of...

© 2015 National Council of Teachers of Mathematics

www.nctm.org/profdev

NAME _____________________

Learning Together About Building on Informal

Understandings of Fractions

Problem Set

Three children want to share 12 cookies so each child receives the same number of cookies. How many cookies should each child get? Show how children might work out the problem.

If one more child joins the group, how many cookies should each child get?

If three more children join the group, how many cookies should each get?

Two children want to share five apples that are the same size so that both have the same amount to eat. Draw a picture to show what each child should receive.

What is another way children might solve the problem?

Using at least two different representations, show how three children share five apples.



NAME _____________________

Learning Together About Building on Informal

Understandings of Fractions

3. Show two different ways eight children could share four pizzas.

What does this sharing look like if the group splits into two tables?

What does it look like if the group splits into four tables?



NAME _____________________

Brown Rectangle Problem

How might upper elementary school students respond to these questions?

The Brown Rectangle Problem is drawn from: Ball, D. L., & Shaughnessy, M. (2012). 2012 Grand Rapids Elementary Mathematics Laboratory: Lesson plan for Monday, August 13, 2012, Lab Class #1

(a) What fraction of the rectangle below is shaded brown?

______________________

(b) What fraction of the rectangle below is shaded brown?

______________________



NAME _____________________



NAME _____________________

Ordering Fractions

What strategies can you use to compare these fractions?

, ,

, ,

, ,

, , , ,



NAME _____________________

Fractions on A Numberline

Locating Fractions on the Number Line Estimate the location of each number on the number line.

, , , , , , , , , , , , , , ,

What benchmark fractions did you locate on your number line?

Explain how you located on the number line.

Explain how you located and on your number line.



NAME _____________________

Understanding Fraction Addition

Which problem or problems would be solved by adding + ?

1. Ari pours of a cup of sand into an empty box. Then Ari pours of a

cup of sand into the box. How many cups of sand are in the box?

2. Tom has a full glass of water. Tom pours cup of water from the

glass into an empty bowl. Then Tom pours in another of the water

from the glass into the bowl. How many cups of water are in the bowl now?

3. of the boys in the class are wearing tennis shoes. of the girls in the

class are wearing tennis shoes. What fraction of the class is wearing

tennis shoes?

4. of the children at Russell Elementary School say they would like to

visit the zoo. of the children at Russell Elementary School say they

would like to visit the Science Museum. What fraction of the children at Russell Elementary School would like to visit the zoo or the science

museum?



NAME _____________________

Understanding Fraction Addition

Rewrite the problems that CANNOT be solved by adding + so that they

can be solved by adding + .

What are the important characteristics of problems that can be solved by

adding the fractions mentioned in the problem?

Adapted from Putting Essential Understanding of Fractions into Practice

(NCTM 2013)



NAME _____________________

Representing Fraction Addition

Select one of the problems that would be solved by

adding + . In the space below, solve the problem using

at least three different strategies.

Your strategies may include, but are not limited to, the

following:

converting the fractions to fractions with common

denominators

drawing a diagram

using a number line

converting the fractions to decimals



NAME _____________________

Understanding and Representing Fraction Subtraction

1. Write a problem that can be solved by subtracting –

2. Compare your problem with others at your table and revise if needed.

3. Select one of the problems from your table that would be solved by

subtraction – . In the space below, solve the problem using at least

three different strategies.

Your strategies may include, but are not limited to, the following: converting the fractions to fractions with common denominators

drawing a diagram using a number line

converting the fractions to decimals



NAME _____________________

Understanding and Representing Fraction Multiplication

Write three different word problems that illustrate the following:

1. A whole number times a fraction.

2. A fraction times a whole number.

3. A fraction times a fraction.

Share your problems with others at your table and revise if necessary.

As a group, choose one problem of each type and represent it using at least 2 different strategies.

Understanding and Representing Fraction Division

1. Use a bar model to solve the following problem:

You have 6 feet of ribbon and want to cut it into pieces that are 2 feet long. How many pieces can you make?

What division problem did you solve? _________________________ Share with others at your table and revise if necessary. 2. Use a bar model to solve the following problem:

You have 6 feet of ribbon and want to cut it into pieces that are !! foot

long. How many pieces can you make?

What division problem did you solve? _________________________ Share with others at your table and revise if necessary. 3. Use a bar model to solve the following problem:

Your team of four is responsible for cleaning up !! mile of beach. How

much do you each need to clean, assuming you all clean the same amount of beach?

What division problem did you solve? _________________________ Share with others at your table and revise if necessary.

4. Write and solve a division problem that can be solved with the following expression: 4 !

!

Does your problem represent 4 !

3?

Share with others at your table and revise if necessary. 5. Write and solve a division problem that can be solved with the following expression: !3 4

Does your problem represent !3 4?

Share with others at your table and revise if necessary. Additional problems: 6. 3 !

4

7. !4 3

8. 3 !6

9. !6 3



NAME _____________________

Ordering Fractions

learning together about building on informal ... · © 2015 national council of teachers of...

Documents