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Toy Train Tracks: Build Fractions from Track Pieces worksheet preview

Worksheet

Toy Train Tracks: Build Fractions from Track Pieces

Grade 4 toy train practice: break fractions and mixed numbers into sums of fractions with the same denominator in more than one way.

Grade 4MathInteractive · Printable

Aligned to4.NF.B.3.b

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What’s included

  • Single worksheet
  • Auto-graded online
  • 1 Common Core standard
  • Printable answer key
  • 11 questions
  • Classroom-ready

Details

Format
Interactive · Printable
Grade
Grade 4
Subject
Math
Question types
Fill in the blank, Multiple choice, Matching, Circle the answer, Sorting, Short answer

About this worksheet

What students practice

  • Students write a fraction as a sum of unit fractions with the same denominator.
  • Students break one fraction into sums of same-denominator fractions in more than one way.
  • Students break a mixed number into wholes and fractions, such as 1 3/4 = 4/4 + 3/4.

How to use

Use after students understand unit fractions. Paper strips cut into equal pieces work well as track pieces for students who want to build each sum before writing it.

Curriculum

Common Core standard covered

4.NF.B.3.b

Break a fraction into a sum of fractions with the same denominator in more than one way.

Preview

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Toy Train Tracks: Build Fractions from Track Pieces

Break fractions and mixed numbers into sums in more than one way.

One piece at a time

One loop of track is 1 whole. Each small track piece is a unit fraction of the loop.

1.
A loop of track is made of 6 equal pieces. Nia builds 4/6 of the loop using only 1/6 pieces. Which sum shows her track?
  • A. 1/4 + 1/4 + 1/4 + 1/4
  • B. 4/6 + 1/6
  • C. 1/6 + 1/6 + 1/6 + 1/6
  • D. 1/6 + 1/6 + 1/6
2.
The number line shows one loop of track from 0 to 1, marked in tenths. The point shows where Omar's track ends, at 7/10.

01
7/10 is   pieces that are each 1/10 of the loop.
7/10 = 4/10 +  /10
7/10 = 5/10 +  /10

Many ways to build

There is more than one way to break apart a fraction. Every piece in a sum has the same denominator.

3.
Theo needs a track that is 6/8 of a loop. Write the missing numerator to show four ways he can build it.

6/8 = 2/8 +  /8
6/8 = 3/8 +  /8
6/8 = 1/8 + 1/8 +  /8
6/8 = 2/8 + 2/8 +  /8

4.
Kayla wants a track that is 5/6 of a loop. Circle every sum that equals 5/6.

2/6 + 3/62/6 + 2/61/6 + 4/64/6 + 2/62/6 + 1/6 + 2/61/6 + 1/6 + 1/6 + 1/63/6 + 1/6 + 1/6

5.
A loop is made of 12 equal pieces. Match each track length to a sum that builds it.
  1. 7/12
  2. 9/12
  3. 5/12
  4. 11/12
  1. A. 2/12 + 2/12 + 1/12
  2. B. 8/12 + 2/12 + 1/12
  3. C. 4/12 + 3/12
  4. D. 6/12 + 3/12
6.
Ana is building a track that is 9/10 of a loop. Find the missing piece in each way she tries.

9/10 = 2/10 + 2/10 + 2/10 +  /10
9/10 = 4/10 + 4/10 +  /10
9/10 = 5/10 +  /10

Tracks longer than one loop

A track can be more than one loop long. Break each mixed number into wholes and fractions. One whole loop of fourths is 4/4.

7.
Leo's track is 1 3/4 loops long. Each loop is made of 4 equal pieces.

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

8.
Ruby's track is 2 2/6 loops long. Each loop is made of 6 equal pieces, so one whole loop is 6/6.

2 2/6 = 1 + 1 +  /6
2 2/6 =  /6 + 6/6 + 2/6
2 2/6 = 6/6 + 6/6 + 1/6 +  /6

9.
Dev's track is 1 2/5 loops long. Which sum is not equal to 1 2/5?
  • A. 1 + 2/5
  • B. 1 + 1/5 + 2/5
  • C. 5/5 + 1/5 + 1/5
  • D. 1/5 + 1/5 + 1/5 + 1/5 + 1/5 + 2/5
10.
Each loop is made of 8 equal pieces. Sort each sum by the length of track it builds.
3/8 + 2/84/8 + 3/88/8 + 1/81/8 + 1/8 + 3/82/8 + 2/8 + 2/8 + 1/84/8 + 4/8 + 1/82/8 + 3/8 + 4/8
5/8 of a loop7/8 of a loop1 1/8 loops
11.
Jamal says the only way to build 4/5 of a loop is 1/5 + 1/5 + 1/5 + 1/5. Write two other ways to show 4/5 as a sum of fifths. Explain how you know each sum equals 4/5.

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