Section A: Practice Problems Size and Location of Fractions

Section Summary

Details

In this section, we used fraction strips to represent fractions with denominators of 2, 3, 4, 5, 6, 8, 10, and 12. We also used the strips to reason about relationships between fifths and tenths, and between sixths and twelfths.

Fraction strips. 3 rectangles of equal length. Rectangle 1, labeled 1. Rectangle 2, partitioned into 5 equal parts, each labeled one fifth. Rectangle 3, partitioned into 10 equal parts, each labeled one tenth.

Fraction strips. 3 rectangles of equal length. Rectangle 1, labeled 1. Rectangle 2, partitioned into 6 equal parts, each labeled one sixth. Rectangle 3, partitioned into 12 equal parts, each labeled one twelfth.

We learned that 2 tenths are equivalent to 1 fifth, or that splitting 5 fifths into two will produce 10 equal parts or tenths. When the denominator is larger, there are more parts in a whole.

We used what we learned about fraction strips to partition number lines and represent different fractions.

Problem 1 (Pre-Unit)

What fraction of each figure is shaded?

Problem 2 (Pre-Unit)

Explain why the shaded portion represents $\frac{1}{8}$ of the full rectangle.

Problem 3 (Pre-Unit)

Label each tick mark with the number it represents. Explain your reasoning.

Problem 4 (Pre-Unit)

Explain or show why $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions.

Problem 5 (Lesson 1)

The entire diagram represents 1 whole. Shade the diagram to represent $\frac{1}{4}$ .
To represent $\frac{1}{6}$ on the tape diagram, would we shade more or less than what we did for $\frac{1}{4}$ ? Explain your reasoning.

Problem 6 (Lesson 2)

The entire diagram represents 1 whole. What fraction does the shaded portion represent? Explain your reasoning.
Shade this diagram to represent $\frac{2}{10}$ .

Problem 7 (Lesson 3)

For each pair of fractions, decide which is greater. Explain or show your reasoning.

$\frac{1}{8}$ or $\frac{1}{10}$
$\frac{4}{10}$ or $\frac{7}{10}$
$\frac{4}{5}$ or $\frac{5}{4}$

Problem 8 (Lesson 4)

Use the fraction strips to name three pairs of equivalent fractions. Explain how you know the fractions are equivalent.

Two diagrams of equal length. Top diagram, 12 equal parts, each labeled 1 twelfth. Bottom diagram, 6 equal parts, each labeled 1 sixth.

Problem 9 (Lesson 5)

Explain or show why the point on the number line describes both $\frac{3}{5}$ and $\frac{6}{10}$ .
Explain why $\frac{6}{10}$ and $\frac{3}{5}$ are equivalent fractions.

Problem 10 (Lesson 6)

For each question, explain your reasoning. Use a number line if you find it helpful.

Is $\frac{4}{5}$ more or less than $\frac{1}{2}$ ?
Is $\frac{4}{5}$ more or less than 1?

Problem 11 (Exploration)

Make fraction strips for each of these fractions. How did you fold the paper to make sure you have the right-size parts?

$\frac{1}{3}$
$\frac{1}{5}$
$\frac{1}{10}$

Problem 12 (Exploration)

Andre looks at these fraction strips and says “Each $\frac{1}{2}$ is $\frac{1}{3}$ and another half of $\frac{1}{3}$ ”. Do you agree with Andre? Explain your reasoning.
What relationship do you see between $\frac{1}{6}$ and $\frac{1}{4}$ ? Explain your reasoning.
Can you find a relationship between $\frac{1}{6}$ and $\frac{1}{8}$ using fraction strips?