Section A: Practice Problems Introduction to Fractions

Section Summary

Details

In this section, we learned how to partition shapes into halves, thirds, fourths, sixths, and eighths, and how to describe each of those parts in words and using a number.

Diagram. Rectangle partitioned into 2 parts.

Diagram. Rectangle. Partitioned into six parts.

Diagram. Rectangle partitioned into 3 equal parts.

Diagram. Rectangle partitioned into 8 equal parts.

Diagram. Rectangle partitioned into 4 parts.

The numbers we use to describe these equal-sized parts are fractions.

A fraction like $\frac{1}{4}$ is read “one-fourth” because it represents one of the 4 equal parts in a whole.

Diagram. Rectangle partitioned into 4 parts, each labeled one fourth.

A fraction like $\frac{3}{4}$ is read “three-fourths” because it represents 3 parts that are each one-fourth or $\frac{1}{4}$ in size.

Fractions that refer to only one of the equal parts in a whole— like $\frac{1}{2}$ , $\frac{1}{3}$ , $\frac{1}{8}$ —are called unit fractions.

We learned that the bottom part of the fraction tells us how many equal parts we partitioned the whole into. The top part of the fraction tells us how many of the equal parts are being described.

Problem 1 (Pre-Unit)

Partition the rectangle into 10 equal squares.

Problem 2 (Pre-Unit)

Here are two equal-size squares. A part of each square is shaded.

Is the same amount of each square shaded? Explain or show your reasoning.

Diagram. Square partitioned into 4 equal parts, 1 part shaded.

Problem 3 (Pre-Unit)

Label the tick marks on the number line.
Locate and label 45 and 62 on the number line.

Number line. First tick mark 0, last tick mark 100. 9 unlabeled tick marks between 0 and 100.

Problem 4 (Pre-Unit)

Fill in each blank with $<$ or $>$ to compare the numbers.

$718$ $817$
$106$ $89$
$806$ $809$

Problem 5 (Lesson 1)

Partition the rectangle into 6 equal parts.

Problem 6 (Lesson 2)

What fraction of the rectangle is shaded?
Partition the rectangle into 8 equal parts.
What fraction of the whole rectangle does each part represent?

Problem 7 (Lesson 3)

What fraction of the rectangle is shaded? Explain how you know.
Shade $\frac{4}{6}$ of the rectangle.

Problem 8 (Lesson 4)

Jada walks across the street at a stoplight $\frac{5}{6}$ of her way from home to school. Represent the situation on the fraction strip. Explain your reasoning.

Problem 9 (Exploration)

Write a situation represented by the diagram. Explain why the diagram represents your situation.

Diagram. Rectangle partitioned into 8 equal parts, 6 parts shaded.

Problem 10 (Exploration)

Lin shaded part of some fraction strips. What fraction did she shade in each one? Explain how you know.