Lesson 5Say It with Decimals
Learning Goal
Let’s use decimals to describe increases and decreases.
Learning Targets
I can use the distributive property to rewrite an equation like
. I can write fractions as decimals.
I understand that “half as much again” and “multiply by 1.5” mean the same thing.
Lesson Terms
- long division
- percentage
- rational number
- repeating decimal
- tape diagram
- unit rate
Warm Up: Notice and Wonder: Fractions to Decimals
Problem 1
A calculator gives the following decimal representations for some unit fractions:
What do you notice? What do you wonder?
Activity 1: Repeating Decimals
Problem 1
Use long division to express each fraction as a decimal.
Problem 2
What is similar about your answers to the previous question? What is different?
Problem 3
Use the decimal representations to decide which of these fractions has the greatest value. Explain your reasoning.
Are you ready for more?
Problem 1
One common approximation for
Activity 2: More and Less with Decimals
Problem 1
Match each diagram with a description and an equation.
Diagrams:
Descriptions:
An increase by
An increase by
An increase by
A decrease by
A decrease by
Equations:
Problem 2
Draw a diagram for one of the unmatched equations.
Activity 3: Card Sort: More Representations
Problem 1
Your teacher will give you a set of cards that have proportional relationships represented 2 different ways: as descriptions and equations. Mix up the cards and place them all face-up.
Take turns with a partner to match a description with an equation.
For each match you find, explain to your partner how you know it’s a match.
For each match your partner finds, listen carefully to their explanation, and if you disagree, explain your thinking.
When you have agreed on all of the matches, check your answers with the answer key. If there are any errors, discuss why and revise your matches.
Lesson Summary
Long division gives us a way of finding decimal representations for fractions.
For example, to find a decimal representation for
So
Sometimes it is easier to work with the decimal representation of a number, and sometimes it is easier to work with its fraction representation. It is important to be able to work with both. For example, consider the following pair of problems:
Priya earned
dollars doing chores, and Kiran earned as much as Priya. How much did Kiran earn?
Priya earned
dollars doing chores, and Kiran earned 1.2 times as much as Priya. How much did Kiran earn?
Since
When we work with percentages in later lessons, the decimal representation will come in especially handy.