Item 3 Supporting Activities
Use any combination of the following suggestions. The amount of support increases with each subsequent activity.
Activity 3.A 10 minutes
The following activity may be appropriate for students who incorrectly answer the core assessment item.
Materials—S: Tenths in Decimal Form and Fraction Form, scissors
Students may need support representing tenths in decimal form. This activity engages students in relating decimal form to fraction form while recording both representations on a number line, and then reading and writing measurements in fraction form and decimal form. Addressing this need prepares students for modeling decimals to the thousandths.
Invite students to draw a number line from 0 to 1, partition it into tenths, and label the tenths along the bottom of the number line in fraction form as you do the same.
Label 1 10 as 0.1 above the number line. Invite students to do the same.
This is another way to write 1 tenth. We can read this number as zero point one or as 1 tenth.
Repeat the process with 0.2 and 0.3. Point to the next tick mark.
How do you think we should label this tick mark? Why?
We should write zero point four for 4 tenths.
I notice a pattern. 1 tenth has a 1 to the right of the decimal point. 2 tenths has a 2, and 3 tenths has a 3. I think the pattern will continue.
Invite students to label 0.4 through 0.9 as you do the same.
Point to the fractions written below the number line.
What is the same about all the fractions?
They are all tenths.
A fraction with a denominator of 10 is an example of a decimal fraction. Decimal fractions can be written by using a decimal point.
Point to the numbers above the number line.
A number that is written with a decimal point is written in decimal form. A number written in decimal form is called a decimal number. We can write fractions with the unit tenths in decimal form.
We can write a number in decimal form or fraction form. Both are different ways to record the same number.
Consider having students label the numbers on the number line with the terms decimal fractions, decimal numbers, fraction form, and decimal form.
Invite students to turn and talk about how writing tenths in fraction form and in decimal form is similar and different.
Pair students and distribute Tenths in Decimal Form and Fraction Form to each student pair. Then have partners cut out the cards, shuffle them, and stack them face down.
Give pairs 3 minutes to
• pick one card;
• write the number in both fraction form and decimal form;
• compare answers, making corrections as needed; and
• repeat the process until they have used all the cards.
Circulate as students work. Ensure that students correctly use a denominator of 10 for each fraction and the leading 0 and decimal point for each number written in decimal form.
Gather students and invite some of them to share how they wrote each number. Which two numbers from the measurements are the same?
The softball and the juice box both have measurements with the number 2 tenths.
Write 2 tenths = 2 10 = 0.2.
Invite students to turn and talk about how they know the statement is true. There are different ways to represent tenths. The statement shows the same number written in different forms.
Each of the numbers represent the same point on the number line. We can read each of the numbers the same way: two tenths.
Activity 3.B 15 minutes
The following activity may be appropriate for students who incorrectly answer the core assessment item.
Materials—T: Meter stick; S: Hundredths in Decimal Form and Fraction Form, scissors
Students may need support representing hundredths in decimal form. This activity engages students in relating decimal form to fraction form while recording both representations on a number line, and then reading and writing measurements in fraction form and decimal form. Addressing this need prepares students for modeling decimals to the thousandths.
Show students a meter stick.
Let’s use a meter stick to think about hundredths.
Point to the markings for centimeters.
How many centimeters are in 1 meter?
100 centimeters
Point to the spaces between the centimeter markings.
What fractional unit does each of these intervals represent? How do you know?
Each interval represents 1 hundredth. There are 100 centimeters in 1 meter, so each centimeter is 1 hundredth of a meter.
Direct students to problem 1. Point to the meter stick as you explain what the number line represents.
The number line from 0 to 1 represents 1 meter decomposed into 100 centimeters. The tick marks are too close together to label, so the other number line zooms in on the first 20 centimeters.
Guide students in labeling 1 100 above the number line. Then label 1 100 as 0.01 below the number line. Invite students to do the same.
This is another way to write 1 hundredth. A fraction with a denominator of 100 is an example of a decimal fraction. So we can write 1 100 by using a decimal point.
What do you notice about the decimal form of 1 hundredth?
There is a 0 to the right of the decimal point and then a 1.
Guide students in labeling the second tick mark 2 100 and 0.02.
How do you think we write 3 hundredths in decimal form? Why?
We write 0.03. It follows the pattern of writing zero point zero, and then the number of hundredths.
Have students continue to label the number line in fraction and decimal form through 9 hundredths.
Invite students to turn and talk about how to label the next tick mark in both fraction and decimal forms.
Write 10 hundredths in fraction and decimal forms on the number line and invite students to do the same.
Does the decimal form of 10 hundredths surprise you? Why?
It does. I thought there would still be a 0 to the right of the decimal point and it would be 0.010.
It does not. In whole numbers, when you get to 10, you write the 1 to the left of where the 9 was. 0.10 follows that pattern from 0.09.
What are the similarities and differences between 1 tenth and 10 hundredths?
1 tenth and 10 hundredths are at the same place on the number line. The fractions have different denominators. There are 10 groups of 10 hundredths in 1 and there are 10 tenths in 1. In decimal form, both numbers have a 1 to the right of the decimal point. But 10 hundredths has another 0 to the right of the 1. 1 10 and 10 100 are equivalent fractions. I can multiply the numerator and the denominator of 1 10 by 10 to get 10 100 .
Direct students to work with a partner to label 11 hundredths to 20 hundredths in fraction form and in decimal form on the number line.
How do you think we write 65 hundredths in decimal form? Why?
We write 0.65 because it follows the pattern of having two digits to the right of the decimal point when it is hundredths.
How do you think we write 40 hundredths in decimal form? Why?
We write 0.40 because it is similar to 10 hundredths and 20 hundredths. We write the 40 to the right of the decimal point.
Invite partners to turn and talk about how to record 0 hundredths and 100 hundredths. Then demonstrate recording 0 hundredths as 0 100 and 0.00 and recording 100 hundredths as 100 100 and 1.00
Invite students to turn and talk about how writing hundredths in fraction form and in decimal form is similar and different.
Pair students and distribute Hundredths in Decimal Form and Fraction Form to each student pair. Then have partners cut out the cards, shuffle them, and stack them face down.
Give pairs 3 minutes to
• pick one card;
• write the number in both fraction form and decimal form;
• compare answers, making corrections as needed; and
• repeat the process until they have used all the cards.
Circulate as students work. Ensure that students correctly use a denominator of 100 for each fraction and that they correctly use a leading 0 and decimal point for each number written in decimal form.
Gather students and invite some of them to share how they wrote each number. Which two numbers from the measurements are the same?
The carrot and the smallest amount of water both have measurements with the number 7 hundredths.
Write 7 hundredths = 7 100 = 0.07.
Invite students to turn and talk about how they know the statement is true. There are different ways to represent hundredths. The statement shows the same number written in different forms.
Each of the numbers represent the same point on the number line.
Each of the numbers can be read the same way: seven hundredths.
Direct students to problem 2, the Pre-Module Assessment item, to determine whether students can complete each equation.
2. Complete each equation. Write one number from the given answer choices in each blank.