Decimal Fraction Buddies

Game and activity

In this game and activity, students identify pairs of decimal fractions that add up to 1 and 0.5. (The copymasters for this game are at the end of these notes.) The students need to already be familiar with decimal fractions to 3 decimal places and should be able to add numbers such as 0.23 + 0.56 mentally, perhaps using a place value strategy (2 tenths + 5 tenths = 7 tenths, and 3 hundredths + 6 hundredths = 9 hundredths; 7 tenths and 9 hundredths can be written as 0.79).
With a group that is going to work independently, go over the instructions for the game and then, as a check, ask the students to find one pair of numbers on the board that add up to 1.
With a guided teaching group, write the following numbers on the board and ask the students to talk with a classmate to decide what decimal fraction each number needs to add up to 1 whole: 0.9, 0.7, 0.5, 0.99, 0.75, 0.08
Ask them to share their strategies for solving the problems and any patterns they notice that helped them. For example:
“For 0.9, I know that you need 10 tenths to make a whole, and those 10 tenths could be made up of 9 tenths and 1 tenth.”
“To work out what makes 1 with 0.75, I can see there’s already 7 tenths and 5 hundredths, so I’ll need 2 more tenths and 5 more hundredths, and that’s 0.25”
“I know that 0.75 is 75 hundredths. I think to myself ‘75 hundredths and how many more hundredths make 100 hundredths?’ because I know 100 hundredths is the same as 1 whole. I can work out how many more hundredths are needed by adding on: 75 hundredths + 5 hundredths is 80 hundredths and another 20 hundredths makes 100 hundredths. So it’s 25 hundredths, which is written as 0.25”
Encourage the students to describe decimal fractions using language that differentiates the fractions from whole numbers or from other uses of the decimal point, such as in money: Say 14.56 as “14 point five six” or “14 plus 5 tenths plus 6 hundredths”. Physical models, such as deci-pipes or decimats, are also useful.
Ask: Why might it be useful to be able to work out very quickly (or to know off by heart) pairs of numbers that add up to 1? Give me an example of a problem where you might find it useful.
Two possible examples:

• Say you were adding decimal fractions and you wanted to use the strategy of adding to build up to tidy numbers. Instead of building up to numbers that end in 0 as you do with whole numbers, you could build to whole numbers, for example, for
12.75 + = 14.2: 12.75 + 0.25 =13, 13 + 1.2 = 14.2, 0.25 + 1.2 = 1.45

 

• If you want to add or subtract a tidy number and then compensate, knowing pairs that make 1 whole will help you to know how much to compensate. For example,
for 3.6 – 1.85 = : 3.6 – 2 = 1.6, 1.6 + 0.15 = 1.75

Get the students to look at the game board and see if they can each find two numbers that add up to 1. Then explain the rules of the game and get them to play it with a classmate.
If the students need support to find pairs of numbers that add to 0.5, ask questions such as:
How big is 0.5 compared to 1? (It’s half the size.)
How many tenths are there in 0.5? (5)
If one of your numbers was 2 tenths, what would its partner have to be to add up to 5 tenths? (3 tenths, written as 0.3)
What other pairs can you find using tenths?
What’s the fraction that’s equivalent to 5 tenths using hundredths in the denominator? (50 hundredths, written as 0.50, which is the same as 0.5)
If one of your numbers was 43 hundredths, what would its partner have to be to add up to 50 hundredths? (7 hundredths, written as 0.07)
What’s the fraction that’s equivalent to 5 tenths using thousandths in the denominator? (500 thousandths, written as 0.500, which is the same as 0.5)
If one of your numbers was 485 thousandths, what would its partner have to be to add up to 500 thousandths? (15 thousandths, written as 0.015)

Extension

Challenge the students to apply what they have learned in the game and in the follow-up activity by asking them the following questions as think-pair-share discussion starters:
Make a list of the pairs of numbers that add up to 1 that you now know off by heart.
Can you use a pair that adds up to 1 to help you solve these problems?
Try using a strategy in which you add to build up to tidy numbers or you add or subtract a tidy number and then compensate.
• For 0.48 +  = 1.23:
0.48 + 0.52 = 1, 1 + 0.23 = 1.23, 0.52 + 0.23 = 0.75

• For 4.85 +  = 7.73:
4.85 + 0.15 = 5, 5 + 2.73 = 7.73, 0.15 + 2.73 = 2.88
 

• For 8.22 – 2.89 = :
8.22 – 3 = 5.22, 5.22 + 0.11 = 5.33

Make up a problem of your own in which it would be useful to know a pair that adds up to 1 to help solve the problem. Get a classmate to solve it.

Answers to Activity

Game
A game for finding decimal fraction addition pairs
Activity
1. Games will vary.
2. Answers will vary. Strategies could be similar to these:
• I know that there are 5 tenths in 0.5, so I found pairs of tenths that add up to5 tenths, such as 2 tenths + 3 tenths = 5 tenths (0.2 + 0.3 = 0.5).
• I know that 5 tenths is equivalent to 50 hundredths, so I found pairs of hundredths that add up to 50 hundredths, such as 43 hundredths + 7 hundredths = 50 hundredths (0.43 + 0.07 = 0.5).
• I know that 5 tenths is equivalent to 500 thousandths, so I found pairs of thousandths that add up to 500 thousandths, such as 485 thousandths + 15 thousandths = 500 thousandths (0.485 + 0.15 = 0.5).