Additive Strategies progression, 5th step
The purpose of the activity
In this activity, the learners use strategies, traditional written methods and calculators to solve subtraction problems that contain decimal fractions. The aim of exploring the three computation options is to encourage the learners to anticipate from the complexity and structure of a problem the approach that is best suited to that problem.
The learners should be familiar with the concepts addressed in the “Addition and subtraction strategies I and II” activities before starting this activity. This activity could follow or be completed in conjunction with the “Adding decimals” activity.
The teaching points

Addition and subtraction with decimals builds on the same concept used with whole numbers, that is, you add or subtract numbers of like position values. For example, hundredths are added to or subtracted from hundredths.

Different problems lend themselves to different strategies, and competent learners have a range of strategies to choose from.

There are three main calculating approaches: using strategies to calculate a problem mentally, using traditional written methods (algorithms) and using calculators. The complexity of the problem determines the most effective and efficient calculating approach.

Irrespective of the computation approach used, it is important that learners are able to judge the reasonableness of their answer in relation to the problem posed.

The decimal point is a convention that indicates the units, place. The role of the decimal point is to indicate the units, or ones, place in a number, and it does that by sitting immediately to the right of that place. Consequently the decimal point also works to separate the units (on the left) from parts of the unit (on the right).

Like any other digit, 0 indicates the number of items in the place (or column) in which it appears. The 0 can also be considered a place holder. For example, in 6.05, the 0 holds the tenths place so that the 5 appears in the hundredths place. The 0 is not needed as a place holder when it is not between a digit and the decimal point, for example 1.50 and 1.5 are the same.

Discuss with learners relevant or authentic situations where the addition and subtraction of decimals occurs (for example, carpentry when measurements are given as parts of metres, time when measured to milliseconds).
Resources
The guided teaching and learning sequence
1. Write the following problem on the board:
31.37 – 29.27 =
Discuss with the learners reallife situations for that calculation. Possibilities include calculations that involve money, measurements in metres or kilograms, time. For example, Kate swam the first 50 metres in 31.37 seconds and the second 50 metres in 29.27 seconds. How much faster was her second 50 metres?
2. Discuss with the learners the three options they have for solving the problem:

using a calculator

using a written method

using a strategy.
3. Ask the learners to choose the option that is best suited to them for solving this problem. After giving them time to solve the problem, ask them to share how they solved it with another learner. Remind them they also have to be able to explain why their answer is reasonable (or makes sense) in relation to the problem.
4. Ask the learners to indicate (with a show of hands) which of the three approaches they used. As this is a relatively simple decimal subtraction, the learners should be able to calculate it mentally, using a strategy.
5. Ask for a volunteer who used a calculator to solve the problem.
“Why did you choose to use a calculator?”
“Why is your answer reasonable?” (Encourage the learners to notice that 2.1 is reasonable as 31 is 2 more than 29.)
6. Ask for a volunteer who used a written method to solve the problem.
“Why did you use that method?”
“Show us what you did on the board.”
“How did you know that your answer was reasonable?”
Check that the learner has appropriately lined up the places or positions in each number. This also provides an opportunity to talk about the decimal point and its use as an ‘indicator’ of the ones or units position.
7. Ask for a volunteer who used a mental strategy to solve the problem.
“Why did you decide to use a strategy?”
“Explain what you did to work out the answer.”
“How did you know that your answer was reasonable?”

29.27 + 2 + 0.1 = 31.37 (solving as an addition problem)
8. Pose another problem:
This time, ask the learners to work in pairs to solve the problem, using the three different approaches. As the learners solve the problem, discuss with them their preferred approach.
9. Give the learners the following problems on a sheet of paper. Without actually solving the problems, ask the learners to look at each problem and write down which approach they think they would prefer to use to solve the problem.
10. As a class, discuss which problems seem best suited to mental strategies and which they would prefer to solve with a calculator or written method.
Followup activity
Give the learners cards with a decimal subtraction problem on each card. Have the learners work in pairs to select a computation approach, solve the problem and explain the reasonableness of their answer.
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