Additive Strategies progression, 5th step
The purpose of this activity
In this activity, the learners use strategies, traditional written methods and calculators to solve addition problems that contain decimal fractions. The aim of exploring the three calculating approaches is to encourage the learners to anticipate from the complexity and structure of a problem the approach that best suits the problem and them.
The learners need to be familiar with the concepts addressed in the “Addition and subtraction strategies I and II” activities before starting this 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 calculating 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).

Discuss with the 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

Empty number lines.

Decimal number lines.

Calculators.
The guided teaching and learning sequence
1. Write the following problem on the board:
Sian ran 400 metres in 56.52 seconds. Jason took 1.3 seconds longer. How long did it take Jason to run 400 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 one of the options and solve the problem giving them 2 to 3 minutes to do this. Then ask them to share their solution and how they solved it with another learner. Remind them they also have to be able to explain why the answer they obtained 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 addition, 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 57.82 is reasonable because it is about 1 second more than 56.52.
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 learners have appropriately lined up the places or positions in each number. If the learner has added a 0 to 1.3, ensure everyone understands its use as a ‘place holder’. This also provides an opportunity to talk about the decimal point and its use as an ‘indicator’ of the ones, or units, place.
7. Ask for a volunteer who used a mental strategy to solve the problem.
“Why did you decide to use a mental strategy?”
“Explain what you did to work out the answer.”
“How did you know that your answer was reasonable?”
8. Pose another problem:
Susan took 63.34 seconds to run 400 metres. Kris ran 1.99 seconds faster. How long did Kris take to run the 400 metres.
9. This time ask the learners to work in pairs to solve the problem, using the three different approaches suggested above. As the learners solve the problem, discuss with them their preferred approach.
10. 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.
11. 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 that have a decimal addition 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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