Additive Strategies progression, 3rd step
The purpose of this activity
In this activity, the learners use strings of beads and/ or number lines to develop addition and subtraction mental partitioning strategies for twodigit by onedigit problems, for example, 27 + 8, 36 – 7.
The teaching points

Learners who ‘count on’ (for example, calculating 27 + 8 by counting 27, 28, 29, 30, etc, either using fingers or in their heads) or who can only use a calculator to make calculations will be disadvantaged in completing the numeracy demands of everyday life.

It is not anticipated that you will teach a learner many different strategies for solving a single problem, but rather you will work with one strategy at a time, noting that different problems lend themselves to different strategies.

Learners need to know addition and subtraction facts to 10 + 10 and the place value of digits in whole numbers to 100 before undertaking this activity.

Discuss the strategies and how they can be used with the learners.

Discuss with the learners the contexts or situations where they need to solve addition and subtraction problems mentally.
Note: This learning sequence can be used with singledigit addition and subtraction sito help the learners with their basic 10 + 10 addition and subtraction facts.
Resources

100 beads, 50 of one colour and 50 of another colour, threaded on to a string in blocks of 10 for each colour or number lines marked in ones.

Number lines marked in tens.
The guided teaching and learning sequence
1. Ask the learner(s) to use the string of beads or the number lines marked in ones to solve 27 + 8 in any way they can and explain what they have done. If the learner ‘counts on’, ask if they can see any other way to solve the problem.

If the learner(s) shows evidence of some partitioning strategy, ask them to demonstrate on the beads and continue to develop that strategy throughout the activity.

If the learner(s) shows no evidence of using partitioning strategies, encourage them to use the strategy of ‘making tens’ by:

asking the learner(s) how many beads are needed to get from 27 to 30 and marking + 3 on the number line

asking how many remain of the 8 and marking + 5 on the number line.
2. Repeat the process with a variety of different twodigit by onedigit addition problems.
3. Once the learner(s) is familiar with the process, ask them to do the activity on the number line marked in tens (0, 10, 20, 30, 40 … 100), for example, starting at 27 on the line and marking + 3 to 30 and + 5 to 35.
4. Repeat the process with a variety of twodigit by onedigit addition problems. 5. Once the learners are familiar with the process, repeat each of the steps for twodigit by onedigit subtraction problems, for example 45 – 7.
5. Once the learners are familiar with the process, repeat each of the steps for twodigit by onedigit subtraction problems, for example 45 – 7.
Followup activity
In pairs, the learners make up and solve twodigit by onedigit addition and subtraction problems, sharing the strategies they use with their partner.
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