This is a level 2 number activity from the Figure It Out series. It relates to Stage 5 of the Number Framework.
A PDF of the student activity is included.
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use a mental strategy (through tens) for addition and subtraction problems
show a strategy on a number line
write a number sentence
Empty Number Lines (see Related Resources)
The examples given on page 8 encourage the students to partition numbers (that is, to break them into tens and ones) in order to add and subtract efficiently. They also reinforce the relationship of addition and subtraction as inverse operations.
The strategies used in Different Strokes! (page 2 of the students’ book) are extended here, that is, the students are working up and down through multiples of 10 to solve addition and subtraction problems.
The students record each step of their thinking on an empty number line. Using the empty number line encourages the students to develop their knowledge of number relationships, estimating distances between numbers and situating numbers before/after/between other numbers. For students who no longer need the support of a more structured model (such as a conventional number line), the empty number line is a concise way of presenting their mental strategies.
The last strategy presented on page 8 may raise the issue of what order should be used with the two operations.
The number sentence for this is 100 – 50 + 6 = 56.
The students could explore what happens when 50 and 6 are added before doing the subtraction (that is, 50 + 6 = 56, so the equation becomes 100 – 56 = 44). When addition and subtraction are both included in an equation, the convention is to tackle them in the order in which they occur, that is, 100 – 50 = 50, then 50 + 6 = 56. This convention helps to avoid confusion over the order of operations.
Answers to Activity
Methods will vary. They could include: