Paths and pairs
This is a level 3 number activity from the Figure It Out series. This is focused on solving addition problems using mental strategies. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers’ notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from Materials that come with this resource.
Specific learning outcomes:
- Solve addition problems using mental strategies.
Paths and pairs
Achievement objectives
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
Required materials
- Figure It Out, Level 3, Basic Facts, "Paths and pairs", page 9
- calculator
See Materials that come with this resource to download:
- Paths and pairs activity (.pdf)
Activity
This activity provides an opportunity for students to practise addition skills. The most efficient way to find the correct path is to add the ones digits only to find a number with a six in the ones place. There is only one path that gives an answer with six in the ones place.
Addition pyramids are an easy way of structuring addition calculations. Answers can be easily checked with a classmate or the calculator.
Encourage students to explain the different mental strategies they used to add the numbers. For example, to calculate 47 + 58, students could use any of these strategies:
- Front-ending, that is, 47 + 50 → 97 + 8 → 105
- Adding the tens and then the ones:
40 + 50 → 90 + (7 + 8 = 15) → 105
40 + 50 → 90 + 7 → 97 + 8 → 105
- Adding the ones first and renaming as per the standard written algorithm:
Using this method, students add the ones first, rename the 10 ones as one 10, and then add the tens. Students could design their own pyramids and make them more interesting and challenging by leaving out different numbers in the pyramid.
Students could be encouraged to compare the speed of completing a pyramid using mental calculations with using a calculator.
This activity encourages students to use strategies for adding mentally and to practise their estimation skills. Students could share with a classmate their strategies for finding the sums.
Activity 1
376 + 295 + 437 + 58 = 1166
Activity 2
2.
Activity 3
a. 285 + 396 = 681
b. 138 + 589 = 727
c. 377 + 396 = 773
d. 246 + 174 = 420
e. 467 + 174 = 641
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