This resource can help to identify students' ability to use basic facts and knowledge of place value and partitioning whole numbers to solve multiplication problems.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
This task is looking at multiplication problems that involve single digit multipliers with a two-digit number that result in a two-digit result. The numbers used lend themselves to using doubling and halving and/or partitioning strategies to solve the problems.
Diagnostic and formative information:
Common error
Likely misconception
c) 39, 59, 79, 89
Calculates the 3 x 3 part of the equation correctly but makes an error when multiplying 3 x 20.
Next steps:
Students who calculated the 3 x 3 part of the equation correctly
Have students explain the strategy they used to solve the problem.
If they took the equation apart and solved 3 x 3 = 9, then discuss what the next step would be (3 x 20 = 60). Check for calculation errors and for an understanding of using a part-whole method to solve a problem:
23 x 3 = (20 x 3) + (3 x 3) = 60 + 9 = 69
Doubling and halving
This task lends itself to using doubling or halving strategies to solve the problems:
4 x 23 can be seen as (23 + 23) + (23 + 23) = 46 + 46 = 92
2 x 23 can be seen as either 23 + 23 = 46 or,
if part a) has been solved first, 1/2 of 92 = 46.
To solve part c) students need only add 23 onto their answer to part b), i.e., 46 + 23 = 69 (which does not require crossing the tens boundary).
Students who correctly answered all three questions could explore Packing food for the hāngi - a similar resource at Level 3, using a larger number of people to cater for.
