RIC-0563 Developing algebraic thinking

PROBLEM-SOLVING AND NUMBER TILES
Teachers notes
Activity 1
In many cases, as the first example suggests, students are asked to
find the greatest or least possible answer. These situations provide an
ideal time to initiate class discussion of problem-solving strategies for
finding a particular solution. As students work through the number tile
activities, here are some of the strategies that might be applied:
• Guess and check
• Look for a pattern
• Write an equation
• Solve a simpler problem
• Work backwards
• Estimating
Below are sample activities to use as warm-ups for your class.
Use any 6 tiles to create a 2-digit factor and a 1-digit factor with a correct
3-digit product.
x
The directions make the problem open-ended; any correct solution is
acceptable.
9 7 3 8 5 8 5 3 2 7 2 4 3 2 9 5
x
6
x
5
x
7
x
2
x
4
x
7
x
5
x
8
5 8 2 1 9 0 4 0 6 1 0 6 1 0 8 1 6 8 1 6 0 7 6 0
The least possible product: should have a 1 in the hundreds place.
Therefore, neither factor can contain a 1. Doubling a number in the
fifties provides a good start: 53 x 2 = 106.
The greatest product: requires some simple number sense work to
begin. Since 80 x 9 = 90 x 8 = 720 and 9 and 8 are the greatest digits
for the tens place in the one factor, it appears that the hundreds digit in
the product will be 7. After some testing, 95 x 8 = 760 gives the greatest
product.
R.I.C. Publications ® www.ricgroup.com.au DEVELOPING ALGEBRAIC THINKING 5
ISBN 978-1-74126-088-5