RIC-0563 Developing algebraic thinking

PROBLEM-SOLVING AND NUMBER TILES
Teachers notes
Activity 2
Use any 6 number tiles 0 to 9 to fill in the
squares so that the sum of each lines is
the same.
Let students find solutions for the problem. Display them on the board
or the overhead projector, and discuss patterns that emerge.
8 4 8
6 9 4 5 2 3 0 8 9 5 2 1
7 6 4
Sum = 24 Sum =
13 Sum = 17
Now assign variables to each square and look at the equations that are
created.
e
a b c d
f
a + b + c + d = e + b + f or a + c + d = e + f
The algebra shows that b can be any digit; each time one solution is
found, four others can be found by replacing the tile represented by b
as shown below.
2 2 2 2 2
1 0 3 4 1 5 3 4 1 7 3 4 1 8 3 4 1 9 3
4 6 6 6 6
6
The least sum that satisfies the equation a + c + d = e + f, is 5: 0 + 1 +
4 = 2 + 3. Therefore, the least sum for the problem is 10:
2
0 5 1 4
3
The greatest sum for the problem is 22.
Activity 3
Use all 10 number tiles 0 to 9 to create a 10-digit number divisible by
3.
This is a simple problem that focuses on the divisibility test for 3. Since
the sum of the digits 1 to 9 is 45, and 45 is divisible by 3, any arrangement
of the digits other than 0 in the first place provides a solution.
6 DEVELOPING ALGEBRAIC THINKING www.ricgroup.com.au R.I.C. Publications ®
ISBN 978-1-74126-088-5