PR-0563IRE Developing Algebraic Thinking

PROBLEM-SOLVING AND NUMBER TILES
Teachers notes
Developing algebraic thinking
provides activities to meet some of the
common threads cited in the Foreword. Using number tiles 0 through 9,
pupils are given opportunities to solve a variety of problems involving
algebra ideas. The activities lend themselves to finding solutions
by individuals or small groups, followed by class discussion of the
observable patterns or relationships and the related algebra. With
teacher direction, the emerging patterns in many of the activities provide
an ideal opportunity for discussion of number sense, place value,
basic number theory, variables, and simple algebraic expressions and
equations.
Most of the activities in the book have more than one correct solution.
Sometimes, number tiles may be rearranged to give the same result.
Here are two different examples illustrating this point.
Example 1:
Use any 6 tiles to create two 3-digit numbers whose difference
is the least.
–
There are five solutions to this problem, all giving a difference of 3.
–
3 0 1 4 0 1 5 0 1 6 0 1 7 0 1
2 9 8
– 3 9 8 – 4 9 8 – 5 9 8 – 6 9 8
3 3 3 3 3
Example 2:
Use any 6 tiles to create two 2-digit addends and a 2-digit
sum.
Viewing Sample
+
With a sum of 98, four different solutions exist.
4 2 4 6 4 1 4 7
+
5 6
+ 5 2 + 5 7 + 5 1
9 8 9 8 9 8 9 8
4 DEVELOPING ALGEBRAIC THINKING www.prim-ed.com Prim–Ed Publishing