RIC-0563 Developing algebraic thinking

PROBLEM-SOLVING AND NUMBER TILES
Teachers notes
The book contains 10 sections, each with a part entitled ‘Looking at the
algebra’. In the first section, ‘Place value picks’, students use number
sense ideas involving place value to create various sums, differences,
and products. ‘Same Sums’ requires students to separate the number
tiles into a designated number of groups so that each group has the
same sum. As the activity progresses, teachers can introduce ‘Gauss’
formula for the sum of the first n consecutive counting numbers.
Creating prime numbers and composite numbers of various lengths is
the focus in ‘Primes and composites’. Number sense ideas continue in
the next section, ‘Divisibility rules’, as students create numbers satisfying
divisibility criteria for 2, 3, 4, 5, 6, 8, 9 and 10. ‘Locker numbers’ provides
the first activities where variables can be incorporated into classroom
discussion. Still, number sense ideas—even/odd numbers, multiples,
factors—play an important role in finding solutions.
Activities in ‘Exciting exponents’ stress basic rules of exponents,
along with number theory ideas. ‘Plus and times’ provides students
with opportunities to look for simple arithmetic patterns with sums or
products, and then looks at the associated algebra. Various polygons are
made into number tile problems in the ‘Shapes’ section. From triangles to
pentagons, and finally to a box, the number of variables and the number
of equations increases. ‘Pentomino puzzles’ uses various pentomino
shapes as number tile puzzles, creating lines of digits whose sum will
be the same. The last section, ‘Alphabet algebra’, contains number tile
puzzles for the entire alphabet. As in other sections, each line (or curve,
in some cases) has the same sum. The algebra is more difficult; however,
interesting relationships among the digits do appear.
Let your students create their own number tile problems, expressing
solutions using variables if possible, discussing patterns, verbalising
relationships, and making conjectures. What hexaminoes can be made
into number tile problems? What interesting addition, subtraction,
multiplication or division problems can be made? Developing algebraic
thinking, using only number tiles, can be an exciting, challenging and
rewarding experience for your students.
Reference: Chambers, Donald L. ‘The right algebra for all.’ Educational Leadership 51
(March 1994): 85–86.
R.I.C. Publications ® www.ricgroup.com.au DEVELOPING ALGEBRAIC THINKING 7
ISBN 978-1-74126-088-5