Topic 4 Homework
1. For each of the following, sketch a sequence of minimal arrays with edge
pieces to illustrate each product or quotient. Label the net values of each edge
and each array on each picture. Identify factors, products, dividends, divisors
and quotients.
a. 3 x -4
b. -3 x -4
c. 12 ÷ 3
d. 12 ÷ -3
2. Use black and red tiles with edge pieces and explain, in a way that would make
sense to a middle school student, each of the following. In each case, illustrate
your explanations with clearly labeled sketches.
a. How the signs of factors relate to their product.
b. How the signs of a dividend and divisor relate to their quotient.
c. Why multiplication by 0 gives a product of 0. Do this in two cases: i) With a
minimal array and ii) With a non-minimal array.
d. Why 7 ÷ 0 is not possible. Use a non-minimal edge set for 0.
e. Why 0 ÷ 0 has an infinite number of solutions. Use non-minimal sets for both
the divisor and the dividend.
3. Look at the Grade 6 – 8 Number and Operations Standard. What standard
and expectation(s) does using modeling integer operations with black and red
tiles address? Briefly explain how two activities from Topics 1 – 4 address
these expectations.