MP7, Look For and Make Use of Structure, since the goal of the task is to help students understand the multiplication table from the point of view of factorizations. The main standard for mathematical practice which aligns with this task is The first non-prime number not appearing in the table is $22 = 2 \times 11$, the product of the smallest prime number with the smallest prime number bigger than 9. This makes sense in the context because a prime number cannot be written as a product of two smaller whole numbers.
The last part of this question gives an opportunity for the teacher to discuss prime numbers since the list of numbers the students produce will all be primes. Working through the table to see where different numbers appear, the students will have a good opportunity to observe the symmetry of the table which comes from the commutative property of multiplication: $a \times b = b \times a$. For example, 24 appears 4 times in the table:Ģ4 = 3 \times 8 = 8 \times 3 = 6 \times 4 = 4 \times 6.įor the 9 by 9 multiplication table shown, only the numbers 1 through 9 appear with all of their factorizations. The table shows some, but not necessarily all, factorizations of different numbers. The goal of this task is to encourage students to study the multiplication table, a familiar object, from a novel point of view.
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