Multiplication and Division Concepts 145Perfect Squares and Near Squares
CONCEPT:
What is the Perfect Squares and Near Squares
Concept?
As with adding doubles, there is something uniquely
fascinating about multiplying a number with itself. Often
students’ levels of interest are elevated, prompting them to
master perfect squares earlier than other multiplication facts.
The smaller squares (1 x 1, 2 x 2, 3 x 3, 4 x 4, 5 x 5) and interesting
squares (such as 10 x 10) are commonly learned quickly.
Sometimes the larger squares (6 x 6, 7 x 7, 8 x 8, 9 x 9, 11 x 11,
12 x 12) take more time. Students require many experiences
with perfect squares. When students own these facts, they
are ready to use this knowledge to solve near squares
multiplication problems. When teaching the near squares
concept, encourage students to identify the two perfect
squares that the near square falls between and to use plus or
minus one group to solve the equation. For example, the near
square 8 x 7 = 56 falls between 7 x 7 = 49 and 8 x 8 = 64. If a
student uses 7 x 7, he will add one more group of seven
(49 + 7 = 56). If he uses 8 x 8, he will subtract one group of
eight (64 – 8 = 56). Rather than providing rules for students
to follow, allow them to decide which perfect square fact they
want to use to solve the near square problem so that they
understand the math more completely.CCSS
Operations and Algebraic ThinkingFormative Assessment
Ask the students to solve several squares (3 x 3, 5 x 5, 7 x 7,
9 x 9) and near squares (2 x 3, 5 x 4, 6 x 7, 7 x 8) multiplication
problems. Analyze the level of ownership by the students’
accuracy and speed.