A.)
1. Standards
First
: MGSE1.OA.3 Apply properties of operations as strategies to add and subtract.
Third
: MGSE3.OA.9. Identify arithmetic patterns (including patterns in the addition table
or multiplication table), and explain them using properties of operations.
Fifth
: MGSE5.NBT.2 Explain patterns in the number of zeros of the product when
multiplying a number by powers of 10, and explain patterns in the placement of the
decimal point when a decimal is multiplied or divided by a power of 10. Use whole-
number exponents to denote powers of 10.
2. Examples
First
: If 4 + 7 = 11 is known, then 7 + 4 = ?
Third
: Write examples of the pattern on the board: 14 = 7 + 7,
16= 8 + 8,
6 = 3 + 3, etc
Fifth
: 2.5 x 10^3 = ?
3.
Solutions
First
: 3 + 8 = 11. Students should recognize a pattern with the commutative property of
addition that if 3 + 8 = 11 then it is also known that 8 + 3 = 11.
Third
: Have students notice that even numbers can always be decomposed into 2 equal
addends as shown by the pattern
Fifth
: 3.5 x (10 x 10 x 10) = 3.5
x 1,000 = 3,500
Students should be able to conclude that the exponent above the 10 is how many places
the digits are moving to the left when you multiply by a power of 10.
4.
The chosen standards and problems build student understanding of patterns over the
years by first showing students that there are many different forms of patterns in
numbers. Students should be able to explain the calculations based on the models and
different properties of operations and rules that generate patterns. They are able to
examine number patterns and relate them to a specific rule, graph, or other visual
representation. Students may also use repeated reasoning to comprehend any algorithms
and generalizations associated with the patterns. The standards build upon each other