AOA2-Task 2.docx - A 1 Standards First MGSE1.OA.3 Apply properties of operations as strategies to add and subtract Third MGSE3.OA.9 Identify arithmetic

# AOA2-Task 2.docx - A 1 Standards First MGSE1.OA.3 Apply...

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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  • • • 