Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
16 = 4 X 4 16 is a square number 4=2X2 4 is a square number 1=1x1 1 is a square number Patterns and Algebra 29 Multiplication and Division 27 3 is a triangular number 6 is a triangular number 1 is a triangular number Patterns and Algebra 29 Multiplication and Division 27 Investigation: 1. Select counters and make square arrays. 2. Count the counters. 3. Why is this number a square number? Reflection: What is a square number? Problem Solving Sally stacked 6 cans in a single column to form an equilateral triangle. What would the stack look like? Problem Solving Loretta had between 30 and 40 counters. She used all of her counters to construct a square. How many counters did Loretta have? Problem Solving Mary stacked cans in a single column to form an equilateral triangle. Her stack had 5 layers. How many cans are in Mary’s stack? Patterns and Algebra 29 Multiplication and Division 27 Patterns and Algebra 29 Multiplication and Division 27 Investigation: 1. Select counters and make triangular arrays. 2. Count the counters. 3. Why is this number a triangular number? Reflection: What is a triangular number? Patterns and Algebra 29 Multiplication and Division 27 Investigation: 1. Create square numbers starting with 1. 2. Add counters to make 2 rows of 2 and record 4 as a rectangular number. 3. Add counters to make 3 rows of 3 and record 9 as a rectangular number. 4. Add counters to make 4 rows of 4 and record 16 as a rectangular number. Reflection: How can we create square numbers? Patterns and Algebra 29 Multiplication and Division 27 Investigation: 1. Make a list of the square numbers in order. 2. How many are we adding to get from the first square number to the second square number? 3. How many are we adding to get from the second square number to the third square number? 4. Is there a pattern in the numbers we are adding? Reflection: Is there a pattern in square numbers? Patterns and Algebra 29 Multiplication and Division 27 Investigation: 1. Investigate the following statements: A. A square number can end only with digits 0, 1, 4, 6, 9, or 25 B. Every square number is the sum of 2 triangular numbers C. Every square number is the sum of 2 or more square numbers D. Squares of even numbers are even E. Squares of odd numbers are odd Reflection: Are there patterns and relationships in square numbers? Patterns and Algebra 29 Multiplication and Division 27 Investigation: 1. 2. 3. 4. Add sequential odd numbers and investigate the pattern you find. For example, 1 + 3 = 4 (4 is a square number), 1 + 3 + 5 = 9 (9 is a square number), 1 + 3 + 5 + 7 = 16 (16 is a square number)... Reflection: Are there patterns and relationships in square numbers? Patterns and Algebra 29 Multiplication and Division 27 Investigation: 1. Use dot paper to create square and triangular numbers, for example, Reflection: Are there patterns and relationships in square and triangular numbers? Patterns and Algebra 29 Multiplication and Division 27 Investigation: 1. Add triangular numbers to make square numbers, for example, 10 + 6 = 16 Reflection: Are there patterns and relationships in square and triangular numbers? Patterns and Algebra 29 Multiplication and Division 27