Download What is a square number?

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