Multiples: 100 Facts
Order: ×1, ×10, ×5,
×2, ×9, ×4, squares, ×3,
7 × 6, 7 × 8, 8 × 6
Quantitative Reasoning by Prof. Mahesh Sharma
Number Sense -> Place Value -> Additive Reasoning -> Multiplicative Reasoning -> Proportional Reasoning -> Algebraic Reasoning
Understand the relationships between numbers, the language, the concept, the procedures (concrete and abstract), and the inverse procedures that nullify an action.
Understand the Inverse Relationship of Addition and Subtraction, and Multiplication and Division.
1. Multiplication as Repeated Addition. 1-D
2. Multiplication as Groups Of. 1-D
4. Multiplication as objects Arranged in Arrays. 2-D
5. Multiplication as Area of a Rectangle
Commutative: 3h x 4w = 12 area = 4h x 3w. 2-D
6. Multiplication Story.
100 Multiplication Facts
1 [19 facts] = 81 left
10 [17 facts] = 64 left
5 [15 facts] = 49 left
2 [13 facts] = 36 left
9 [11 facts] = 25 left
4 [9 facts] = 16 left
squares 3×3, 6×6, 7×7, 8×8
3 [3 facts] = 6 left
7 × 6 7 × 8 8 × 6
Squares
1×1 = 1
1
1|1
2×2 = 4
2
2|4
3×3 = 9
3
3|9
4×4 = 16
4
4|16
7×7 = 49
7
7|49
5×5 = 25
5
5|25
6×6 = 36
6
6|36
8×8 = 64
8
8|64
9×9 = 81
9
9|81
10×10 = 100
10
10|100
A square is a rectangle with 4 equal sides and 4 right angles.
Vertical side x horizontal side = area
The area of the square is the product of two same factors.
"4 squared " is 16 because
a 4 by 4 square
is 4 units high and 4 units wide
and contains 16 units inside
the area of the square.
4×4 = 16
4 wide
4 high|16 area
4×4 = 16
quotient
divisor|dividend
100
81
64
49
36
25
16
9
4
16
2
2
2 high x 2 wide
= Area of 4 unit squares
A PERFECT SQUARE is a RECTANGLE with all sides the same size.
The number of unit squares INSIDE the square is its AREA.
The ROOT of a SQUARE is the length of it's bottom.
The size of its bottom is the same as its other sides!
What is the ◾SQUARE ROOT of 4?
What is the ROOT or what would CAUSE
a SQUARE to have an AREA of 4?
Having a side of 2 would cause a square to have an area of 4 because
2 units high by 2 units across
results in 4 units inside the square.
The square root of 4 is 2.
The area of 4 has a
root of 2.
Get to the bottom of it!
Find the root of the problem!
What causes a square to have an area of 4?
A root or side measuring 2 makes a square with an area of 4.
4
The radical symbol can be used instead of the words, "square root."
√4 means, "What is the square root of 4?"
The area number goes inside the square of the radical symbol.
√4 = 2
2
Square a Number
2 squared = 4
2 × 2 = 4
2 = 4
√4 = 2
2|4
√ =
because
2 units wide
2 times
makes a square with
4 units inside,
where the area is 4.
2
2
2
2
2
Squares and Square Roots Many Ways
Three squared means, "What's the area of a square with a side of 3?"
3 squared means, "What's the area of a 3 by 3 square?"
3 means 3 × 3 = 9 area
2
3×3 = 9
3|9
3
3
2
= 3 × 3 = 9
1
2
Square Root 13 Ways
What is the square root of nine?
√9
√9
9
If a square has an area of 9, what is the length of its side?
What is the root of a square with an area of 9?
If a square has an area of 9, how high is it?
What is the height of a square with an area of 9?
If a square has an area of 9, what is its width?
How wide is a square with an area of 9?
What number multiplied by itself is 9?
What number squared is 9?
A square contains nine units. What is the length of its side?
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