Math Mastery

Multiplication, Division, and Fractions

Grade 3 - Ages 8-9
CHILD Math Counting

Learning to count with Yahuah!

Welcome to Grade 3 Math!

This year you will learn three exciting new skills:

"The heavens declare the glory of Elohim; the skies proclaim the work of His hands." - Psalm 19:1

Yahuah created a world full of patterns and numbers. Math helps us understand His amazing creation!

1What is Multiplication?

Key Concept

Multiplication is a fast way to add equal groups! Instead of adding 3 + 3 + 3 + 3, we can multiply: 4 x 3 = 12

The "x" symbol means "groups of." So 4 x 3 means "4 groups of 3."

See It!

4 groups of 3 = 4 x 3 = 12

Noah brought animals onto the ark in groups! "Two of every kind of animal came to Noah and entered the ark." - Genesis 7:9

If 5 pairs of birds came, how many birds in total? 5 x 2 = 10 birds!

Multiplication Vocabulary

Factor - The numbers you multiply together (in 4 x 3 = 12, the factors are 4 and 3)

Product - The answer when you multiply (in 4 x 3 = 12, the product is 12)

Equal groups - Groups that all have the same amount

Tip! The order doesn't matter in multiplication! 4 x 3 = 3 x 4. They both equal 12!

Practice Time!

Write the multiplication equation for each picture:

1. Three groups with 2 dots in each: x =

2. Two groups with 5 dots in each: x =

3. Five groups with 4 dots in each: x =

Fill in the blanks:

4. In the problem 6 x 2 = 12, the factors are and .

5. In the problem 6 x 2 = 12, the product is .

Math in the Bible!

Yahusha fed 5,000 people with 5 loaves and 2 fish. If each loaf was broken into 1,000 pieces, how many pieces of bread were there?

5 x 1,000 = pieces!

2Multiplying by 2

The 2s Pattern

Multiplying by 2 is the same as doubling a number!

2 x 1 = 2, 2 x 2 = 4, 2 x 3 = 6, 2 x 4 = 8...

Notice something? The products are all even numbers!

The 2s Multiplication Table

x2
12
24
36
48
510
612
714
816
918
1020

"And they went in to Noah into the ark, two and two of all flesh." - Genesis 7:15

Animals came in pairs (groups of 2)! Multiplication by 2 helps us count pairs!

Skip Counting! You can find multiples of 2 by skip counting: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

Practice Time!

Multiply by 2:

2 x 3 =
2 x 7 =
2 x 5 =
2 x 9 =
2 x 4 =
2 x 8 =
2 x 6 =
2 x 10 =

Skip count by 2s to fill in the blanks:

2, 4, ___, 8, ___, 12, ___, 16, ___, 20

Word Problem

Sarah has 6 pairs of socks. How many individual socks does she have?

Equation: x =

Answer: Sarah has socks.

3Multiplying by 5

The 5s Pattern

Multiplying by 5 is easy because of the pattern!

Products always end in 0 or 5: 5, 10, 15, 20, 25, 30...

Think of counting nickels (5 cents each) or telling time (5 minutes at a time)!

The 5s Multiplication Table

x5
15
210
315
420
525
630
735
840
945
1050

Real World Connection

Time: Clock numbers go by 5s! The 3 on a clock means 15 minutes (3 x 5).

Money: Nickels are worth 5 cents! 7 nickels = 7 x 5 = 35 cents.

Fingers: Each hand has 5 fingers. 4 people have 4 x 5 = 20 fingers total!

Yahusha fed 5,000 with 5 loaves and 2 fish. The number 5 appears often in Scripture - it often represents Yahuah's grace!

Practice Time!

Multiply by 5:

5 x 2 =
5 x 6 =
5 x 4 =
5 x 8 =
5 x 3 =
5 x 7 =
5 x 9 =
5 x 10 =

Skip count by 5s:

5, 10, ___, 20, ___, 30, ___, 40, ___, 50

Word Problem

A starfish has 5 arms. If there are 8 starfish in a tide pool, how many arms are there in total?

Equation: x =

Answer: There are arms.

Challenge!

If the minute hand is on the 9, how many minutes past the hour is it?

9 x 5 = minutes

4Multiplying by 10

The Easiest Rule!

To multiply any number by 10, just add a zero to the end!

3 x 10 = 30 | 7 x 10 = 70 | 12 x 10 = 120

This works because our number system is based on 10 (decimal system)!

The 10s Multiplication Table

x10
110
220
330
440
550
660
770
880
990
10100

Math in the Bible!

Yahuah gave Moses the TEN Commandments! If 5 families each memorized all 10 commandments, how many commandments were memorized in total?

5 x 10 = commandments!

Practice Time!

Multiply by 10 (just add a zero!):

10 x 4 =
10 x 8 =
10 x 6 =
10 x 9 =
10 x 2 =
10 x 7 =
10 x 5 =
10 x 10 =

Skip count by 10s:

10, 20, ___, 40, ___, 60, ___, 80, ___, 100

Word Problem

A dime is worth 10 cents. If David has 7 dimes, how much money does he have?

Equation: x =

Answer: David has cents (or dollars and cents).

5Multiplying by 3 and 4

The 3s and 4s

3s: Skip count by 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

4s: Skip count by 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

Tip for 4s: Double the 2s table! (4 x 3 = 2 x 3 x 2 = 6 x 2 = 12)

The 3s and 4s Tables

x3
13
26
39
412
515
618
721
824
927
1030
x4
14
28
312
416
520
624
728
832
936
1040

Jonah was in the fish for 3 days and 3 nights. If each day had 24 hours, how many hours was Jonah in the fish? 3 x 24 = 72 hours!

Practice Time!

Multiply by 3:

3 x 4 =
3 x 7 =
3 x 6 =
3 x 9 =

Multiply by 4:

4 x 5 =
4 x 8 =
4 x 6 =
4 x 9 =

Word Problems

1. A tricycle has 3 wheels. How many wheels do 7 tricycles have?

x = wheels

2. A car has 4 wheels. How many wheels do 6 cars have?

x = wheels

6What is Division?

Key Concept

Division is sharing equally or making equal groups!

It's the opposite of multiplication!

If 12 cookies are shared equally among 3 friends, each friend gets: 12 ÷ 3 = 4 cookies

See It!

12 dots divided into 3 equal groups:

12 ÷ 3 = 4 (4 in each group)

Division Vocabulary

Dividend - The number being divided (12 in 12 ÷ 3 = 4)

Divisor - The number you divide by (3 in 12 ÷ 3 = 4)

Quotient - The answer (4 in 12 ÷ 3 = 4)

When Yahusha fed the 5,000, He had the people sit in groups of 50 and 100. Division helps us organize and share!

Multiplication and Division are Related!

If 4 x 3 = 12, then 12 ÷ 3 = 4 AND 12 ÷ 4 = 3

Knowing your multiplication facts helps you divide!

Practice Time!

Use the pictures to divide:

1. 10 apples shared between 2 baskets: 10 ÷ 2 =

2. 15 stars in 5 equal rows: 15 ÷ 5 =

3. 8 cookies for 4 friends: 8 ÷ 4 =

Fill in the blanks using multiplication facts:

4. 3 x 4 = 12, so 12 ÷ 4 =

5. 5 x 6 = 30, so 30 ÷ 6 =

6. 2 x 8 = 16, so 16 ÷ 2 =

7Division Facts for 2, 5, and 10

Using Multiplication to Divide

Think: "What times the divisor equals the dividend?"

20 ÷ 5 = ? Think: "What times 5 equals 20?" Answer: 4! So 20 ÷ 5 = 4

Division Facts

Divide by 2

4 ÷ 2 = 2

8 ÷ 2 = 4

12 ÷ 2 = 6

16 ÷ 2 = 8

20 ÷ 2 = 10

Divide by 5

10 ÷ 5 = 2

20 ÷ 5 = 4

30 ÷ 5 = 6

40 ÷ 5 = 8

50 ÷ 5 = 10

Divide by 10

20 ÷ 10 = 2

40 ÷ 10 = 4

60 ÷ 10 = 6

80 ÷ 10 = 8

100 ÷ 10 = 10

Practice Time!

Divide:

14 ÷ 2 =
25 ÷ 5 =
70 ÷ 10 =
18 ÷ 2 =
45 ÷ 5 =
90 ÷ 10 =

Word Problem

The 12 tribes of Israel were divided into 2 groups - 10 tribes in the north and 2 in the south. If 20 people needed to be divided equally among the 10 northern tribes, how many would each tribe receive?

20 ÷ 10 = people per tribe

8What is a Fraction?

Key Concept

A fraction shows part of a whole!

A fraction has two numbers:

See It!

1
2

1/2
(one half)

1
2
3

1/3
(one third)

1
2
3
4

3/4
(three fourths)

"A tithe of everything from the land... belongs to Yahuah" - Leviticus 27:30

A tithe is 1/10 (one tenth) of what you have! Fractions help us give to Yahuah!

Fraction Vocabulary

Numerator - The top number (tells how many parts you have)

Denominator - The bottom number (tells how many parts make the whole)

Unit fraction - A fraction with 1 as the numerator (like 1/2, 1/3, 1/4)

Practice Time!

Name the fraction shown (shaded parts / total parts):

1. A pizza cut into 4 slices, with 1 slice eaten: is left

2. A rectangle divided into 3 parts, with 2 parts colored: is colored

3. A pie cut into 8 pieces, with 5 pieces remaining: remains

Label the parts:

4. In the fraction 3/4, the numerator is and the denominator is .

9Comparing Fractions

Which Fraction is Bigger?

When fractions have the same denominator, compare the numerators!

3/4 is greater than 1/4 because 3 is greater than 1.

When comparing unit fractions (1/2, 1/3, 1/4), the larger denominator means a smaller piece!

See It!

1/2

1/3

1/4

Notice: 1/2 > 1/3 > 1/4 (Half is the biggest piece!)

Remember: When the numerator is the same, the fraction with the smaller denominator is actually bigger! Think of it: if you share a pizza with 2 people (1/2 each), you get more than if you share with 4 people (1/4 each)!

Practice Time!

Compare using > (greater than), < (less than), or = (equal to):

1. 2/4 ___ 3/4

2. 1/2 ___ 1/4

3. 5/8 ___ 3/8

4. 1/3 ___ 1/6

5. 2/5 ___ 4/5

Word Problem

David ate 1/4 of a pizza. Daniel ate 1/2 of the same size pizza. Who ate more pizza?

Answer: ate more because is greater than .

10Fractions on a Number Line

Key Concept

Fractions can be shown on a number line between 0 and 1!

The denominator tells us how many equal parts to divide the line into.

The numerator tells us how many parts to count from 0.

See It!

Fourths on a Number Line:

0
1/4
2/4
3/4
1

Life is a journey, like walking along a number line. Sometimes we're at the beginning (0), and Yahuah helps us move forward toward our goals (1)! Each step is progress!

Practice Time!

Name the fraction at each point:

1. The point halfway between 0 and 1 is at:

2. If a number line is divided into 3 equal parts, the first mark after 0 is at:

3. On a number line divided into 8 parts, the mark at 6 parts from 0 is:

True or False:

4. 1/2 is at the same location as 2/4 on a number line.

5. 3/4 is closer to 1 than to 0.

11Equivalent Fractions

Key Concept

Equivalent fractions are fractions that show the same amount!

1/2 = 2/4 = 3/6 = 4/8 (These all show half!)

See It!

1/2

2/4

Both show the same amount shaded! 1/2 = 2/4

How to Find Equivalent Fractions:

Multiply (or divide) the numerator AND denominator by the same number!

1/2 x 2/2 = 2/4 | 1/2 x 3/3 = 3/6 | 1/2 x 4/4 = 4/8

Practice Time!

Find the equivalent fraction:

1. 1/3 = __/6

2. 2/4 = 1/__

3. 1/4 = __/8

4. 3/6 = __/2

Are these fractions equivalent? Write Yes or No:

5. 2/3 and 4/6

6. 1/2 and 3/4

7. 2/5 and 4/10

12Review and Mastery

You've Learned So Much!

Let's review everything: multiplication, division, and fractions!

Section 1: Multiplication Review

3 x 7 =
5 x 8 =
4 x 6 =
2 x 9 =
10 x 7 =
3 x 9 =

Section 2: Division Review

18 ÷ 2 =
35 ÷ 5 =
24 ÷ 4 =
21 ÷ 3 =
80 ÷ 10 =
30 ÷ 5 =

Section 3: Fraction Review

1. Name this fraction: 3 parts shaded out of 8 total parts =

2. Compare: 2/5 ___ 4/5

3. Compare: 1/3 ___ 1/6

4. Find the equivalent fraction: 1/2 = __/4

Word Problems

Problem 1

Moses led 12 tribes of Israel. If each tribe had 5 leaders, how many leaders were there in total?

x = leaders

Problem 2

Yahusha had 12 disciples. If they divided into 3 equal groups to teach, how many disciples were in each group?

÷ = disciples per group

Problem 3

A family gave 1/10 of their harvest as a tithe. If their harvest filled 10 baskets, how many baskets did they give?

Answer: basket(s)

Final Challenge: Bible Math!

Jacob worked 7 years for Rachel. Then he worked 7 more years. Then he worked 6 more years for flocks.

Total years: 7 + 7 + 6 = years

Or using multiplication: (2 x 7) + 6 = + 6 = years

Answer Key

For Parents/Teachers

Lesson 1: What is Multiplication?

1. 3 x 2 = 6 | 2. 2 x 5 = 10 | 3. 5 x 4 = 20

4. 6 and 2 | 5. 12 | Bible Math: 5,000

Lesson 2: Multiplying by 2

6, 14, 10, 18, 8, 16, 12, 20

Skip count: 6, 10, 14, 18

Word problem: 6 x 2 = 12 socks

Lesson 3: Multiplying by 5

10, 30, 20, 40, 15, 35, 45, 50

Skip count: 15, 25, 35, 45

Word problem: 8 x 5 = 40 arms

Challenge: 45 minutes

Lesson 4: Multiplying by 10

40, 80, 60, 90, 20, 70, 50, 100

Skip count: 30, 50, 70, 90

Word problem: 7 x 10 = 70 cents (70 cents or $0.70)

Lesson 5: Multiplying by 3 and 4

3s: 12, 21, 18, 27 | 4s: 20, 32, 24, 36

Word problems: 7 x 3 = 21 wheels | 6 x 4 = 24 wheels

Lesson 6: What is Division?

1. 5 | 2. 3 | 3. 2 | 4. 3 | 5. 5 | 6. 8

Lesson 7: Division Facts

7, 5, 7, 9, 9, 9

Word problem: 2 people per tribe

Lesson 8: What is a Fraction?

1. 3/4 | 2. 2/3 | 3. 5/8

4. Numerator: 3, Denominator: 4

Lesson 9: Comparing Fractions

1. < | 2. > | 3. > | 4. > | 5. <

Daniel, 1/2, 1/4

Lesson 10: Fractions on a Number Line

1. 1/2 | 2. 1/3 | 3. 6/8

4. True | 5. True

Lesson 11: Equivalent Fractions

1. 2/6 | 2. 1/2 | 3. 2/8 | 4. 1/2

5. Yes | 6. No | 7. Yes

Lesson 12: Review

Multiplication: 21, 40, 24, 18, 70, 27

Division: 9, 7, 6, 7, 8, 6

Fractions: 1. 3/8 | 2. < | 3. > | 4. 2

Word problems: 12 x 5 = 60 | 12 ÷ 3 = 4 | 1 basket

Bible Math: 20, 14 + 6 = 20