Multiplication, Division, and Fractions
Grade 3 - Ages 8-9
Learning to count with Yahuah!
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!
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."
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!
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
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 .
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!
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!
| x | 2 |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |
| 6 | 12 |
| 7 | 14 |
| 8 | 16 |
| 9 | 18 |
| 10 | 20 |
"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!
Multiply by 2:
Skip count by 2s to fill in the blanks:
2, 4, ___, 8, ___, 12, ___, 16, ___, 20
Sarah has 6 pairs of socks. How many individual socks does she have?
Equation: x =
Answer: Sarah has socks.
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)!
| x | 5 |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 4 | 20 |
| 5 | 25 |
| 6 | 30 |
| 7 | 35 |
| 8 | 40 |
| 9 | 45 |
| 10 | 50 |
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!
Multiply by 5:
Skip count by 5s:
5, 10, ___, 20, ___, 30, ___, 40, ___, 50
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.
If the minute hand is on the 9, how many minutes past the hour is it?
9 x 5 = minutes
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)!
| x | 10 |
|---|---|
| 1 | 10 |
| 2 | 20 |
| 3 | 30 |
| 4 | 40 |
| 5 | 50 |
| 6 | 60 |
| 7 | 70 |
| 8 | 80 |
| 9 | 90 |
| 10 | 100 |
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!
Multiply by 10 (just add a zero!):
Skip count by 10s:
10, 20, ___, 40, ___, 60, ___, 80, ___, 100
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).
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)
| x | 3 |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
| 5 | 15 |
| 6 | 18 |
| 7 | 21 |
| 8 | 24 |
| 9 | 27 |
| 10 | 30 |
| x | 4 |
|---|---|
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
| 5 | 20 |
| 6 | 24 |
| 7 | 28 |
| 8 | 32 |
| 9 | 36 |
| 10 | 40 |
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!
Multiply by 3:
Multiply by 4:
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
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
12 dots divided into 3 equal groups:
12 ÷ 3 = 4 (4 in each group)
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!
If 4 x 3 = 12, then 12 ÷ 3 = 4 AND 12 ÷ 4 = 3
Knowing your multiplication facts helps you divide!
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 =
Think: "What times the divisor equals the dividend?"
20 ÷ 5 = ? Think: "What times 5 equals 20?" Answer: 4! So 20 ÷ 5 = 4
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
Divide:
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
A fraction shows part of a whole!
A fraction has two numbers:
1/2
(one half)
1/3
(one third)
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!
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)
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 .
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!
1/2
1/3
1/4
Notice: 1/2 > 1/3 > 1/4 (Half is the biggest piece!)
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
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 .
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.
Fourths on a Number Line:
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!
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.
Equivalent fractions are fractions that show the same amount!
1/2 = 2/4 = 3/6 = 4/8 (These all show half!)
1/2
2/4
Both show the same amount shaded! 1/2 = 2/4
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
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
Let's review everything: multiplication, division, and fractions!
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
Moses led 12 tribes of Israel. If each tribe had 5 leaders, how many leaders were there in total?
x = leaders
Yahusha had 12 disciples. If they divided into 3 equal groups to teach, how many disciples were in each group?
÷ = disciples per group
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)
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
For Parents/Teachers
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
6, 14, 10, 18, 8, 16, 12, 20
Skip count: 6, 10, 14, 18
Word problem: 6 x 2 = 12 socks
10, 30, 20, 40, 15, 35, 45, 50
Skip count: 15, 25, 35, 45
Word problem: 8 x 5 = 40 arms
Challenge: 45 minutes
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)
3s: 12, 21, 18, 27 | 4s: 20, 32, 24, 36
Word problems: 7 x 3 = 21 wheels | 6 x 4 = 24 wheels
1. 5 | 2. 3 | 3. 2 | 4. 3 | 5. 5 | 6. 8
7, 5, 7, 9, 9, 9
Word problem: 2 people per tribe
1. 3/4 | 2. 2/3 | 3. 5/8
4. Numerator: 3, Denominator: 4
1. < | 2. > | 3. > | 4. > | 5. <
Daniel, 1/2, 1/4
1. 1/2 | 2. 1/3 | 3. 6/8
4. True | 5. True
1. 2/6 | 2. 1/2 | 3. 2/8 | 4. 1/2
5. Yes | 6. No | 7. Yes
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