Learn and practice multiplication and division, dividing fractions, or using algebra to solve complex word problems, students are building their math fluency and using deductive reasoning skills to problem solve.
4. Warm-up Discussion
12 ÷ 3 = 4
The dividend (12) is the number being that is being
divided into. This is total number of items.
The divisor (3) is the number that it is being divided by.
This is the number of groups that we want to split our
items into.
The quotient (4) is the answer. This is the amount of
items in each group.
Quotient
Dividend Divisor
5. Thinking of Division as Sharing
We have 10 apples and we must share them equally between
2 children. How many apples will each be given?
Discuss:
1. What multiplication sentence should we write?
2. ______ is being shared among ______.
6. Thinking of Division as Sharing
10 ÷ 2 = 5
Quotient
Dividend Divisor
In this example, we shared our 10 total
apples with 2 groups. Once we split
our apples up, it turns out that each
group (child) gets 5 apples.
7. Thinking of Division as Grouping
Mr. Tom has 8 students in his online Zoom class.
He wants to split his students into 4 equal
breakout rooms. How many students will be in
each room?
Discuss:
1. What multiplication sentence should we
write?
2. ________ is being grouped into _________.
8. Thinking of Division as Grouping
8 ÷ 2 = 4
Quotient
Dividend Divisor
In this example, we grouped our 8 total students
into 4 equal groups. Once we split our students up,
it turns out that each room has 2 students.
9. 15 ÷ 3 = 5
Quotient
Dividend Divisor
3 x 5 = 15
Relationship between Division
and Multiplication
Discuss
How does division relate to multiplication?
Factor Factor
Product
10. Write the formula that represents each image and solve
for the total number of subject.
Multiplication by Array
Number
Of Rows
Number of
columns
Product
(total amount)
4 × 5 = 20
× = × =
12. How Multiplication and Division Are
Connected
Multiplicatio
n
3 × 4 = 12
Division
12 ÷ 3 = 4
Amount in
each equal
group
Total
“Product”
Number of
equal groups
Amount in
each equal
group
“quotient”
Total
Number of
equal
groups
Multiplication is to add equal groups to find a total.
The answer is called the product.
Division starts with a total and breaks it up into equal groups.
The answer is called the quotient.
13. First, review the 4s multiplication table by filling out the
skip count table. Then, use it to solve the problems.
1. Write the multiplication sentence the column with “24”
shows.
2. 24 ÷ 4 = ____ 3. 20 ÷ 4 = ____
__ __ __ __ __ __ __
Division by 4 with Skip
Counting
8 24 36
14. Related Facts Visualized
16 divided into
into sets of 4
÷ =
4 sets of 4
× =
24 divided
into sets of 4
÷ =
6 sets of 4
× =
Exampl
e
Circle
First, circle and group the sets. Next, write the related facts
that represent the image.
15. When to Regroup with Addition
Thousand Hundred Tens Ones
0 3 5 + 1 6
0 4 6 8
14
+
First, set up the numbers in a
place value chart.
Ones: 6 + 8:
Regrouping is needed
because 6 + 8 > 10
Thousand Hundred Tens Ones
0 3 + 1 5 + 1 6
0 4 6 8
8 12 14
Next, add the tens column.
Regrouping is needed
because 4 + 6 ≥ 10
The sum of 10 tells us that we have 10 tens, or 1 hundred.
Therefore, we add 1 to the tens column while taking away 10
from the ones.
+
Example: Find 356 + 468
Think of 0
when there is
no digit in a
place.
18. Place Value and Periods
Place value is the value of a digit, or how much a certain
digit of a number is width.
This value is based on the digit’s position.
The digits in large numbers are arranged in groups of
three called periods.
Commas are used to separate these periods.
Thousands Period Ones Period
260, 111
One hundred
Thousands
Ten
Thousands
One
Thousands
Hundred
s
Tens
One
s
2 6 0 1 1 1
Value 200,000 60,000 0 100 10 1
19. Comparing Large Numbers
• When we compare large numbers, we only need to
compare corresponding digits.
• We start comparing from the leftmost common digit.
• The moment one number has a digit greater than a
digit in the same spot of another, that number is
larger!
23,643
23,987
2 = 2
The first two digits we compare are equal. However,
23,987 has a greater hundreds digit than 23,643. We do
not need to check the remaining digits. 23,987 > 23,643
Ten Thousands Thousands Hundreds Tens Ones
2 3 6 4 3
2 3 9 8 7
3 = 3 9 > 6
20. Shape Pattern
• Can consist of one shape
• Can have many shapes
• Repeating patterns can be color patterns
• The same color sequence repeats itself.
22. Use the place-value chart to compare the following
decimals to 0.59. Find the decimals that are less than
0.59. Circle the letter of all that apply.
A 0.07
B 0.4
C 0.6
D 0.55
Compare Decimals
Ones . Tenths Hundredths < 0.59
0 . 5 9
A .
B .
C .
D .
23. Compare Decimals as Mixed Numbers
Package A weighs 1.401 kilograms. Package B weighs 1.29
kilograms. Write an inequality statement comparing the weights of
the packages.
Express the weights as mixed numbers with like denominators.
Then compare.
1.401 = 1
401
1000
1.29 = 1
29
100
= 1
290
1000
1
401
1000
is greater than 1
290
1000
So, 1.401 > 1.29. The weight of Package A is greater than
the weight of Package B.
24. How to Find Prime Numbers
Step 1: Check the units place of that number. If it ends with 0, 2, 4,
6 and 8, it is not a prime number.
Note: “Numbers ending with 0, 2, 4, 6 and 8 are never
prime numbers.”
Step 2: Take the sum of the digits of that number. If the sum is
divisible by 3, the number is not a prime number.
Note: “Numbers whose sum of digits are divisible by 3 are
never prime numbers.”
Step 3: After confirming the falsity of steps 1 and 2, find the
square root of the given number.
Step 4: Divide the given number by all the prime numbers below
its square root value.
Step 5: If the number is divisible by any of the prime numbers
less than its square root, it is not a prime number;
otherwise, it is prime.
25. How to Quickly Find Prime Numbers up to 100
Step 1: Write all the numbers
from 1 to 100 with 6 numbers in a
row.
Step 2: As the square root of 100
is ±10, the multiples of numbers
till 10 has to be crossed out.
Step 3: Choose 2 and the
multiple of 2 (4, 6) and cross the
entire column.
Step 4: Move to 3 and cross out
the entire column.
Step 5: Take 5 and the multiple of
5 and cross out the diagonally
towards left. All the multiples of 5
are crossed out.
Step 6: Choose 7 and the
numbers divisible by 7 and cross
out diagonally towards the right.
leaves no multiples of 7 on the
list.
