Constructing MATH
Concepts for Parents
What are these teachers doing??
Why are they doing it??
FLORIDA STANDARDS
Presenter: Laurana Werts
District Math Coach
Why Florida Standards Matter

Our goal is to ensure Florida’s students graduate high school
ready for success in college, career and life. In order to
prepare our students for success and make them competitive
in the global workplace, we must provide them with a set of
clear, consistent and strong academic standards.

The Florida Standards will equip our students with the
knowledge and skills they need to be ready for careers and
college-level coursework. Having the best and highest
academic standards for our students today will prepare them
for the jobs of tomorrow.
MULTIPLICATION
STANDARDS

3.OA.1.1 – Interpret products of whole numbers, e.g., interpret 5x7
as the total number of objects in 5 groups of 7 objects each. For
example, describe a context in which a total number of objects can
be expressed as 5x7.

3.OA.2.5 – Apply properties of operations as strategies to multiply
and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also
known. (Commutative property of multiplication.) 3 × 5 × 2 can be
found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 =
30. (Associative property of multiplication.) Knowing that 8 × 5 =
40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2)
= 40 + 16 = 56. (Distributive property.) 3.OA.2.6
EQUAL GROUPS

Equal groups have the same number in each group.
There are 3 tulips in each of 4 vases. How many tulips are there
in all?
1. Step 1 Think: there are 4 vases, so draw 4 circles
to show 4 equal groups.
2. Step 2 Think: there are 3 tulips in each vase, so draw
3 dots in each group.
3. Step 3 Skip count by 3s to find how many in all: 3, 6, 9, 12
There are 4 equal groups with 3 tulips in each group.
So, there are 12 tulips in all.
MODEL WITH ARRAYS

An array is a set of objects arranged in rows and columns.
Write a multiplication sentence for each array.
1. This array has 2 rows and 5 columns.
Count by fives.
2 rows of 5 are 10.
2. The multiplication sentence is
2 X 5 = 10.
3. This array has 5 rows and 2 columns.
Count by twos.
5 rows of 2 are 10.
The multiplication sentence is 5 X 2 = 10.
COMMUTATIVE PROPERTY

The Commutative Property of Multiplication states that you can
change the order of the factors and the product stays the same.
1.
There are 4 rows of 5 tiles.
(Think: 4 equal groups of 5)
2.
5 + 5 + 5 + 5 = 20
Multiply. 4 X 5 = 20
3.
There are 5 rows of 4 tiles.
(Think: 5 equal groups of 4)
4 + 4 + 4 + 4 + 4 = 20
Multiply. 5 X 4 = 20. The factors are 4 and 5. The product is 20.
ASSOCIATIVE PROPERTY

You can use the Associative Property of Multiplication
to multiply 3 factors. If you change the grouping of factors,
The product remains the same.
1.
4 X(3 X 1) Start inside the parentheses. 3 x 1 = 3
Multiply by 4, the number outside the parentheses. 4 x 3 = 12
(4 x 3) x 1 Start inside the parentheses 4 x 3 = 12
2.
Multiply by 1, the number outside the parentheses. 12 x 1 = 12
DISTRIBUTIVE PROPERTY
A garden has 4 rows of 7 corn stalks. How many corn stalks
in all are in the garden?
You can use the Distributive Property to break an array
into smaller arrays to help you find the answer.
STANDARDS
 4.NBT.2.5
– Multiply a whole number of up
to four digits by a one-digit whole number,
and multiply two two-digit numbers, using
strategies based on place value and the
properties of operations. Illustrate and
explain the calculation by using equations,
rectangular arrays, and/or area models.
MULTIPLY BY TENS, HUNDREDS,
AND THOUSANDS
You can use a pattern to multiply with tens, hundreds, and thousands.
Count the number of zeros in the factors.4 x 6 = 24 ← basic fact
1.
4 x 60 = 240 ← When you multiply by tens, the last digit in the
product is 0.
2.
4 x 600 = 2,400 ← When you multiply by hundreds, the last
digits in the product are 0.
3.
4 × 6,000 = 24,000 ← When you multiply by thousands, the last
digits in the product are 0.
When the basic fact has a zero in the product, there will be an extra zero
in the final product:
5 x 4 = 20, so 5 x 4,000 = 20,000
ESTIMATE PRODUCTS

You can use rounding to estimate products.
Round the greater factor. Then use mental math to estimate the
product.
6 X 95
Step 1 Round 95 to the nearest hundred.
Step 2 Use patterns and mental math.
95 rounds to 100.
6 X1=6
6 X 10 = 60
6 X 100 = 600
MULTIPLY USING EXPANDED FORM
Think and Write
You can use expanded form or a model to find products.
Step
Step
Step
Step
Multiply. 3 X 26
1 Write 26 in expanded form
20 = 20 + 6
3 x 26 = 3 x (20 + 6)
2 Use the Distributive Property
3 x 26 = (3 x 20) + (3 x 6)
3 Multiply the tens. Multiply the ones
=
60
+
18
4 Add the partial products 60 + 18 = 78
MULTIPLY USING EXPANDED FORM
Use a Model
Step 1 Show 3 groups of 26
Step 2 Break Model into Tens and Ones
(3 x 2 tens)
60
Step 3 Add to find the total product:
60 + 18 = 78
(3 x 6 ones)
18
MULTIPLY USING THE DISTRIBUTIVE
PROPERTY

You can use rectangular models to multiply 2-digit numbers by 1-digit
numbers.
Find 9 X 14.
Step 1 Draw a 9 by 14 rectangle on grid paper.
Step 2 Use the Distributive Property and products you know to
break apart the model into two smaller rectangles.
(Think: 14 = 10 = 4)
Step 3 Find the product each smaller rectangle represents.
9 X 10 = 90
and
9 X 4 = 36
Step 4 Find the sum of the products.
90 + 36 = 126