Array Architects Slides Visual Math Strategy
Step-by-Step Guide
Multiplication with Arrays
Learn how to read multiplication facts and build simple arrays to solve any basic problem.
1
Read
Rows × Items in each
2
Build
Draw rows & columns
3
Solve
Skip count for total
What is an Array?
Math Definition
An array is an organized grid of items arranged in neat rows and columns .
Rows Go Across (↔)
Side to side, like lines on notebook paper.
Columns Stand Tall (↕)
Up and down, like tall building pillars.
Simple Example Grid
Row 1 →
• • • •
Row 2 →
• • • •
Row 3 →
• • • •
↑
Golden Rule of Arrays: Count ROWS first (across), then COLUMNS second (down)!
1
Step 1: Read the Problem
What to Think to Yourself
When you see a multiplication fact, say what it means in your head:
3 Number of Rows
×
4 How many are in each row
Say to yourself: "3 rows of 4."
2 × 5
2 rows of 5
4 × 3
4 rows of 3
5 × 2
5 rows of 2
The first number tells you how many rows to start drawing!
2
Step 2: Draw the Starting Rows
Problem: 3 × 5
Look at the First Number
In 3 × 5, the first number is 3. That means you need 3 rows .
Draw 3 Dots Straight Down
Put 3 dots down the left side of your paper. Each dot is the start of one row.
Teacher Tip: Leave plenty of space between each dot so your rows stay straight and clean!
What Your Paper Looks Like:
1 ← Row 1 starts here
2 ← Row 2 starts here
3 ← Row 3 starts here
Now your 3 rows are set up! Next, put the items in each row.
3
Step 3: Fill Each Row & Count
Problem: 3 × 5 = ?
Look at the Second Number
In 3 × 5, the second number is 5. Put 5 items in each of your 3 rows.
Skip Count Row by Row
Count by 5s for each row to find the total product:
5 10 15
Final Answer:
3 × 5 = 15
Completed 3 × 5 Array
Row 1:
• • • • •
→ 5
Row 2:
• • • • •
→ 10
Row 3:
• • • • •
→ 15
Skip counting row by row is much faster than counting one-by-one!
Practice Together!
Try This Fact
Let's solve:
4 × 3
Question 1
How many rows?
4 Rows
Question 2
How many in each?
3 in each row
Question 3
Skip count by:
3, 6, 9, 12
Product
4 × 3 = 12
Great job! 4 rows of 3 gives 12 total items.
The Turn-Around Fact
Cool Math Secret
Look at this array:
3 × 4 = 12
3 rows of 4
Turn it sideways:
4 × 3 = 12
4 rows of 3
Both equal 12! Turning an array doesn't change the total product.
Your 3 Quick Steps
Ready for Worksheet!
1
READ
First number = Rows .How many in each row .
Say: "___ rows of ___"
2
DRAW
Put starting dots straight down for each row, then draw across.
Keep rows neat & spaced
3
COUNT
Skip count row by row to find the total product.
Total dots = Product!
Time to practice on your worksheet!
You've got this!
Array Architects Worksheet Math Strategy Multiplication with Arrays
Array Architects Worksheet
Name:
Date:
How to Read a Multiplication Problem Rows = Across (↔) • Columns = Down (↕)
First Number
Number of Rows
Groups going across (↔)
×
Multiplication
Second Number
How many in each row
Items placed in each row (•)
1
Read the Problem: What Do You Think to Yourself?
Fill in the blanks to say what each multiplication problem means in words.
3 × 4
rows of
5 × 2
rows of
2 × 7
rows of
4 × 6
rows of
2
Guided Practice: Follow the 3 Steps
Follow each step to build your array and find the total product.
Problem A: 3 × 3 "3 rows of 3"
Step 1: Number of Rows
Draw 3 starting dots straight down:
Step 2: How Many in Each Row
Put 3 dots across in every row:
Step 3: Skip Count to Solve
Skip count by 3s:
, ,
3 × 3 =
Problem B: 2 × 5 "2 rows of 5"
Step 1: Number of Rows
How many rows?
rows
Step 2: How Many in Each Row
Put 5 dots in each row:
Step 3: Skip Count to Solve
Skip count by 5s:
,
2 × 5 =
Array Architects • Page 1 of 2 Turn page for Independent Practice →
Independent Practice: Build & Solve
Part 3, 4 & 5
3
Draw the Arrays & Skip Count
Draw neat dots for each fact. Write your skip count and final product.
1. Fact: 4 × 3 "___ rows of ___"
Count:
4 × 3 =
2. Fact: 3 × 4 "___ rows of ___"
Count:
3 × 4 =
3. Fact: 5 × 4 "___ rows of ___"
Count:
5 × 4 =
4. Fact: 2 × 6 "___ rows of ___"
Count:
2 × 6 =
4
Write the Equation from the Array
Count the rows first, then how many in each row, and write the equation.
rows of
× =
rows of
× =
5
Real-World Problem
Array Architects Answer Key Answer Key • Teacher Reference Multiplication with Arrays
Array Architects Worksheet Solutions
Grading Guide Total: 25 Points
Core Principle: 1st Number = Number of Rows (↔) • 2nd Number = How many in each row (↕) VERIFIED KEY
1
Read the Problem: Translation Key
4 Points (1 pt each)
3 × 4
3 rows of 4
5 × 2
5 rows of 2
2 × 7
2 rows of 7
4 × 6
4 rows of 6
2
Guided Practice: Model Solutions
6 Points (3 pts per problem)
Problem A: 3 × 3 Target Product: 9
Step 1: Number of Rows
3 starting dots down:
Step 2: How Many in Each
3 in each row:
Step 3: Skip Count
Skip count by 3s:
3, 6, 9
3 × 3 = 9
Problem B: 2 × 5 Target Product: 10
Step 1: Number of Rows
How many rows?
2 rows
Step 2: How Many in Each
5 dots in each row:
Step 3: Skip Count
Skip count by 5s:
5, 10
2 × 5 = 10
Array Architects Answer Key • Page 1 of 2 Page 1 Subtotal: 10 Points
Independent Practice Solutions
Page 2 Subtotal: 15 Points
3
Build & Solve: Completed Arrays
8 Points (2 pts each)
1. Fact: 4 × 3 "4 rows of 3"
Count: 3, 6, 9, 12 4 × 3 = 12
2. Fact: 3 × 4 "3 rows of 4"
Count: 4, 8, 12 3 × 4 = 12
3. Fact: 5 × 4 "5 rows of 4"
Count: 4, 8, 12, 16, 20 5 × 4 = 20
4. Fact: 2 × 6 "2 rows of 6"
Count: 6, 12 2 × 6 = 12
4
Write Equations from Arrays
4 Points (2 pts each)
4 rows of 5
4 × 5 = 20
3 rows of 3
3 × 3 = 9
5
Real-World Problem • Solution
3 Points Total
4 rows with 7 solar panels in each row.
Sentence:
4 × 7 = 28
Maya installs 28 panels.
Array Architects Answer Key • Page 2 of 2 Total Score: 25 / 25 Points
