How to Use Grids to Multiply One-digit Numbers By Teen Numbers

A Step-by-step Guide to Using Grids to Multiply One-digit Numbers By Teen Numbers

Of course, let’s break down how we can multiply one-digit numbers by teen numbers using a grid.

Here’s an example: Let’s multiply \(4 x 13\).

Step 1: Break Down the Teen Number

Teen numbers are numbers from 10 to 19. They can be split into 10 and a single-digit number. In our example, 13 can be broken down into 10 and 3.

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Step 2: Draw the Grid

Draw a simple 2-row grid. The rows will represent the two parts of the teen number (10 and 3), and the single column will represent the one-digit number (4).

 | 4 -----------
10 | -----------
3 | 

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Step 3: Multiply

Now, multiply the number in each row by the number in the column. So, you’ll multiply 4 by 10 and 4 by 3.

 | 4 -----------
10 | 40
-----------
3 | 12

Step 4: Add the Results

Now, add the results of the two multiplications together. In this case, \(40 + 12 = 52\).

So, \(4 x 13 = 52\).

This grid method is a helpful way to understand multiplication with teen numbers, as it breaks the process down into simpler steps. It’s particularly useful for visual learners and those who might struggle with traditional multiplication methods.

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Deep Dive: Using Grids to Multiply One-Digit Numbers by Teen Numbers

Grid multiplication is a super cool way to break down bigger multiplication problems into easy pieces. Let’s learn!

Why Use Grids?

Instead of doing 4 × 13 in your head (hard!), you can split 13 into 10 and 3, multiply each part, then add them together. A grid helps you see exactly what you’re doing!

What Is a Grid?

A grid is a box divided into sections. Each section shows one part of your problem. When you add up all the sections, you get your answer!

Think of it like a chocolate bar. If you have 4 rows and 13 squares across, you count: 4 rows of 10 squares, plus 4 rows of 3 squares.

Step-by-Step: How to Use a Grid

Step 1: Write Your Problem
You want to multiply a one-digit number by a teen number.
Example: 4 × 13

Step 2: Break Down the Teen Number
Break the teen number into tens and ones.
– 13 = 10 + 3

Step 3: Draw Your Grid
Draw a rectangle divided into 2 sections (one for tens, one for ones).

Step 4: Multiply Each Part
Fill in each box:
– 4 × 10 = 40
– 4 × 3 = 12

Step 5: Add Everything Up
40 + 12 = 52

So 4 × 13 = 52

Worked Examples

Example 1: 6 × 12
Break 12 into 10 + 2
Multiply: 6 × 10 = 60 and 6 × 2 = 12
Add: 60 + 12 = 72
Answer: 6 × 12 = 72

Example 2: 3 × 19
Break 19 into 10 + 9
Multiply: 3 × 10 = 30 and 3 × 9 = 27
Add: 30 + 27 = 57
Answer: 3 × 19 = 57

Example 3: 7 × 15
Break 15 into 10 + 5
Multiply: 7 × 10 = 70 and 7 × 5 = 35
Add: 70 + 35 = 105
Answer: 7 × 15 = 105

Example 4: 8 × 14
Break 14 into 10 + 4
Multiply: 8 × 10 = 80 and 8 × 4 = 32
Add: 80 + 32 = 112
Answer: 8 × 14 = 112

Example 5: 9 × 18
Break 18 into 10 + 8
Multiply: 9 × 10 = 90 and 9 × 8 = 72
Add: 90 + 72 = 162
Answer: 9 × 18 = 162

Common Mistakes Kids Make

Mistake 1: Forgetting the Tens Place
A student multiplies 5 × 16 and only does 5 × 6 = 30, forgetting about the 10.
– Correct: 5 × 10 = 50, and 5 × 6 = 30. Add them: 50 + 30 = 80

Mistake 2: Breaking Down Wrong
A student breaks 17 into 7 and 10 instead of 10 and 7.
– Correct: Always split into tens first, then ones. 17 = 10 + 7

Mistake 3: Forgetting to Add
A student finds 4 × 10 = 40 and 4 × 3 = 12 but doesn’t add them together.
– Correct: Always add your answers: 40 + 12 = 52

Mistake 4: Counting Grid Boxes Instead of Multiplying
The grid isn’t meant to be counted; it’s a tool to organize your thinking!
– Correct: Multiply, don’t count

Mistake 5: Making the Grid Too Complicated
Some students add too many boxes or sections.
– Correct: For one digit × teen, you need exactly 2 boxes (one for tens, one for ones)

Practice Tips

1. Always Use Grid Paper: Make your boxes neat and the same size.
2. Use Colored Pencils: Color each section a different color. It helps you see what you’re doing!
3. Say It Out Loud: “Five times ten is fifty. Five times three is fifteen. Fifty plus fifteen is sixty-five.”
4. Start with Easier Teen Numbers: Practice with 10, 11, 12 before moving to 18, 19.
5. Check with Repeated Addition: 4 × 13 means 13 + 13 + 13 + 13. Count on your fingers to double-check!

FAQ: Questions Kids Ask

Q: How do you multiply using a grid?
A: To multiply using a grid, split one factor into place-value parts, write the parts along the edge of a grid, multiply each part by the other factor, and add the boxes. For 6 × 17, split 17 into 10 and 7. The boxes hold 6 × 10 = 60 and 6 × 7 = 42, and 60 + 42 = 102. The grid keeps every partial product in view, so nothing gets lost.

Q: How do you multiply 1-digit numbers by teen numbers using grids?
A: Break the teen number into 10 and its ones digit, then make a grid with one box for each part. Multiply the one-digit number by 10 and by the ones digit, then add. For 8 × 15: 8 × 10 = 80 and 8 × 5 = 40, so 8 × 15 = 120. Because every teen number starts with 10, the first box is always easy: just put a zero after the one-digit number.

Q: How does the grid method work for 2-digit by 1-digit multiplication?
A: It works the same way as with teen numbers, except the tens part can be any multiple of ten. Split the 2-digit number into tens and ones, multiply each part by the 1-digit number, and add. For 7 × 34: 7 × 30 = 210 and 7 × 4 = 28, so the answer is 238. Teen numbers make a good starting point because their tens part is always 10.

Q: Can you use a grid to multiply 3-digit by 1-digit numbers?
A: Yes. Split the 3-digit number into hundreds, tens and ones, so the grid gets three boxes instead of two. For 3 × 245: 3 × 200 = 600, 3 × 40 = 120 and 3 × 5 = 15. Add them: 600 + 120 + 15 = 735. Once a student is comfortable splitting teen numbers into 10 and ones, this bigger grid is the natural next step.

Real-World Uses

– Fruit Stand: A farmer has 6 baskets with 14 apples each. How many apples? Use a grid! 6 × 10 = 60, 6 × 4 = 24. Total: 84 apples.
– Stickers: You buy 8 sheets with 13 stickers each. Grid it: 8 × 10 = 80, 8 × 3 = 24. You have 104 stickers!
– Birthday Treats: Making 7 bags with 12 candies in each. Grid: 7 × 10 = 70, 7 × 2 = 14. Total: 84 candies.
– Desk Arrangement: 5 rows of chairs with 11 chairs in each row. Grid: 5 × 10 = 50, 5 × 1 = 5. Total: 55 chairs.

Summary

Grid multiplication turns hard problems into easy ones. Break the teen number into tens and ones, multiply each part separately, then add everything up. Draw your grid, fill in the boxes, and you’ve got your answer! This method works for any one-digit number times any teen number, and you can even use it for bigger numbers later!