Solved Exercises on Multiplying by 10 Khan Academy Style in Grade 3

Master multiplying by 10 with Khan Academy-style lessons: place value shifts, patterns, and real-world applications through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Place value shifting
Exercise 1
What is \(8 \times 10\)? Show how the digits move.
Definition:

Multiplication by 10: Each digit moves one place value position to the left

Multiply by 10 method:
  1. Take the original number
  2. Add a zero to the end
  3. Or move each digit one place to the left
Original
\(8\)
After ×10
\(80\)
Tens
8
Ones
0
↓ ×10 ↓
Hundreds
0
Tens
8
Ones
0
Step 1: Start with the original number

8 in the ones place

Step 2: Multiply by 10

Each digit moves one place to the left

Step 3: Fill empty places with zeros

8 moves to tens place, ones place gets 0

\(8 \times 10 = 80\)
Final answer:

\(8 \times 10 = 80\)

Applied rules:

• Place value shift: Each digit moves one place to the left

• Zero rule: Add a zero to the end of the number

• Digit movement: 8 ones become 8 tens

2 Array representation
Exercise 2
Show \(5 \times 10\) using an array
Definition:

Array: Rectangular arrangement of objects in rows and columns

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Expression
\(5 \times 10\)
Rows × Columns
\(5 \times 10\)
Total Count
\(50\)
Step 1: Identify the factors

\(5 \times 10\) means 5 rows and 10 columns

Step 2: Draw the array

Create 5 rows with 10 items in each row

Step 3: Count the total

Count all items: \(5 \times 10 = 50\)

\(5 \times 10 = 50\)
Final answer:

\(5 \times 10 = 50\)

Applied rules:

• Array model: Visual representation of multiplication

• Rows × Columns: Total items in rectangular array

• Visual grouping: Helps understand multiplication concept

3 Real-world application
Exercise 3
A school has 7 classrooms, and each classroom has 10 desks. How many desks are there in total?
Definition:

Real-world application: Using math to solve practical problems

Given
7 classrooms × 10 desks
Operation
\(7 \times 10\)
Result
\(70\)
Step 1: Identify the key information

7 classrooms, each with 10 desks

Step 2: Determine the operation

We need to find the total number of desks: 7 groups of 10

Step 3: Apply multiplication by 10 rule

\(7 \times 10 = 70\) (add zero to 7)

Step 4: State the answer

There are 70 desks in total

There are 70 desks in total
Final answer:

There are 70 desks in total

Applied rules:

• Problem-solving: Identify key information and operation needed

• Equal groups: Multiplication represents equal-sized groups

• Real-world connection: Connect math to everyday situations

Multiplication Chart (Up to 10×10)
Multiplication Table
×
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
10
2
2
4
6
8
10
12
14
16
18
20
3
3
6
9
12
15
18
21
24
27
30
4
4
8
12
16
20
24
28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
20
30
40
50
60
70
80
90
100
Multiplication Facts for 10
1×10=10, 2×10=20, 3×10=30, 4×10=40, 5×10=50, 6×10=60, 7×10=70, 8×10=80, 9×10=90, 10×10=100
Key definitions:

Multiplication: Adding equal groups together quickly

Factors: Numbers being multiplied together

Product: Result of a multiplication problem

Multiplication strategies:
  1. Repeated addition: \(4 \times 3 = 4 + 4 + 4\)
  2. Arrays: Organizing items in rows and columns
  3. Number lines: Skip counting
  4. Groups: Equal sets of objects
Tip 1: Practice with small numbers first, then increase gradually.
Tip 2: Use arrays or grouping to visualize multiplication.
Tip 3: Remember that multiplication is commutative: \(4 \times 3 = 3 \times 4\).
Tip 4: Use the multiplication table to find patterns and shortcuts.
Important property: Any number multiplied by 0 equals 0.
Important property: Any number multiplied by 1 equals itself.
Multiplication Concepts and Properties
\(a \times b = c\)
Basic Multiplication
Commutative Property
\(a \times b = b \times a\)
Order doesn't matter
Identity Property
\(a \times 1 = a\)
Multiplying by 1
Zero Property
\(a \times 0 = 0\)
Multiplying by 0
Associative Property
\(a \times (b \times c) = (a \times b) \times c\)
Grouping doesn't matter
Patterns in Multiplication (1-10)
Pattern
Example
Rule
Why
Visual
×2
2×4=8
Double
Add to itself
●●●● + ●●●●
×5
5×6=30
Ends in 0 or 5
Skip count by 5s
5,10,15,20,25,30
×10
10×7=70
Add zero
Place value shift
7→70
×3
3×4=12
Triple
Add three times
●●● + ●●● + ●●●
×1
1×7=7
Same number
One group
●●●●●●●
Multiplication Practice and Tips
\(3 \times 4 = 12\)
Three Groups of Four
Key concepts:

Equal groups: Multiplication shows equal-sized groups

Arrays: Visual representation in rows and columns

Repeated addition: Another way to think about multiplication

Problem-solving steps:
  1. Read the problem: Understand what is being asked
  2. Find key information: Identify numbers and relationships
  3. Choose operation: Decide if multiplication is needed
  4. Solve: Calculate the multiplication
  5. Check: Make sure the answer makes sense
Tip 1: Practice skip counting (2, 4, 6, 8...) to learn multiplication facts.
Tip 2: Draw pictures or use objects to represent multiplication problems.
Tip 3: Notice patterns in the multiplication table to help with memorization.
Tip 4: Use known facts to figure out unknown ones (e.g., 4×3 = 3×4).
Common error: Confusing multiplication with addition. Remember: multiplication is repeated addition.
Practice tip: Start with smaller numbers and work up. Master 1-5 before moving to 6-10.
Important multiplication facts to remember:

• Any number × 0 = 0

• Any number × 1 = that number

• Multiplication is commutative: 3×4 = 4×3

• Multiplication by 10 adds a zero to the end

• Multiplication by 5 ends in 0 or 5

Questions & Answers

Question: Why does any number times 10 equal itself with a zero added? That seems strange!

Answer: It's not strange at all! Think about it this way: when you multiply by 10, you're saying "I have 10 groups of this number."

For example:

  • 5 × 10 means "10 groups of 5" = 50 items
  • 8 × 10 means "10 groups of 8" = 80 items
  • 12 × 10 means "10 groups of 12" = 120 items

You're not adding more groups, just counting the total in 10 groups!

Question: My child is having trouble memorizing multiplication facts. How can I help?

Answer: Here are effective strategies to help with multiplication facts:

  • Start with concrete objects: Use counters, blocks, or toys to show equal groups
  • Draw arrays: Create visual representations of multiplication
  • Practice daily: Even 10-15 minutes of focused practice helps
  • Use songs and rhymes: Musical memory aids can be very effective
  • Play games: Multiplication games make learning enjoyable

Focus on understanding the concept first, then work on memorization.

Question: Is it okay to count on my fingers when learning multiplication?

Answer: Absolutely! Using your fingers is a great way to learn multiplication.

For example, to solve 4 × 3, you can hold up 4 fingers on one hand and 4 on another, then count them all (4 + 4 + 4 = 12).

Finger counting and other physical methods help you understand what multiplication really means. As you practice more, you'll start to remember the facts automatically, but using your fingers while learning is perfectly fine and helpful.

Detailed Summary: Multiplying by 10

Definitions of Key Concepts

  • Multiplication: A mathematical operation that represents repeated addition of equal groups
  • Factor: A number that is multiplied by another number in a multiplication problem
  • Product: The result of a multiplication problem
  • Multiplication Table: A grid showing the products of numbers multiplied together
  • Array: A rectangular arrangement of objects in rows and columns
  • Equal Groups: Sets of items that contain the same number of elements

Core Rules and Principles

  • Identity Property: Any number multiplied by 1 equals itself (\(a \times 1 = a\))
  • Zero Property: Any number multiplied by 0 equals 0 (\(a \times 0 = 0\))
  • Commutative Property: The order of factors doesn't change the product (\(a \times b = b \times a\))
  • Repeated Addition: Multiplication is equivalent to adding the same number multiple times
  • Pattern Recognition: Multiplication facts follow predictable patterns
  • Sequential Learning: Master smaller numbers before advancing to larger ones

Step-by-Step Methods and Procedures

  1. Understanding Multiplication:
    • Recognize multiplication as repeated addition
    • Understand it represents equal groups of items
  2. Learning Multiplication Facts:
    • Start with 1 and 2 facts
    • Progress to 3, then 4, then 5
    • Practice each set until automatic
  3. Using Visual Models:
    • Create arrays to represent multiplication
    • Draw equal groups to visualize the concept
    • Use number lines for skip counting

Multiple Concrete Examples (Simple → Advanced)

  • Simple (1-2): \(1 \times 4 = 4\), \(2 \times 3 = 6\), \(1 \times 5 = 5\)
  • Moderate (3-4): \(3 \times 4 = 12\), \(4 \times 2 = 8\), \(3 \times 5 = 15\)
  • Advanced (5): \(5 \times 4 = 20\), \(5 \times 5 = 25\), \(4 \times 5 = 20\)
  • Word Problems: "If 4 friends each have 3 stickers, total = \(4 \times 3 = 12\)"

Tips, Tricks, and Common Pitfalls

  • Tip 1: Use the commutative property - if you know \(4 \times 3 = 12\), then \(3 \times 4 = 12\)
  • Tip 2: For multiplying by 2, just double the number
  • Tip 3: For multiplying by 5, the answer always ends in 0 or 5
  • Common Pitfall: Confusing multiplication with addition
  • Common Mistake: Forgetting that order doesn't matter in multiplication

Key Notes and Takeaways for Memorization

  • Memory Aid: "Times 1 keeps the number, times 0 gives zero"
  • Pattern: 2s are doubles, 5s end in 0 or 5
  • Strategy: Use known facts to build unknown ones (e.g., \(4 \times 3 = 3 \times 3 + 3\))
  • Practice: Daily review of facts helps with automatic recall

Clear Explanations Written for Students

Multiplication is like having equal groups of things and counting them all at once. Instead of adding 3 + 3 + 3 + 3, you can just multiply 3 × 4 = 12. The numbers you multiply are called factors, and the answer is called the product. When you multiply by 1, the number stays the same. When you multiply by 0, you always get 0. There are cool patterns in multiplication - like when you multiply by 5, the answer always ends in 0 or 5! Learning multiplication facts takes practice, but once you know them, math becomes much easier.