Patterns of Ten Worksheet
EMBARC Math
Grade 4 • Module 3 • Lesson 4
Problem Set • Place Value Patterns
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Date:
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Learning Goal: Interpret and represent patterns when multiplying by 10, 100, and 1,000 using place value disks, unit form, and equations. CCSS 4.NBT.1 • 4.NBT.5
1
Place Value Models: Multiply by 10, 100, and 1,000
Draw place value disks to represent each multiplication expression. Show bundling or movement across place values as you multiply.
a. Represent: \(2 \times 3\) and \(2 \times 30\)
Thousands
Hundreds
Tens
Ones
\(2 \times 3 \text{ ones} =\) ones \(=\)
\(2 \times 3 \text{ tens} =\) tens \(=\)
b. Represent: \(3 \times 400\)
Thousands
Hundreds
Tens
Ones
\(3 \times 4 \text{ hundreds} =\) hundreds
\(3 \times 400 =\)
2
Unit Form & Associative Strategy
Think in Units: \(4 \times 30 = 4 \times (3 \text{ tens}) = 12 \text{ tens} = 120\). Rename the multiple of 10 to multiply simply.
a. \(5 \times 20\)
\(= 5 \times (\) tens\()\)
\(=\) tens \(=\)
b. \(6 \times 40\)
\(= 6 \times (\) tens\()\)
\(=\) tens \(=\)
c. \(7 \times 300\)
\(= 7 \times (\) hundreds\()\)
\(=\) hundreds \(=\)
d. \(4 \times 500\)
\(= 4 \times (\) hundreds\()\)
\(=\) hundreds \(=\)
e. \(8 \times 2{,}000\)
\(= 8 \times (\) thousands\()\)
\(=\) thousands \(=\)
f. \(9 \times 4{,}000\)
\(= 9 \times (\) thousands\()\)
\(=\) thousands \(=\)
EMBARC Grade 4 • Module 3 • Topic B Continue to Page 2 →
EMBARC Math • Grade 4 Module 3 Lesson 4
Name:
3
Pattern Power: Fluency Sprint
Solve each column. Notice the pattern in each column as the factor increases by a power of ten.
Set A: Factor of 4
\(4 \times 2 =\)
\(4 \times 20 =\)
\(4 \times 200 =\)
\(4 \times 2{,}000 =\)
Set B: Factor of 7
\(7 \times 5 =\)
\(7 \times 50 =\)
\(7 \times 500 =\)
\(7 \times 5{,}000 =\)
Set C: Factor of 8
\(8 \times 6 =\)
\(8 \times 60 =\)
\(8 \times 600 =\)
\(8 \times 6{,}000 =\)
4
Word Problems in Context
Problem 4: The community center orders 6 crates of juice boxes for sports day. Each crate contains 40 juice boxes. How many juice boxes did the community center order in total?
Model / Tape Diagram:
Equation:
Answer: boxes
Problem 5: A book distributor packs 5 pallets of textbooks. Each pallet holds 800 textbooks. How many textbooks are packed altogether?
Model / Tape Diagram:
Equation:
Answer: textbooks
5
Math Talk: Error Analysis & Reasoning
Critique Maya's Thinking: Maya solves \(5 \times 600\) and writes \(3{,}000\). Her classmate Leo argues: "That cannot be right because 600 only has two zeros, so your answer should only have two zeros." Who is correct? Explain using unit form or basic facts.
EMBARC Grade 4 • Module 3 • Lesson 4 Self-Check: Did you label all units and count all place values accurately?
