Decimal Architect Teacher Guide Decimal Architect
Unit 5: Place Value Patterns & Decimal Operations
Implementation Notes
VNPS: Tasks should be completed on Vertical Non-Permanent Surfaces (whiteboards, windows) in random groups of 3.
Thin-Slicing: Tasks build in complexity. Don't reveal Task 2 until the majority of groups have solved or reached a pivot point in Task 1.
Flow: Maintain a high tempo. If a group finishes early, use the "High Ceiling" extension provided.
IM Standards
5.NBT.A.1 5.NBT.A.3 5.NBT.B.7
A
Add & Subtract Decimals
Task 1: The Target Ten
Low Floor
Use the digits 1, 2, 3, 4, 5, 6 exactly once to fill the boxes and make a sum closest to 10: _ . _ + _ . _ + _ . _
High Ceiling: Can you get exactly 10.0? If not, what is the absolute closest possible value?
Task 2: Missing Links
Mid-Tier
Fill in the missing digits to make the equation true: 3 . □ 4 + □ . 2 □ = 5.61. Is there more than one solution?
High Ceiling: Find all possible solutions and explain how you know you have them all.
Task 3: The Great Difference
High Ceiling
Place the digits 0-9 in the boxes to create the largest possible difference: _ _ . _ - _ _ . _
High Ceiling: Constraints: You must use at least one zero and the result must be a decimal between 25 and 50.
B
Multiply Decimals
Task 1: Half and Half
Low Floor
Draw an area model for \(0.5 \times 0.5\). Then, use that same model to show \(0.5 \times 0.6\). What is the relationship between the two results?
High Ceiling: Create a multiplication problem where the product is exactly half of the first factor.
Task 2: The Grid Challenge
Mid-Tier
Find two decimals with tenths that, when multiplied, result in a product with a "5" in the hundredths place. (e.g., \(0.\_ \times 0.\_ = \_. \_ 5\))
High Ceiling: Find two decimals that produce a product with three decimal places (e.g., \(\_. \_ \_ 5\)).
Task 3: Power Move
High Ceiling
A product is \(1.44\). What could the factors be? Find at least 5 different pairs of decimals. One factor must be a whole number, and one must be a decimal.
High Ceiling: Find a pair where both factors are decimals less than 2.0.
C
Divide Decimals
Task 1: Sharing Scraps
Low Floor
A rope is \(1.5\) meters long. If you cut it into \(3\) equal pieces, how long is each? What if you cut it into \(6\) equal pieces?
High Ceiling: How many pieces of \(0.15\) meters can you get from the rope?
Task 2: Quotients and Dividends
Mid-Tier
Find a division problem where the quotient is exactly double the dividend. (Example: \(10 \div \_ = 20\))
High Ceiling: Find a problem where the quotient is \(100\) times larger than the dividend.
Task 3: The Remainder Mystery
High Ceiling
In decimal division, we usually don't have "remainders" because we keep dividing. Find a division problem that results in exactly \(0.125\).
High Ceiling: Can you find three different ways to get that same quotient using different dividends and divisors?
Decimal Architect Slides Thinking Task Treasury
Decimal Architect
Unit 5: Place Value & Operations
Section A
Addition & Subtraction
3 Tasks
TASK 1
The Target Ten
Use the digits 1, 2, 3, 4, 5, 6 exactly once to fill the boxes. Make a sum closest to 10.
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Section B
Multiplication
3 Tasks
TASK 1
Half and Half
Draw an area model for \(0.5 \times 0.5\).
Use the same model to show \(0.5 \times 0.6\).
TASK 2
The Grid Challenge
Find two decimals with tenths that produce a product with a 5 in the hundredths place.
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×
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=
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5
Section C
Division
3 Tasks
TASK 2
Double Dividend
Find a division problem where the quotient is exactly double the dividend.
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2X
Operation Station Teacher Guide Operation Station
Unit 6: Multi-Digit Multiplication, Division & Fractions
Thinking Strategy
Focus on **estimation** and **number sense** before jumping to algorithms. Encourage students to "break" the algorithm to see how it works.
"Don't tell them how to do it; ask them what happens if they change one digit."
IM Standards
5.NBT.B.5 5.NBT.B.6 5.NF.A.1
A
Multi-Digit Multiplication
Task 1: The Product Peak
Low Floor
Use the digits 1, 2, 3, 4, 5 once each to create the largest possible product: _ _ _ × _ _
High Ceiling: Now, use the same digits to make the smallest possible product. How did your strategy change?
Task 2: Digit Swap
Mid-Tier
Consider \(24 \times 15\) and \(14 \times 25\). Predict which is larger before calculating. Then calculate both. Why does swapping the tens digits affect the product this way?
High Ceiling: Does this swap rule work for any two 2-digit numbers? Test with \(38 \times 42\) and \(48 \times 32\).
Task 3: Zero Quest
High Ceiling
Find a 3-digit by 2-digit multiplication problem where the product ends in exactly three zeros. (Example: \(\_ \_ \_ \times \_ \_ = \_ , 000\))
High Ceiling: Can you find factors that don't end in zero but produce a product ending in three zeros?
B
Multi-Digit Division
Task 1: Target Quotient
Low Floor
Find a division problem with a 4-digit dividend and a 2-digit divisor where the quotient is exactly 12.
High Ceiling: Find a solution where none of the digits in the dividend or divisor are the same.
Task 2: Division Detective
Mid-Tier
Fill in the missing digits: _ _ _ _ ÷ 14 = 8_. How many different solutions can you find?
High Ceiling: What is the largest possible quotient you can make with a 4-digit dividend and a divisor of 14?
Task 3: The Remainder King
High Ceiling
What is the largest possible remainder when dividing any number by 25? Prove it with a 4-digit dividend.
High Ceiling: Create a problem with a divisor of 25 where the remainder is exactly half the divisor.
C
Fraction Operations
Task 1: The Whole Puzzle
Low Floor
Find three different unit fractions (fractions with a numerator of 1) that add up to exactly 1. (Example: \(1/2 + \dots\))
High Ceiling: Can you find four different unit fractions that sum to 1? Five?
Operation Station Slides Thinking Task Treasury
Operation Station
Unit 6: Mult-Digit Ops & Fractions
Section A
Multiplication Mastery
3 Tasks to Break the Algorithm
The Product Peak
TASK 1
Use the digits 1, 2, 3, 4, 5 once each to create the largest possible product.
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Section B
Division Detectives
3 Mystery Tasks
Division Detective
TASK 2
Fill in the missing digits to complete the schematic:
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14
=
8
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Section C
The Whole Puzzle
Fraction Construction Tasks
The Whole Puzzle
TASK 1
Find 3 different unit fractions (numerator of 1) that add up to exactly 1.
1
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1
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1
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1
Coordinate Quest Teacher Guide Coordinate Quest
Unit 7: Shapes on the Coordinate Plane
Spatial Reasoning
Encourage students to visualize the grid before drawing. Use colored markers to distinguish between different patterns or rules.
IM Standards
5.G.A.1 5.G.A.2 5.OA.B.3
A
The Coordinate Plane
Task 1: Hidden Triangle
Low Floor
Find three points on the coordinate plane that create a **right triangle** with an area of exactly **6 square units**. Plot them and prove it.
High Ceiling: Find another set of points that creates a *different* right triangle with the same area, but where none of the sides are horizontal or vertical.
Task 2: Reflective Points
Mid-Tier
If point (3, 4) is reflected over a "magic line" to become (7, 4), where is the line? What is the reflection of (5, 2) over that same line?
High Ceiling: What happens to points that are actually *on* the magic line?
Task 3: Midpoint Mystery
High Ceiling
Find the exact coordinates of the point that is exactly **halfway** between (1, 2) and (9, 8). Explain your strategy.
High Ceiling: Can you find the "quarter-way" point between them?
B
Numerical Patterns
Task 1: Rule Runner
Low Floor
Rule 1: Start at 0, add 3. Rule 2: Start at 0, add 6. Create coordinate pairs (Rule 1, Rule 2). What do you notice about the relationship between x and y?
High Ceiling: If the x-coordinate is 45, what is the y-coordinate without generating the whole list?
Task 2: The Intersection
Mid-Tier
Rule A: Start at 2, add 4. Rule B: Start at 10, add 2. After how many steps will the values from both rules be exactly equal?
High Ceiling: What happens if Rule B starts at 11? Will they ever be equal?
Task 3: Pattern Prediction
High Ceiling
Rule X: add 5. Rule Y: add 10. Both start at 0. If the x-coordinate is **100**, what is the y-coordinate? If the **sum** of x and y is **300**, what are the coordinates?
High Ceiling: Create your own "Secret Rule" that generates a straight line that doesn't pass through (0,0).
Coordinate Quest Slides Thinking Task Treasury
Coordinate Quest
Unit 7: Shapes & Patterns
Section A
The Grid
Coordinate Geometry Tasks
Hidden Triangle
TASK 1
Find three points on the grid that create a:
RIGHT TRIANGLE
AREA = 6 UNITS²
Section B
The Flow
Numerical Pattern Tasks
The Intersection
TASK 2
RULE A
Start @ 2
RULE B
Start @ 10
After how many steps will the values be EQUAL?
Master Builder Teacher Guide Master Builder
Unit 8: Putting it All Together
Synthesis Strategy
These tasks require students to pull from all previous units. Focus on the **connections** between decimals, fractions, and geometry.
IM Standards
5.NBT.B 5.NF.B 5.MD.C
A
Operational Synthesis
Task 1: The $50 Challenge
Low Floor
You have **$50**. You spend **1/4** on a book and **0.2** on a snack. How much money do you have left? Express your answer as both a decimal and a fraction.
High Ceiling: If you want to spend exactly $40 total, what other purchase (as a fraction of your remaining money) could you make?
Task 2: Operational Loop
Mid-Tier
Start with **1.2**. (1) Multiply by 3. (2) Subtract 0.6. (3) Divide by 3. (4) Add **1/2**. What is your final number? Write the whole process as one single expression.
High Ceiling: Create your own 4-step loop that starts and ends with the same number using at least one fraction and one decimal.
Task 3: Target 100 Mixed
High Ceiling
Use exactly one fraction and one decimal to make a product as close to **100** as possible. You cannot use the number 100 itself.
High Ceiling: Can you get within 0.01 of 100?
B
Volume & Properties
Task 1: Fixed Volume
Low Floor
Find three different rectangular prisms with a volume of exactly **36 cubic units**. At least one prism must have a fractional side length.
High Ceiling: Find a prism with volume 36 where all three side lengths are different and at least two are decimals.
Task 2: The Hollow Box
Mid-Tier
A larger prism (5 × 4 × 3) has a smaller prism (2 × 2 × 2) removed from its center. What is the remaining volume? If you fill the hole with water, how many cubic units are left empty?
High Ceiling: What size smaller prism would you need to remove to leave exactly 50% of the volume?
Task 3: Scaling Up
High Ceiling
If you **double** the length, width, and height of a cube, what happens to the volume? Is it doubled? Explain your discovery.
High Ceiling: What happens to the volume if you only double *one* dimension? *Two* dimensions?
C
The Grand Finale
Task 1: Party Planner
Low Floor
A class of 24 needs juice. Each person drinks **0.25 liters**. How many **2-liter bottles** are needed to make sure everyone gets enough?
High Ceiling: If the juice costs $2.50 per bottle, what is the total cost? How much does it cost per person?
Master Builder Slides Thinking Task Treasury
Master Builder
Unit 8: The Grand Finale
Section A
Operational Synthesis
Fractions + Decimals + Logic
Operational Loop
TASK 2
1 Start with 1.2
2 Multiply by 3
3 Subtract 0.6
4 Divide by 3
5 Add 1/2
What is your FINAL number?
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Section B
Volume & Scaling
3D Construction Tasks
Scaling Up
TASK 3
If you DOUBLE the length, width, and height of a cube...
What happens to the VOLUME?
Section C
The Grand Finale
Real-World Logic Tasks
The Party Budget
TASK 2
Total Budget: $100
1/2
FOOD
0.3
DECOR
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MUSIC
