Baking Arrays Slides 🧁 Sweet Array Bakery
Lesson 1: Array Foundations
✨ Welcome, Pastry Chef! ✨
Baking with Arrays!
Discover how organizing delicious treats in neat rows and columns unlocks the magic of multiplication!
🍪 Equal Rows
🍓 Equal Columns
⚡ Quick Counting!
🔍 What is an Array?
Visual Math Rules
👉
Rows go ACROSS
Think of shelves in our bakery display case that run left-to-right.
👇
Columns go DOWN
Think of tall bakery pillars or candles standing straight up-and-down.
Fresh Cookie Sheet: 3 Rows × 4 Columns
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Every single row has the exact same amount!
Rule of Arrays: There cannot be any empty spaces or crooked rows!
➕ Connecting Addition to Multiplication
Row by Row
Strawberry Cupcake Tin
Row 1:
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5
Row 2:
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5
Row 3:
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5
Repeated Addition
5 + 5 + 5 = 15
We add 5 three times!
Multiplication Equation
3 × 5 = 15
3 groups of 5 equal 15 cupcakes in all!
Multiplication is the baker's shortcut for repeated addition!
📝 The Baker's Array Formula
Equation Builder
Rows
Number of rows
×
Columns
In each row
=
Total
Sweet treats
Example: A tray has 4 rows of 6 macarons.
4 × 6 = 24 macarons!
✨ Rows first • ✨ Columns second • ✨ Total product!
👩🍳 Quick Kitchen Check!
Can You Solve It?
Doughnut Glazing Tray
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How many rows? How many columns?
Number of Rows:
2 rows going across
Items in each column:
4 doughnuts in each row
Multiplication Equation:
2 × 4 = 8 doughnuts!
🎉 You are ready to bake your own arrays on the Cookie Tray Worksheet!
Cookie Tray Worksheet 🍪
Sweet Array Bakery
Cookie Tray Worksheet • Lesson 1
Name:
Date:
Chef's Rule: Rows go across (👉). Columns go down (👇).
Rows × Columns = Total Treats
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Part 1: Read the Fresh Baking Trays
Tray A: Choco-Chip
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How many rows?
Cookies in each row?
Repeated Addition Sentence:
Multiplication Equation:
Tray B: Strawberry Swirls
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How many rows?
Cookies in each row?
Repeated Addition Sentence:
Multiplication Equation:
Tray C: Mint Sugar Stars
⭐⭐⭐⭐⭐⭐ ⭐⭐⭐⭐⭐⭐
How many rows?
Stars in each row?
Repeated Addition Sentence:
Multiplication Equation:
Turn the page to design your very own bakery arrays! 🧁
Sweet Array Bakery
Cookie Tray Worksheet • Page 2: Chef's Studio
Draw & Solve
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Part 2: Draw the Bakery Trays
Draw neat circles, stars, or cookies in rows and columns to match the bakery order.
Order #1: Cinnamon Rolls
Draw an array of: 3 rows of 6 rolls
Multiplication: =
Order #2: Vanilla Cupcakes
Draw an array of: 5 rows of 4 cupcakes
Multiplication: =
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Part 3: Master Baker Story Challenge
🧁 Chef Maya's Cake Pop Order: Chef Maya is preparing cake pops for a school carnival. She arranges them on a display board with 6 rows . Each row holds 7 cake pops . How many cake pops are on the display board in all?
Sketch Maya's Array:
Multiplication Sentence:
Final Answer with Units:
💡 Baker's Think-Aloud:
Why does arranging cookies in an array make counting them faster than counting one-by-one?
Sweet Array Bakery • 3rd Grade Mathematics Great Work, Chef! ⭐⭐⭐
Tray Turner Slides 🔄 Sweet Array Bakery
Lesson 2: Commutative Property
✨ The Baker's Secret Rotation Trick ✨
Tray Turner Magic!
What happens when you spin a baking tray? Let's discover how factors swap places while the total treats stay identical!
🎁 Macaron Gift Boxes
💫 Turn 90° Degrees
🎯 Identical Product!
🔄 Turn the Tray: Watch What Happens!
Rotational Proof
Horizontal Tray: 3 × 5
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3 rows of 5 macarons
3 × 5 = 15
Turned 90°: 5 × 3
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5 rows of 3 macarons
5 × 3 = 15
✨ 3 × 5 = 5 × 3 = 15 macarons! The total never changed! ✨
💡 The Commutative Property of Multiplication
Math Superpower
The Commutative Property says:
You can multiply numbers in any order, and the product is always the same!
🍓
Berry Tarts
4 × 6 = 24
and 6 × 4 = 24
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Lemon Drops
2 × 9 = 18
and 9 × 2 = 18
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Glazed Rings
7 × 3 = 21
and 3 × 7 = 21
If you get stuck on a hard fact like 8 × 3, flip it to 3 × 8 and skip count by 8s!
🍫 Splitting Big Arrays: The Brownie Pan
Break Apart Strategy
Big Brownie Pan: 6 Rows of 7
Top 3 rows of 7: (3 × 7 = 21)
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Bottom 3 rows of 7: (3 × 7 = 21)
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Original Tricky Problem:
6 × 7 = ?
Split into two smaller facts:
(3 × 7) + (3 × 7)
21 + 21 = 42 brownies!
Breaking an array into smaller friendly pieces makes calculating big numbers up to 100 super easy!
Every large array can be cut into smaller arrays that you already know!
⚡ Find the Commutative Twin!
Quick Match
🧁
4 × 8
Whose twin is it?
8 × 4 = 32
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5 × 7
Whose twin is it?
7 × 5 = 35
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9 × 6
Whose twin is it?
6 × 9 = 54
🚀 Head to the Macaron Box Worksheet to match and decompose your own sweet arrays!
Macaron Box Worksheet 🎁
Sweet Array Bakery
Macaron Box Worksheet • Lesson 2
Name:
Date:
Commutative Property: Changing factor order does not change the product!
\(a \times b = b \times a\)
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Part 1: The Rotating Macaron Box
Look at how rotating the box changes rows and columns, but keeps the total macarons identical.
Position A: Wide Display
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Rows: × Columns: = Total:
Position B: Turned 90°
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Rows: × Columns: = Total:
Write the Twin Equation: × = × = macarons
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Part 2: Match the Bakery Twins
Draw a line connecting each expression on the left with its commutative twin on the right.
A. \(4 \times 7\) (Lemon Tarts)
B. \(5 \times 9\) (Sugar Cookies)
C. \(8 \times 3\) (Mini Pies)
D. \(6 \times 8\) (Choco Truffles)
1. \(3 \times 8 = 24\)
2. \(8 \times 6 = 48\)
3. \(7 \times 4 = 28\)
4. \(9 \times 5 = 45\)
Turn to page 2 to decompose large brownie trays! 🍫
Sweet Array Bakery
Macaron Box Worksheet • Page 2: Array Slicing
Decomposing Facts
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Part 3: Slice and Solve the Brownie Pan
Baker Maya is baking a sheet of fudge brownies with 6 rows of 8 brownies . She slices it horizontally across the middle to make it easier to count!
Top Piece: 3 rows of 8
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✂️ Cut Line
Bottom Piece: 3 rows of 8
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1. Top Piece Equation:
3 × 8 = brownies
2. Bottom Piece Equation:
3 × 8 = brownies
3. Combine the Two Pieces:
+ =
So, 6 × 8 = brownies!
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Part 4: The 36 Lemon Tart Dilemma
🍋 Order: Chef Chloe just baked 36 lemon tarts . She needs to arrange all 36 into equal rectangular arrays for the store window.
Can Chloe make a tray with 4 rows of 9? Explain why or why not:
If she rotates that tray, what is the twin equation?
What square array can Chloe also make using all 36 lemon tarts?
⭐ Pastry Chef Check-In:
Which multiplication fact twin do you find easiest to remember? Why?
Bakery Orders Slides 🎂 Sweet Array Bakery
Lesson 3: Problem Solving
🎉 Grand Celebration Orders 🎉
Party Order Solvers!
Step into the role of Head Pastry Chef! Use arrays to crack missing factor mysteries and fulfill giant catering orders within 100 treats!
❓ Missing Factors
📦 Multi-Tray Orders
🏆 Master Baker Badge
🕵️♀️ The Missing Factor Mystery
Array Detective
The Mystery Order:
"A customer ordered 36 mini fruit tarts for a party. The bakery tray has 4 rows. How many tarts must go in each row?"
Equation with Missing Factor:
4 × ❓ = 36
How to Solve with an Array:
1. We know there are 4 rows .
2. Deal out 36 treats equally across the 4 rows.
3. Count how many are in each column: 9 tarts!
Solution:
4 × 9 = 36
Each row holds exactly 9 fruit tarts!
Multiplication and division work together like butter and flour!
🎉 Birthday Bash: Two-Tray Order
Multi-Step Magic
Tray 1: Velvet Cupcakes 🧁
4 rows of 6 cupcakes
4 × 6 = 24
Tray 2: Chocolate Glazed Donuts 🍩
3 rows of 8 donuts
3 × 8 = 24
Combine both trays for the grand total:
24 + 24 = 48 treats in all!
📋 The 4-Step Word Problem Recipe
Chef Checklist
1
Read & Circle
Circle the number of rows, columns, or total treats.
2
Sketch Array
Draw a quick grid or dots to visualize the baking pan.
3
Write Equation
Set up Rows × Columns = Product with the numbers.
4
Answer & Unit
Write the final number with the treat label (e.g. 48 cookies).
Following this 4-step recipe ensures you never make a mistake on big orders!
🌟 Master Pastry Chef Challenge
Time to Shine!
👩🍳✨🎂
You Are Now Head of the Bakery!
The Grand Spring Festival order has just arrived. You have the tools, the arrays, and the math magic to calculate every single treat up to 100!
Open the Grand Order Worksheet & Solve!
🍪 Rows & Columns • 🔄 Commutative Twins • 🎂 Total Party Orders
Grand Order Worksheet 🎂
Sweet Array Bakery
Grand Order Worksheet • Lesson 3
Name:
Date:
Pastry Chef Recipe: 1. Circle numbers • 2. Sketch the array • 3. Write the equation • 4. Label units
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Part 1: Missing Factor Bakery Mysteries
Find the missing row or column to make each customer order complete.
Mystery A: Rainbow Cupcakes 🧁
A baker puts 45 cupcakes into a large box with 5 rows . How many cupcakes are in each row?
Equation: 5 × = 45
Cupcakes in each row:
Mystery B: Glazed Donuts 🍩
A catering tray holds 56 donuts in 8 columns . How many rows of donuts are on the tray?
Equation: × 8 = 56
Number of rows:
2
Part 2: Elena's Birthday Celebration Order
Elena ordered two customized trays for her birthday party. Calculate each tray, then find the combined total.
Tray 1: Frosted Sugar Cookies
6 rows of 6 frosted cookies
Equation: =
Tray 2: Berry Muffins
4 rows of 8 fresh muffins
Equation: =
Total Treats for Elena's Party:
Turn to page 2 for the Grand Festival Catering Invoice! 🎪
Sweet Array Bakery
Grand Order Worksheet • Page 2: Festival Invoice
Catering Challenge
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Part 3: Spring Festival Catering Invoice
Complete the order invoice for the school's annual festival. Calculate each line item using arrays.
Item Description Array Arrangement Multiplication Sentence Total Treats 🥐 Vanilla Eclairs 7 boxes of 5 eclairs 🍓 Strawberry Tartlets 6 trays of 7 tartlets Subtotal Baked So Far:
⭐ Festival Target: 100 Treats in Total!
The festival committee ordered exactly 100 sweet treats . Using your subtotal above, how many more treats must the bakery prepare?
Equation: 100 − = more treats needed
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Part 4: Design Your Own Showstopper Array
Design an array for between 20 and 50 treats of your favorite bakery item!
Master Baker Guide 📖
Sweet Array Bakery
Teacher Facilitation Guide • 3rd Grade Unit
Grade 3 • Operations & Algebraic Thinking
Unit Learning Trajectory
Lesson 1: Foundations
Concrete & pictorial arrays. Differentiating rows (across) vs columns (down). Connecting repeated addition to \(r \times c\).
Lesson 2: Commutativity
Rotating trays 90° to prove \(a \times b = b \times a\). Decomposing large arrays (distributive property foundation).
Lesson 3: Problem Solving
Real-world catering word problems, missing factors (\(r \times ? = p\)), and multi-step totals within 100 treats.
Recommended Bakery Manipulatives
1. Color Tiles / "Sugar Cubes": Use square inch tiles to let students physically slide and rotate rectangles on desk mats.
2. Egg Cartons / Muffin Tins: Real tins with plastic counters or pom-poms create tactile row-column mapping.
3. Grid Paper / "Baking Sheets": Have students outline and shade arrays with colored pencils to visualize products.
3 Common 3rd Grade Misconceptions & Fixes
Misconception 1: Confusing Rows and Columns
Coaching Script: "Remember: Rows go across like the horizon or bakery display shelves. Columns go down like tall columns holding up a pastry shop roof!"
Misconception 2: Adding Factors Instead of Multiplying
Coaching Script: "A student sees \(4 \times 6\) and writes 10. Prompt: 'Look at the 4 rows. Does each row only have 1 cookie? Count by 6s four times: 6, 12, 18, 24!'"
Misconception 3: Believing Rotated Trays Have Different Quantities
Coaching Script: "Have the student count a physical 3×5 tray. Then physically turn it in front of them without adding or taking away any pieces. Did any cookies disappear?"
High-Impact Discussion Prompts
• "How does looking at an array help you check if your answer makes sense?"
• "If you forget what \(8 \times 6\) is, how can you use two easier arrays to figure it out?"
• "How is finding a missing factor in an array like solving a bakery mystery puzzle?"
Sweet Array Bakery • Teacher Facilitation Guide Turn to page 2 for Master Answer Keys 🔑
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Master Answer Key
Complete Solutions for Lessons 1, 2, and 3
Teacher Reference Only
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Lesson 1: Cookie Tray Worksheet Solutions
Tray A: 3 rows, 4 per row. Addition: \(4+4+4=12\). Eq: \(3 \times 4 = 12\).
