Math Bootcamp Slides
6TH GRADE RETEACH
MATH BOOTCAMP
Fifth Grade
Essentials Review
Mastering expressions, decimals, and fractions for a solid foundation in 6th grade math!
Targeting Crucial 5th Grade Standards
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BOOSTER
Today's Mission & Warm-Up
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Mission Objectives
- ✓ Write & interpret expressions
- ✓ Master place value & powers of 10
- ✓ Perform decimal arithmetic fluently
- ✓ Add, subtract, & multiply fractions
Get ready to write, compute, and conquer!
Warm-Up Challenge
3 MINS
Solve mentally as quickly as you can:
15 - (3 + 4) × 2
Remember: Order of Operations (PEMDAS)!
What is the correct value? Explain why!
Focus standards: 5.OA.A.2, 5.NBT.A.2 Let's build deep understanding!
BLOCK 1
Algebraic Thinking & Numerical Patterns
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5.OA.A.2
Translating Expressions
Translate math verbs to symbols without evaluating them!
"Sum" / "More" → +
"Difference" → -
"Product" / "Times" → ×
"Quotient" → ÷
"Add 8 and 7, then multiply by 2" → (8 + 7) × 2
5.OA.B.3
Numerical Patterns
Generate sequences with two different rules and compare.
X Rule: Start at 0, add 3 [0, 3, 6, 9]
Y Rule: Start at 0, add 6 [0, 6, 12, 18]
Pro-Tip: Y values are always exactly double the corresponding X values! Form ordered pairs: (0,0), (3,6), (6,12), (9,18).
Maneuvering in the Middle - Algebraic Thinking Block Unit 1, Session 1
LET'S TRY IT
Block 1: Guided Practice
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TEACHER MODEL (I DO)
Write a numerical expression for the phrase:
"Subtract 4 from 12, then multiply by 5"
Step 1: Identify operations ("Subtract", "Multiply")
Step 2: Group first part with parentheses: (12 - 4)
Step 3: Write final expression: (12 - 4) × 5
GUIDED PRACTICE (WE DO)
Write a numerical expression for the phrase:
"Double the sum of 15 and 9"
Think-Pair-Share Questions:
- What operation is implied by "double"?
- Which part must happen first and requires parentheses?
- Can you write it in two different ways?
Focus: Writing expressions with correct grouping symbols Remember: order matters!
BLOCK 2
Decimals: Place Value & Powers of 10
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5.NBT.A.2
Powers of 10 Shifts
Multiply by 101 (10) Shift 1 place RIGHT
Multiply by 102 (100) Shift 2 places RIGHT
Divide by 101 (10) Shift 1 place LEFT
Divide by 102 (100) Shift 2 places LEFT
Example: 3.45 × 102 = 345
5.NBT.A.3
Forms & Comparisons
Decimals to Thousandths:
Standard: 4.073
Expanded: 4 × 1 + 7 × (1/100) + 3 × (1/1000)
Word Name: Four and seventy-three thousandths
To compare, line up decimal places!
4.073 > 4.07
Place value names: tenths, hundredths, thousandths Watch out for the zeros!
BLOCK 2
Decimal Operations Checklist
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Addition
Line up the decimals! Pad empty places with zeros if needed.
1.24 + 0.30 = 1.54
-
Subtraction
Line up the decimals! Regroup across zeros if necessary.
5.00 - 1.25 = 3.75
×
Multiplication
Ignore decimals! Multiply as whole numbers, then count decimal places.
0.3 × 0.2 = 0.06
÷
Division
Make divisor a whole number by shifting decimals on both sides!
4.8 ÷ 0.6 = 8
Standard: 5.NBT.B.7 Precision is the secret to decimal accuracy!
LET'S TRY IT
Block 2: Decimals Practice
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PROBLEM A: EXTREME SHIFTING
Compute:
18.52 × 103
- Identify power: 103 means 1000.
- Which direction does decimal point travel?
- How many places? Do we need to pad placeholders with zeros?
PROBLEM B: DIVISION CHECK
Solve:
3.6 ÷ 0.09
- What must we multiply the divisor 0.09 by to make it a whole number?
- What happens to the dividend 3.6?
- Rewrite: 360 ÷ 9
Look closely at your place values! Be exact!
BLOCK 3
Fraction Action: Unlike Denominators & Multiplication
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5.NF.A.1
Add & Subtract with Unlike Denominators
Find a common multiple (least common denominator) to rewrite your fractions!
Problem: 1/2 + 2/3
LCD of 2 & 3: 6
Equivalents: 3/6 + 4/6
Result: 7/6 = 1 1/6
5.NF.B.4
Multiplying Fractions
Simply multiply numerators together, then denominators!
Formula: (a/b) × (c/d) = (a × c) / (b × d)
Example: 2/3 × 4/5
Result: 8/15
Pro-Tip: Whole numbers have a hidden denominator of 1! (e.g., 5 → 5/1)
Do not add denominators together! Keep it straight! Simplifying is optional but awesome!
LET'S TRY IT
Block 3: Fraction Practice
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PROBLEM A: FRACTION COMBAT
Solve:
3/4 - 1/3
- What is the Least Common Denominator of 4 and 3?
- Convert both fractions to have denominator 12.
- Perform subtraction: 9/12 - 4/12 = 5/12
PROBLEM B: MIXED MULTIPLY
Compute:
2/5 × 15
- Convert 15 to a fraction: 15/1
- Multiply numerators: 2 × 15 = 30
- Multiply denominators: 5 × 1 = 5
- Simplify: 30 ÷ 5 = 6
Verify your work step-by-step! Simplifying makes answers cleaner!
ROTATION
Bootcamp Station Activities
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Station 1: Operations
Crack decimal equations and match standard word descriptions to correct amounts.
Target: 5.NBT.B.7, 5.NBT.A.3
Station 2: Expressions
Translate numerical word descriptions to algebraic representations and evaluate pattern values.
Target: 5.OA.A.2, 5.OA.B.3
Station 3: Fractions
Add, subtract, and multiply fractional amounts in visual standard formats.
Target: 5.NF.A.1, 5.NF.B.4
"Math is not about numbers, equations, or algorithms: it is about understanding." — William Paul Thurston
Get your Guided Notes Packet ready! Let's begin rotations!
Math Bootcamp Notes
6th Grade Reteach
Math Bootcamp Guided Notes
Name: ________________________
Date: ________________________
My Mission Checklist
Block 1: Expressions Block 2: Decimal Ops Block 3: Fraction Action
BLOCK 1
Algebraic Thinking & Numerical Patterns
Part A: Writing & Translating Expressions (5.OA.A.2)
1. A numerical expression contains numbers and operations, but has no ________________________.
2. Grouping symbols like parentheses ( ) or brackets [ ] tell us which operation to do ________________________.
| Word Phrase | Numerical Expression (Write it!) |
|---|
| "Subtract 4 from 12, then multiply by 5" | Example: (12 - 4) × 5 |
| "Double the sum of 15 and 9" | |
| "The difference between 20 and 8, divided by 3" | |
Part B: Generating Patterns (5.OA.B.3)
Complete the table using the given rules. Then answer the comparison question.
| Term | X: Start 0, Add 3 | Y: Start 0, Add 6 | Ordered Pair (X, Y) |
|---|
| 1st | 0 | 0 | (0,0) |
| 2nd | 3 | 6 | |
| 3rd | 6 | 12 | |
| 4th | | | |
Identify the Relationship:
Compare terms. The value of Y is always _________________ the value of X.
If X is 15, Y = _________________
Extra Expressions / Patterns Workspace
Use this space for an additional practice problem or customized teacher model.
Maneuvering in the Middle Inspired Reteach Series Page 1 of 3
Math Bootcamp Review Student Guided Notes
BLOCK 2
Decimals Mastery: Place Value, Powers of 10, & Operations
Part A: Powers of 10 Shifts & Comparison (5.NBT.A.2, 5.NBT.A.3)
Powers of 10 Shifts:
• Multiplying moves decimal to the ____________________.
• Dividing moves decimal to the ____________________.
Compute: 18.52 × 103 = ______________
Comparing Decimals:
• ____________________ up decimal points to compare place by place!
• Compare standard numbers using <, >, or = :
Math Practice Stations
Independent Practice
Bootcamp Station Task Cards
6 Station Cards • Print & Cut
STATION 1
5.OA.A.2: Expressions
Translate the Phrase
"Subtract the product of 3 and 4 from 25, then add 8."
Write the numerical expression. Do not solve!
STATION 2
5.OA.B.3: Patterns
Relationship Rule
X-Rule: Start 0, add 4.
Y-Rule: Start 0, add 12.
Find the 4th coordinate pair. How is Y related to X?
STATION 3
5.NBT.A.2: Powers of 10
Decimal Shifter
A) 4.59 × 103
B) 781.4 ÷ 102
Compute the final answers for both calculations.
STATION 4
5.NBT.A.3b: Decimals
Comparison Battle
Order from least to greatest:
8.34, 8.304, 8.4, 8.034
Compare carefully by aligning decimal places.
STATION 5
5.NF.A.1: Fractions
The Common Ground
5/6 - 2/3
Solve. Express your final answer in simplest form!
STATION 6
5.NF.B.4: Fractions
Multiply Action
3/8 × 16
Solve. Show how you converted the whole number.
Each station focuses on a key core standard. Page 1 of 3
Math Bootcamp Independent Homework
Show all your step-by-step math setups in the provided workspace boxes.
Name: ________________________
Date: ________________________
Q1: Translating Word Patterns Write an expression for: "Double the quotient of 20 and 5."
Workspace
Q2: Powers of 10 Shifts Solve: 12.5 ÷ 103
Workspace
Q3: Comparing Decimals Use <, >, or = to compare:
14.05 ______ 14.050 3.28 ______ 3.208
Workspace
Q4: Decimal Addition Find the sum: 4.56 + 12.8
Workspace
Q5: Unlike Denominator Fractions Compute: 3/4 + 1/8
Workspace
Q6: Fraction Multiplication Solve: 4/5 × 10
Workspace
Completed homework is due tomorrow morning. Page 2 of 3
EXIT TICKET: VERSION A
Bootcamp Quick Check Name: ________________________ Date: ________
1. Translate & Write
"5 times the sum of 8 and 3."
2. Decimal Solve
Evaluate: 1.2 × 0.6
