Checkpoint Booster Skills Packet
ILEARN Checkpoint 2 Booster
Ratios & Unit Rates Power-Up
Name
Date
Strategy Anchor: Finding the Unit Rate (Cost per 1)
Step 1: Set up a Ratio Table
Example: 3 notebooks cost $6. How much for 1 notebook?
<table class="w-full text-center border-collapse border border-slate-300 text-xs"><tbody><tr class="bg-slate-100 font-semibold"><td class="border border-slate-300 p-1">Notebooks</td><td class="border border-slate-300 p-1 bg-yellow-50 text-indigo-700 font-bold">3</td><td class="border border-slate-300 p-1 bg-green-50 text-emerald-700 font-bold">1</td></tr><tr><td class="border border-slate-300 p-1 font-semibold">Cost ($)</td><td class="border border-slate-300 p-1 bg-yellow-50">$6.00</td><td class="border border-slate-300 p-1 bg-green-50 font-bold text-emerald-700">$2.00</td></tr></tbody></table>
Step 2: Divide to Find Rate for 1
\( \text{Unit Price} = \frac{\text{Total Cost}}{\text{Quantity}} = \frac{\$6.00}{3} = \$2.00 \text{ per notebook} \)
Always divide cost by amount to find the cost per ONE item.
Guided Practice
Problem 1: Juice Box Value
A pack of 5 juice boxes costs $4.00. Complete the table to find the cost of 1 juice box, then use that rate to find the cost of 8 juice boxes.
| Juice Boxes | 5 | 1 (Unit Rate) | 8 |
|---|
| Cost ($) | $4.00 | | |
| $ _______ | | | |
|
$ _______
|
Show Division:
Independent Practice
ILEARN-Style Checkpoint Questions
Problem 2: Marcus walks 12 laps around the school track in 4 minutes.
Part A: What is Marcus's unit rate in laps per minute?
Rate: laps per minute
Part B: At this same rate, how many laps will Marcus walk in 9 minutes?
Answer: laps
Problem 3: Better Buy Comparison
Store A sells 4 markers for $5.00. Store B sells 6 markers for $6.60. Which store offers the lower price per marker? Show your calculations.
Store A Unit Price:
Price per marker = $
Store B Unit Price:
Price per marker = $
Better Buy (Circle One): Store A Store B
Tip: "Unit rate" means quantity for 1 single item. Page 1 of 3
ILEARN Checkpoint 2 Booster
Dividing Fractions & Integers
Name
Strategy 1: "How Many Pieces Fit?" (Tape Model)
Think of division as grouping: \( \frac{3}{4} \div \frac{1}{8} \) means "How many \( \frac{1}{8} \) pieces fit inside \( \frac{3}{4} \)?"
Whole unit partitioned into eighths: Shaded area = 6/8 = 3/4
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
Count the shaded \( \frac{1}{8} \) pieces: There are exactly 6 pieces. So, \( \frac{3}{4} \div \frac{1}{8} = 6 \).
Problem 4
A chef has \( \frac{2}{3} \) cup of sugar. Each mini-cake recipe needs \( \frac{1}{6} \) cup. How many cakes can the chef make?
Fill in the tape model divided into sixths:
1/6
1/6
1/6
1/6
1/6
1/6
Answer: mini-cakes
Problem 5
Calculate using the algorithm (Keep-Change-Flip):
\( \frac{4}{5} \div \frac{2}{3} = \)
Keep: 4/5
Change (\( \div \) to \( \times \)): \( \times \)
Flip \( \frac{2}{3} \) to:
Final Answer:
Strategy 2: Integers, Opposites & Value on Number Line
Numbers to the left of 0 are negative. Numbers further left are smaller (\( -8 < -3 \)). The opposite of \( +a \) is \( -a \).
-5
-4
-3
-2
-1
0
1
2
3
4
5
A. Compare using >, <, or = :
\( -7 \) \( -2 \)
\( |-9| \) \( 9 \)
B. Real-World Integer Context:
A submarine is at 140 feet below sea level (\( -140 \)). A diver is at 45 feet below sea level (\( -45 \)). Who is deeper?
Deeper:
Absolute value \( |x| \) is distance from zero (always positive!). Page 2 of 3
ILEARN Checkpoint 2 Booster
Expressions & One-Step Equations
Name
Strategy: Keep the Balance Equal (Inverse Operations)
Addition ↔ Subtraction
Solve: \( x + 8 = 21 \)
\( x + 8 - 8 = 21 - 8 \)
\( x = 13 \)
Undo \( +8 \) by subtracting 8 from BOTH sides.
Multiplication ↔ Division
Solve: \( 4y = 28 \)
\( \frac{4y}{4} = \frac{28}{4} \)
\( y = 7 \)
Undo \( \times 4 \) by dividing BOTH sides by 4.
Writing Expressions
Match the Math Clue Words to the Correct Algebraic Expression
1. "8 less than a number \( n \)" n - 8
2. "The product of 6 and \( m \)"
3. "15 shared equally among \( p \) students"
4. "7 more than twice a number \( x \)"
Problem 8: Solve and Check Inverse Operation: Subtract
Solve: \( w + 14 = 39 \)
Value of \( w \) =
Check Your Solution:
Substitute your answer back in: Does \( \text{answer} + 14 = 39 \)?
Problem 9: Solve and Check Inverse Operation: Multiply
Solve: \( \frac{k}{5} = 12 \)
Value of \( k \) =
Check Your Solution:
Substitute your answer back in: Does \( \frac{\text{answer}}{5} = 12 \)?
Always do the exact same operation to both sides of the equals sign! Page 3 of 3
Targeted Checkpoint Mini Assessment
ILEARN Practice Checkpoint 2
Math Readiness Check
Name
Date
Score
/ 10
Instructions: Read each question carefully. Show your mathematical thinking in the work boxes. No Calculator Allowed
Question 1 (6.RP.A.2) 1 point
A hybrid car travels 180 miles using 6 gallons of gasoline. How many miles does the car travel per gallon of gasoline?
A 20 miles per gallon
B 28 miles per gallon
C 30 miles per gallon
D 32 miles per gallon
Show Work / Division:
Question 2 (6.RP.A.3a) 1 point
Which of the following ratios are equivalent to \( 3 : 5 \)? Select ALL that apply.
6 to 10
9 to 20
12 to 20
15 to 25
Question 3 (6.NS.A.1) 1 point
Find the quotient: \( \frac{5}{6} \div \frac{1}{3} \). Give your answer in simplest form or as a mixed number.
Work space (Keep - Change - Flip):
Quotient
Question 4 (6.NS.C.7) 1 point
Four divers explore ocean caves at the following depths relative to sea level: -14 ft, -32 ft, 0 ft, -5 ft. Order the depths from deepest (coldest/lowest) to highest.
Lowest (Deepest)
<
2nd Lowest
<
3rd Lowest
<
Highest
Turn page for Questions 5 through 7 and Reflection Page 1 of 2
ILEARN Practice Checkpoint 2
Expressions & Problem Solving
Part 2: Equations & Reflection
Question 5 (6.EE.A.2a) 1 point
Admission to a school fun fair costs $8.00. Each game ticket costs $1.50. Write an algebraic expression that represents the total cost for admission and \( t \) game tickets.
Identify the pieces:
• Fixed entry fee = $8.00
• Rate per ticket = $1.50 times \( t \)
Your Expression:
Question 6 (6.EE.B.7) 1 point
Solve for \( m \): \( 9m = 72 \)
Show Inverse Operation:
Check Your Answer:
Does \( 9 \times (\text{your value}) = 72 \)?
Value of \( m \) =
Question 7 (6.EE.B.7 / 6.RP.A.3) — Two-Part Item 2 points total
Maya bought 4 identical notebooks and spent a total of .
Checkpoint Intervention Teacher Guide
Educator Resource • Checkpoint 2
Intervention Guide & Solutions
Full Answer Key
Part 1: Skills Packet Worked Answers
Page 1: Ratios & Rates
Prob 1: Unit rate = \( \$4.00 \div 5 = \$0.80 \) per box. For 8 boxes: \( 8 \times 0.80 = \mathbf{\$6.40} \).
Prob 2A: \( 12 \div 4 = \mathbf{3 \text{ laps/min}} \).
Prob 2B: \( 9 \times 3 = \mathbf{27 \text{ laps}} \).
Prob 3: Store A: \( \$5.00 \div 4 = \mathbf{\$1.25} \). Store B: \( \$6.60 \div 6 = \mathbf{\$1.10} \). Better Buy: Store B.
Page 2: Fractions & Integers
Prob 4: \( \frac{2}{3} = \frac{4}{6} \). 4 pieces of \( \frac{1}{6} \) fit inside. Answer = 4 mini-cakes.
Prob 5: Flip \( \frac{2}{3} \) to \( \frac{3}{2} \). \( \frac{4}{5} \times \frac{3}{2} = \frac{12}{10} = \mathbf{\frac{6}{5} \text{ or } 1\frac{1}{5}} \).
Prob 6A: \( -7 < -2 \) (further left). \( |-9| = 9 \), so \( |-9| = 9 \).
Prob 6B: The submarine is deeper (\( -140 < -45 \)).
Page 3: Equations
Prob 7 (Expressions):
2. \( 6m \) or \( 6 \cdot m \)
3. \( \frac{15}{p} \) or \( 15 \div p \)
4. \( 2x + 7 \)
Prob 8: \( w + 14 = 39 \implies w = 39 - 14 = \mathbf{25} \). Check: \( 25 + 14 = 39 \) ✓.
Prob 9: \( \frac{k}{5} = 12 \implies k = 12 \times 5 = \mathbf{60} \). Check: \( \frac{60}{5} = 12 \) ✓.
Part 2: Checkpoint Practice Assessment Answer Key
| Item | Standard | Correct Answer | Scoring Notes & Common Student Traps |
|---|
| Q1 | 6.RP.A.2 | C (30 mpg) | \( 180 \div 6 = 30 \). Trap: Students who make division errors often select 28 or 32. |
| Q2 | 6.RP.A.3a | 6 to 10 & 15 to 25 | Multiselect item (must select both). Both simplify to \( 3/5 \) by scale factors 2 and 5. Trap: selecting 9 to 20 because \( 3 \times 3 = 9 \). |
| Q3 | 6.NS.A.1 | \( \frac{5}{2} \) or \( 2\frac{1}{2} \) | \( \frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2} \). Common error: Multiplying straight across without reciprocating (\( 5/18 \)). |
