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Review
Mastering Number Sense, Ratios, and Algebraic Foundations for 6th Grade.
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Target: Number Sense
6.NS.1
The Key Concept
Numbers represent real-world directions from zero.
Positive: Above sea level, deposits, earning money, ascending.Negative: Below sea level, withdrawals, debt, descending.Zero: Ground level, sea level, starting point.
Guided Practice
Elevation Exploration
Chicago has an elevation of 600 feet above sea level.below sea level.
Which value could represent the location of Seeley?
A. 500 ft.
B. -200 ft.
C. 0 ft.
D. 600 ft.
Target: Ratios & Conversions
6.RP.1
Percent to Fraction
Put it over 100 and simplify!
40% = 40/100 = 2/5
Fraction to Decimal
Divide the top by the bottom.
3/5 = 0.6
Equivalent values represent the same amount.
Guided Practice
Equivalent Search
Select the TWO values that are equivalent to 60% .
A. 1/6
B. 3/5
C. 6.0
D. 0.6
Target: Substitution
6.AF.2
The "Plug & Chug" Rule
To check if a number is a solution , replace the variable with that number and see if the math stays true!
Equation (=)
Must be exactly equal on both sides.
Inequality (<, >)
Must make the statement true (e.g., is 5 less than 10?).
Guided Practice
Substitution Challenge
An inequality is given:
c ≤ 3.25
Which values of c make this true?
1.6
3.95
3.24
Remember: "≤" means less than OR equal to!
Target: Solving Equations
6.AF.3
The Inverse Operation
To solve, do the opposite to both sides.
+ Addition
−
Subtract
− Subtraction
Add
× Multiply
÷
Divide
÷ Division
×
Multiply
Guided Practice
Solve It Fast
Challenge A
Solve for x:
x + 212 = 423
Think: 423 − 212 = ?
Challenge B
Solve for f:
3f = 63
Think: 63 ÷ 3 = ?
Score Booster Worksheet ILEARN Score Booster
Standards Review: 6.NS.1, 6.RP.1, 6.AF.2, 6.AF.3
Name
Date
PART 1
Real-World Integers & Zero
1. Chicago, Illinois has an elevation of 600 feet. Seeley, California is located below sea level.
Select all values that could represent the location of Seeley.
a) -0.5 ft
b) 0.5 ft
c) 0 ft
d) -12.5 ft
2. Which situation is best represented by a negative number?
a) The elevation of a mountain top
b) The total number of students in a class
c) A withdrawal of $25 from a bank account
d) Temperature on a hot summer day
PART 2
Fractions, Decimals, & Percents
3. What is 0.125 written as a percent? Show your thinking.
4. Which fraction is equivalent to \( 0.\overline{1} \)?
a) 1/8
b) 1/9
c) 1/11
d) 2/8
5. Select the two values that are equivalent to 60%.
a) 1/6
b) 3/5
c) 0.6
d) 0.06
PART 3
Equations & Inequalities
6. An inequality is given: \( c \leq 3.25 \). Determine whether each value of \( c \) makes the inequality true.
Value of \( c \) Yes (True) No (False) 1.6
|
| 3.95 |
|
|
| 3.25 |
|
|
| 4.0 |
|
|
PART 4
Solving Real-World Equations
7. A student read a whole book on Monday and Tuesday.
On Monday, the student read \( x \) pages.
On Tuesday, the student read 212 pages.
The book has 423 total pages.
Part A: Select the equation that models this situation.
a) \( 212 + 423 = x \)
b) \( 212x = 423 \)
c) \( 212 + x = 423 \)
d) \( 212 - x = 423 \)
Part B: How many pages did the student read on Monday? Show your work.
8. Solve the following equation for \( x \):
\( \frac{5}{8}x = 40 \)
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Official Resource
Standards Alignment
6.NS.1: Integers
6.RP.1: Conversions
6.AF.2: Substitution
6.AF.3: Solving
1 Real-World Integers
Correct Answers: a) -0.5 ft and d) -12.5 ft
Rationale: "Below sea level" must be modeled by negative numbers. Values of -0.5 and -12.5 both represent locations lower than sea level (0).
Correct Answer: c) A withdrawal of $25 from a bank account
Rationale: A withdrawal represents taking money out, which reduces the balance and is best modeled by a negative number.
2 Conversions
Correct Answer: 12.5%
Rationale: To convert a decimal to a percent, multiply by 100 or move the decimal point two places to the right (0.125 becomes 12.5%).
Correct Answer: b) 1/9
Rationale: Any single-digit repeating decimal (0.n repeating) is equivalent to the fraction n/9. Thus, 0.1 repeating equals 1/9.
Correct Answers: b) 3/5 and c) 0.6
Rationale: 60% = 60/100, which simplifies to 6/10 and then 3/5. As a decimal, 60/100 is 0.60 or simply 0.6.
3 Substitution
Table Results for \( c \leq 3.25 \):
1.6: YES (True)
3.95: NO (False)
3.25: YES (True)
4.0: NO (False)
Rationale: 1.6 and 3.24 are less than 3.25. 3.25 is exactly equal to 3.25. All other values are greater than 3.25.
4 Solving Equations
Part A: c) 212 + x = 423
Part B: 211 pages
Steps: Using the inverse operation of subtraction, 423 - 212 = 211. Therefore, x = 211.
Correct Answer: x = 64
Steps: Multiply both sides by the reciprocal (8/5). 40 times 8 equals 320. 320 divided by 5 equals 64.
