Math IA Review Worksheet
Class Lesson Material • Guided Instruction & Practice Target Standard: 6.G.A.1
Grade 6 Math IA Review: Class Practice
Student:
Date:
Team / Homeroom:
Question Type 1: Area of Parallelograms Formula: \(A = b \times h\)
Teacher Model 1 Find the area of the parallelogram:
I DO
b = 8 cm h = 7 cm 4 cm
A. 28 sq. cm
B. 32 sq. cm
C. 56 sq. cm
D. 84 sq. cm
Show work:
Correct Answer:
Practice 1 Find the area of the parallelogram:
YOU DO
b = 9 in. h = 6 in. 3 in.
A. 27 sq. in.
B. 36 sq. in.
C. 54 sq. in.
D. 72 sq. in.
Show work:
Correct Answer:
Practice 2 Find the area of the parallelogram:
YOU DO
b = 12 m h = 5 m 4 m
A. 30 sq. m
B. 48 sq. m
C. 60 sq. m
D. 80 sq. m
Show work:
Correct Answer:
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.RP.A.1
Question Type 2: Identifying Equivalent Ratios
Select TWO correct answers
Teacher Model 2 Sports Equipment Display:
I DO
A gym teacher displays 4 basketballs and 12 soccer balls. Which ratios show the relationship of the number of basketballs to the number of soccer balls? (Select TWO correct answers)
A. 1 : 3
B. 1 : 4
C. 3 : 1
D. 4 : 12
E. 4 : 16
Show work & ratio simplification:
Selected Letters:
Practice 1 Classroom Technology Cart:
YOU DO
A charging cart contains 6 laptops and 18 tablets. Which ratios show the relationship of the number of laptops to the number of tablets? (Select TWO correct answers)
A. 1 : 2
B. 1 : 3
C. 6 : 18
D. 3 : 1
E. 6 : 24
Show work & ratio simplification:
Selected Letters:
Practice 2 Art Studio Display:
YOU DO
An art table has 8 paintbrushes and 12 paint jars. Which ratios show the relationship of the number of paintbrushes to the number of paint jars? (Select TWO correct answers)
A. 2 : 3
B. 3 : 2
C. 8 : 12
D. 4 : 5
E. 8 : 20
Show work & ratio simplification:
Selected Letters:
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.RP.A.3a
Question Type 3: Preserving Ratios in Tables
Proportional Reasoning
Teacher Model 3 Art Supply Box:
I DO
| Item | Quantity |
|---|
| Markers | 15 |
| Colored Pencils | 10 |
| Glue Sticks | 5 |
A teacher adds more items to the box without changing the ratios among the three supplies. If he adds 4 more colored pencils, how many more markers and how many more glue sticks should he add?
Show all steps & unit rate / multiplier:
Add markers
Add glue sticks
Practice 1 Snack Packs:
YOU DO
| Snack | Quantity |
|---|
| Granola Bars | 18 |
| Fruit Snacks | 12 |
| Pretzel Bags | 6 |
A coach adds snacks to the cooler without changing the ratio among the three snacks. If she adds 6 more fruit snacks, how many more granola bars and how many more pretzel bags should she add?
Show all steps & unit rate / multiplier:
Add granola bars
Add pretzel bags
Practice 2 Garden Seedlings:
YOU DO
| Plant | Quantity |
|---|
| Tomato | 20 |
| Pepper | 12 |
| Basil | 8 |
A gardener adds more seedlings without changing the ratios among the three plants. If she adds 6 more pepper seedlings, how many more tomato seedlings and basil seedlings should she add?
Show all steps & unit rate / multiplier:
Add tomato
Add basil
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.G.A.1
Question Type 4: Missing Dimensions from Area
Formula: \(A = l \times w \implies w = A \div l\)
Teacher Model 4 Solve for the unknown width:
I DO
Maya's rectangular patio has an area of 54 square feet. The patio is 9 feet long. What is the width of the patio?
A. 6 feet
B. 8 feet
C. 45 feet
D. 63 feet
Show division equation & work:
Correct Answer:
Practice 1 Solve for the unknown width:
YOU DO
Marcus builds a rectangular raised garden bed with an area of 72 square feet. The garden bed is 8 feet long. What is the width of the garden bed?
A. 7 feet
B. 9 feet
C. 36 feet
D. 64 feet
Show division equation & work:
Correct Answer:
Practice 2 Solve for the unknown width:
YOU DO
Elena designs a rectangular school banner with an area of 48 square feet. The banner is 6 feet long. What is the width of the banner?
A. 8 feet
B. 12 feet
C. 24 feet
D. 42 feet
Show division equation & work:
Correct Answer:
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.EE.A.1
Question Type 5: Evaluating Numerical Expressions with Exponents
Identify Greatest Value
Teacher Model 5 Which expression below has the greatest value?
I DO
A. \(2^4\)
B. \(5^2\)
C. \(3^3\)
D. \(4^2\)
Evaluate each expression (write as repeated multiplication):
A: ____________
B: ____________
C: ____________
D: ____________
Greatest Value Option:
Practice 1 Which expression below has the greatest value?
YOU DO
A. \(2^5\)
B. \(6^2\)
C. \(3^3\)
D. \(4^3\)
Evaluate each expression (write as repeated multiplication):
A: ____________
B: ____________
C: ____________
D: ____________
Greatest Value Option:
Practice 2 Which expression below has the greatest value?
YOU DO
A. \(7^2\)
B. \(2^6\)
C. \(3^4\)
D. \(5^3\)
Evaluate each expression (write as repeated multiplication):
A: ____________
B: ____________
C: ____________
D: ____________
Greatest Value Option:
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.G.A.1
Question Type 6: Decomposing Polygons into Triangle & Trapezoid
Multi-Part Area Decomposition
Teacher Model 6 Figure PQRS: Base PS = 18 cm, PT = 4 cm, QR = 10 cm, height QT = 6 cm.
I DO
P Q R S T 10 cm 6 cm 4 cm Total PS = 18 cm
Part A: Length of segment TS = cm
Part B: Area of \(\triangle PQT\) = sq. cm
Part C: Area of trapezoid QTRS = sq. cm
Part D: Total Area of PQRS = sq. cm
Show work for Parts B, C, & D:
Practice 1 Figure ABCD: Base AD = 16 in., AF = 4 in., BC = 8 in., height BF = 5 in.
YOU DO
A B C D F 8 in. 5 in. 4 in. Total AD = 16 in.
Part A: Length of segment FD = in.
Part B: Area of \(\triangle ABF\) = sq. in.
Part C: Area of trapezoid FBCD = sq. in.
Part D: Total Area of ABCD = sq. in.
Show work for Parts B, C, & D:
Practice 2 Figure WXYZ: Base WZ = 20 m, WK = 5 m, XY = 11 m, height XK = 8 m.
YOU DO
W X Y Z K 11 m 8 m 5 m Total WZ = 20 m
Part A: Length of segment KZ = m
Part B: Area of \(\triangle WXK\) = sq. m
Part C: Area of trapezoid KXYZ = sq. m
Part D: Total Area of WXYZ = sq. m
Show work for Parts B, C, & D:
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.RP.A.1
Question Type 7: Interpreting Ratio Relationships
Multiplicative vs Additive Comparisons
Teacher Model 7 Bakery Batch Ratio Statement:
I DO
A baker is making blueberry muffins and bran muffins. For every 48 blueberry muffins the baker makes, he makes 16 bran muffins. Based on this information, which of the following statements is true?
A. The ratio of bran muffins to blueberry muffins is 48:16 because 48 bran muffins are made for every 16 blueberry muffins.
B. The ratio of bran muffins to blueberry muffins is 48:16 because there are always 32 fewer bran muffins made than blueberry muffins.
C. The ratio of bran muffins to blueberry muffins is 16:48 because 16 bran muffins are made for every 48 blueberry muffins.
D. The ratio of bran muffins to blueberry muffins is 16:48 because there are always 32 fewer bran muffins made than blueberry muffins.
Explain why the wrong options fail (order of terms & subtraction misconception):
Correct Option:
Practice 1 Athletic Hydration Order:
YOU DO
A coach orders 75 bottles of water and 25 bottles of sports drink for field day. Based on this information, which of the following statements is true?
A. The ratio of sports drinks to water bottles is 75:25 because 75 sports drinks are ordered for every 25 water bottles.
B. The ratio of sports drinks to water bottles is 25:75 because 25 sports drinks are ordered for every 75 water bottles.
C. The ratio of sports drinks to water bottles is 25:75 because there are always 50 fewer sports drink bottles ordered than water bottles.
D. The ratio of sports drinks to water bottles is 75:25 because there are always 50 more water bottles than sports drinks.
Explain why the wrong options fail (order of terms & subtraction misconception):
Correct Option:
Practice 2 Library Book Delivery:
YOU DO
A library receives 60 graphic novels and 15 poetry books. Based on this information, which of the following statements is true?
A. The ratio of poetry books to graphic novels is 60:15 because 60 poetry books are received for every 15 graphic novels.
B. The ratio of poetry books to graphic novels is 15:60 because there are always 45 fewer poetry books received than graphic novels.
C. The ratio of poetry books to graphic novels is 15:60 because 15 poetry books are received for every 60 graphic novels.
D. The ratio of poetry books to graphic novels is 60:15 because there are always 45 fewer graphic novels than poetry books.
Explain why the wrong options fail (order of terms & subtraction misconception):
Correct Option:
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.G.A.4
Question Type 8: Cube Nets & Surface Area to Edge Length
Formula: \(SA = 6s^2 \implies s = \sqrt{SA \div 6}\)
Teacher Model 8 Nets and Cube Surface Area:
I DO
Part A: Which net can be folded into a cube?
Net 1
Net 2
Part B: Surface Area Calculation
The surface area of a cube is 96 square centimeters. What is the length of one edge of the cube?
A. 4 cm
B. 8 cm
C. 16 cm
D. 576 cm
Show work (divide by 6 faces, then find square root):
Part A Net:
Part B Edge:
Practice 1 Nets and Cube Surface Area:
YOU DO
Part A: Which net can be folded into a cube?
Net 1
Net 2
Part B: Surface Area Calculation
The surface area of a cube is 150 square inches. What is the length of one edge of the cube?
A. 5 inches
B. 12 inches
C. 25 inches
D. 900 inches
Show work (divide by 6 faces, then find square root):
Part A Net:
Part B Edge:
Practice 2 Nets and Cube Surface Area:
YOU DO
Part A: Which net can be folded into a cube?
Net 1
Net 2
Part B: Surface Area Calculation
The surface area of a cube is 24 square feet. What is the length of one edge of the cube?
A. 2 feet
B. 4 feet
C. 6 feet
D. 144 feet
Show work (divide by 6 faces, then find square root):
Part A Net:
Part B Edge:
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.G.A.1
Question Type 9: Right Trapezoid Area Expressions & Evaluation
Additive & Subtractive Area Models
Teacher Model 9 Right Trapezoid Expressions:
I DO
8 cm 4 cm 14 cm 5 cm
Part A: Which expression(s) find the area? (Select each correct expression)
A. \((8 \times 4) + \frac{6 \times 4}{2}\)
B. \((14 \times 4) - \frac{6 \times 4}{2}\)
C. \((8 \times 4) + (14 \times 5)\)
D. \((14 \times 4) - \frac{1}{2}(6 \times 5)\)
Show computation for Part B (Rectangle + Triangle):
Part A Expressions:
Part B Total Area: sq. cm
Practice 1 Right Trapezoid Expressions:
YOU DO
5 in. 4 in. 9 in. 5 in.
Part A: Which expression(s) find the area? (Select each correct expression)
A. \((5 \times 4) + \frac{4 \times 4}{2}\)
B. \((9 \times 4) - \frac{4 \times 4}{2}\)
C. \((5 + 4) + (9 + 5)\)
D. \((9 \times 4) - \frac{1}{2}(4 \times 5)\)
Show computation for Part B (Rectangle + Triangle):
Part A Expressions:
Part B Total Area: sq. in.
Practice 2 Right Trapezoid Expressions:
YOU DO
7 m 6 m 11 m 7 m
Part A: Which expression(s) find the area? (Select each correct expression)
A. \((7 \times 6) + \frac{4 \times 6}{2}\)
B. \((11 \times 6) - \frac{4 \times 6}{2}\)
C. \((7 \times 6) + (11 \times 7)\)
D. \((11 \times 6) - (4 \times 6)\)
Show computation for Part B (Rectangle + Triangle):
Part A Expressions:
Part B Total Area: sq. m
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.RP.A.1, 6.RP.A.3
Question Type 10: Ratio Error Analysis When Changing Quantities
Constructed Response & Justification
Teacher Model 10 Error Analysis with Pen Counts:
I DO
A box contains only black and blue pens. There are a total of 40 pens in the box. There are 3 black pens for every 2 blue pens. A student removes 1 blue pen and reasons that the ratio of black to blue pens is now 3:1 since \(2 - 1 = 1\).
1. Explain the error in the student's reasoning:
2. Compute the correct ratio of black to blue pens (show actual counts):
Correct New Ratio:
Practice 1 Error Analysis with Fruit Crate:
YOU DO
A fruit crate contains only apples and oranges. There are a total of 35 pieces of fruit. There are 4 apples for every 3 oranges. A student removes 1 orange and reasons that the ratio of apples to oranges is now 4:2 (or 2:1) since \(3 - 1 = 2\).
1. Explain the error in the student's reasoning:
2. Compute the correct ratio of apples to oranges (show actual counts):
Correct New Ratio:
Practice 2 Error Analysis with Trading Cards:
YOU DO
A binder has only baseball and soccer cards. There are a total of 30 cards. There are 3 baseball cards for every 2 soccer cards. A collector removes 1 soccer card and reasons that the ratio of baseball to soccer cards is now 3:1 since \(2 - 1 = 1\).
1. Explain the error in the collector's reasoning:
2. Compute the correct ratio of baseball to soccer cards (show actual counts):
Correct New Ratio:
Grade 6 Math IA Review • Guided & Independent Practice Target Standard: 6.RP.A.1
Question Type 11: Part-to-Part Ratios in Simplest Form
Simplifying Ratios from Totals
Teacher Model 11 Robotics Team Members:
I DO
A school robotics team has 45 members. There are 30 sixth graders and 15 seventh graders on the team. What is the ratio of the number of sixth graders to the number of seventh graders on the team?
A. 1 : 2
B. 30 : 45
C. 2 : 1
D. 15 : 30
Show work & greatest common factor simplification:
Correct Option:
Practice 1 Youth Choir Singers:
YOU DO
A community youth choir has 40 singers. There are 24 sopranos and 16 altos in the choir. What is the ratio of the number of sopranos to the number of altos in the choir?
A. 2 : 3
B. 3 : 2
C. 24 : 40
D. 16 : 24
Show work & greatest common factor simplification:
Correct Option:
Practice 2 Sports Camp Athletes:
YOU DO
A sports camp has 36 athletes. There are 27 soccer players and 9 track runners at the camp. What is the ratio of the number of soccer players to the number of track runners at the camp?
A. 1 : 3
B. 3 : 1
C. 27 : 36
D. 9 : 27
Show work & greatest common factor simplification:
Correct Option:
