Mathematics Supplement

Anchor the 10× / 1⁄10 relationship and read place value through thousandths.

Part 1 — 10-times and 1/10 relationships

1. In 4,444, the value of the 4 in the hundreds place is _____ times the value of the 4 in the tens place.
2. In 88,888, the value of the 8 in the tens place is _____ of the value of the 8 in the hundreds place.
3. In 7,777, the value of the 7 in the thousands place is _____ times the value of the 7 in the hundreds place.
4. In 5,555, the value of the 5 in the ones place is _____ of the value of the 5 in the tens place.
5. In 333,333, the 3 in the ten-thousands place is _____ times the 3 in the thousands place.

Part 2 — Place value to thousandths

1. In 2.456, the digit 5 is in the _____ place and has a value of _____.
2. In 0.789, the digit 9 is in the _____ place and has a value of _____.
3. In 3.142, the digit in the hundredths place is _____ and its value is _____.
4. In 7.085, the digit in the thousandths place is _____ and its value is _____.
5. Write in standard form: 4 ones + 2 tenths + 7 hundredths + 9 thousandths = ______.

Part 3 — Word problems

1. Maria has a bag of 100 pennies arranged in 10 equal stacks. How many in each stack? Explain how this shows the 1/10 relationship.
2. Carlos says: 'In 6,600, the 6 in the thousands place is 10 times the 6 in the hundreds place.' Is he correct? Show why.

Scoring: Practice — not scored. Use Part 1 to diagnose 10× understanding before Quiz 1.1.

Word ↔ standard form, comparison, and rounding for decimals to thousandths.

Part 1 — Write each decimal in word form

1. 0.6
2. 0.45
3. 0.123
4. 7.05
5. 12.408

Part 2 — Standard form

1. three and four tenths
2. two hundredths
3. seventy-five thousandths
4. eight and ninety-two hundredths
5. one and three hundred forty-five thousandths

Part 3 — Compare with <, >, =

1. 0.4 ___ 0.40
2. 0.567 ___ 0.576
3. 1.23 ___ 1.230
4. 0.08 ___ 0.080
5. 3.45 ___ 3.405
6. 0.999 ___ 1.0

Part 4 — Round

1. Round 4.378 to the nearest tenth.
2. Round 0.892 to the nearest hundredth.
3. Round 12.456 to the nearest whole number.
4. Round 7.205 to the nearest tenth.

Scoring: Practice — not scored.

Evaluate and write expressions with parentheses, brackets, and braces.

Part 1 — Evaluate

1. 6 + (3 × 4) =
2. (8 − 3) × 5 =
3. 12 ÷ (1 + 2) =
4. (15 − 9) + (4 × 2) =
5. 3 × (10 − 4) + 2 =
6. 24 ÷ (8 − 4) =
7. 5 + [(3 × 2) + 4] =
8. [(12 ÷ 4) + 5] × 2 =
9. {[(6 + 2) × 3] − 4} =
10. 20 − [(3 + 2) × 2] =

Part 2 — Write the expression and solve

1. Add 6 and 4. Then multiply by 3.
2. Subtract 5 from 12. Then divide by 7.
3. Multiply 8 by 4. Add 6 to the result.
4. A team scored 12 points in Q1 and 8 in Q2. In Q3 they doubled what they scored in Q2. Write an expression for the total after three quarters and evaluate it.

Scoring: Practice — not scored.

Friday quiz — 10 problems on place value, comparison, and rounding.

1. In 7,777, the value of the 7 in the hundreds place is _____ times the 7 in the tens place.
2. Write 0.348 in word form.
3. Write three and forty-seven thousandths in standard form.
4. Which is greater: 0.65 or 0.605?
5. Compare: 4.32 ___ 4.320.
6. Round 6.482 to the nearest tenth.
7. Round 0.957 to the nearest hundredth.
8. In 5.286, what is the value of the 6?
9. Order from least to greatest: 0.7, 0.07, 0.707, 0.077.
10. A coin is 0.135 cm thick. Round to the nearest hundredth of a centimeter.

Scoring: 10 problems · 8/10 = Meets (3) · 9–10 = Exceeds (4) · 6–7 = Developing (2) · ≤5 = Beginning (1).

Count unit cubes, then move to V = l × w × h with conceptual prompts.

Part 1 — Count unit cubes

1. 3 long × 2 wide × 1 tall = _____ cubic units.
2. 4 × 3 × 2 = _____ cubic units.
3. 5 × 2 × 3 = _____ cubic units.
4. 6 × 4 × 1 = _____ cubic units.
5. 2 × 2 × 2 = _____ cubic units.

Part 2 — Volume by formula V = l × w × h

1. l=5, w=4, h=3
2. l=8, w=2, h=5
3. l=10, w=6, h=4
4. l=7, w=7, h=7

Part 3 — Conceptual

1. Why is volume measured in cubic units instead of square units?
2. A box has volume 24 cm³. Give three different sets of l, w, h (whole numbers).

Scoring: Practice — not scored.

Order of operations and rectangular-prism volume in 10 problems.

1. Evaluate: 5 + (3 × 4) =
2. Evaluate: (12 − 4) ÷ 2 =
3. Evaluate: [(8 + 2) × 3] − 5 =
4. Evaluate: {[(6 × 2) + 4] ÷ 2} =
5. Write an expression for: 'Multiply 7 by 4, then add 5.' Solve.
6. Volume of a prism with l=6, w=3, h=4.
7. A box from 36 unit cubes with base 6 × 2: how tall?
8. Volume of a cube with side 5.
9. Why is the volume of a 10×2×1 prism the same as 5×4×1? Explain.
10. Write the expression: 'Add 6 and 3, then multiply by the difference of 8 and 5.' Solve.

Scoring: 10 problems · same 4-point rubric as Quiz 1.1.

15-problem quarter assessment covering place value, expressions, and volume.

1. In 88,888, the 8 in the thousands place is _____ times the 8 in the hundreds place.
2. Write 12.063 in word form.
3. Write 'five and two hundred eight thousandths' in standard form.
4. Compare: 3.4 ___ 3.40.
5. Order from greatest to least: 1.5, 1.05, 1.55, 1.505.
6. Round 7.428 to the nearest tenth.
7. Round 0.099 to the nearest hundredth.
8. Evaluate: (15 − 6) × 2 =
9. Evaluate: [(4 + 5) × 2] + 6 =
10. Evaluate: 18 ÷ (1 + 2) + 4 =
11. Write the expression: 'Subtract 4 from 12, then divide by 2.' Solve.
12. Volume with l=5, w=3, h=2.
13. A box has volume 48 with base 4 × 3. How tall?
14. In 6.247, what digit is in the thousandths place and what is its value?
15. Hector says (8 + 2) × 3 equals 8 + 2 × 3. Is he correct? Explain.

Scoring: 15 problems · 12/15 (80%) = Meets · keep result for portfolio.

Builds 2×2 → 3×2 → 3×3 fluency, then applies in word problems.

Use the standard algorithm. Show your work.

Part 1 — 2-digit by 2-digit

1. 34 × 27
2. 56 × 43
3. 78 × 19
4. 62 × 85

Part 2 — 3-digit by 2-digit

1. 456 × 23
2. 729 × 38
3. 305 × 47
4. 218 × 64

Part 3 — 3-digit by 3-digit

1. 234 × 156
2. 512 × 248
3. 703 × 109

Part 4 — Word problems

1. A theater has 24 rows of 38 seats. How many seats?
2. A factory makes 156 widgets/hour. How many in 24 hours?
3. 145 boxes × 72 pencils each = how many pencils?

Scoring: Practice — not scored.

10 problems including 3-digit × 3-digit and three multi-step contexts.

1. 47 × 36
2. 83 × 25
3. 256 × 18
4. 419 × 27
5. 624 × 53
6. 187 × 245
7. 503 × 126
8. A bakery sells 234 loaves/day. How many in 28 days?
9. 175 boxes × 48 markers each = ?
10. Carlos drives 67 miles/day. How many in 365 days?

Scoring: 10 problems · 8/10 = Meets.

3-digit ÷ 2-digit through 4-digit ÷ 2-digit, with remainder problem-solving.

Show your work. If there is a remainder, write it as 'R'.

Part 1 — 3-digit ÷ 2-digit

1. 468 ÷ 12
2. 675 ÷ 25
3. 532 ÷ 14
4. 819 ÷ 21

Part 2 — 4-digit ÷ 2-digit

1. 2,184 ÷ 24
2. 4,725 ÷ 35
3. 6,084 ÷ 18
4. 5,432 ÷ 16

Part 3 — Word problems

1. 364 students; buses hold 28 each. How many buses?
2. 1,560 apples in bags of 24. Full bags + leftovers?
3. $2,340 raised; boxes of cookies cost $12. How many boxes sold?

Scoring: Practice — not scored.

10 problems on multi-digit division and contextual interpretation.

1. 256 ÷ 16
2. 432 ÷ 12
3. 585 ÷ 15
4. 1,134 ÷ 21
5. 2,562 ÷ 14
6. 3,876 ÷ 17
7. 4,896 ÷ 32
8. 396 students into teams of 18. How many teams?
9. $2,184 split among 24 winners. Each gets $?
10. 2,520 lb cargo in 24-lb boxes. How many boxes?

Scoring: 10 problems · 8/10 = Meets.

Add/subtract unlike-denominator fractions and mixed numbers; apply in context.

Find a common denominator first. Simplify when possible.

Part 1 — Addition

1. 1/2 + 1/3
2. 2/3 + 1/4
3. 3/5 + 2/10
4. 1/6 + 3/8
5. 5/8 + 1/4

Part 2 — Subtraction

1. 3/4 − 1/3
2. 5/6 − 1/2
3. 7/8 − 1/4
4. 4/5 − 2/10
5. 11/12 − 2/3

Part 3 — Mixed numbers

1. 2 1/3 + 1 1/2
2. 3 1/4 + 1 2/3
3. 4 3/4 − 2 1/3
4. 5 1/2 − 1 3/4

Part 4 — Word problems

1. Selena ate 1/4 and her brother ate 1/3 of the same pizza. How much together?
2. Recipe needs 2 3/4 c flour; Marcus added 1 1/3 c. How much more?
3. Jug had 3 1/2 L; 1 3/4 L left. How much used?

Scoring: Practice — not scored.

10 problems on add/subtract fractions and mixed numbers.

1. 1/2 + 1/4
2. 2/3 + 1/6
3. 5/6 − 1/3
4. 3/4 − 2/5
5. 1 1/2 + 2 1/3
6. 4 1/4 − 1 2/3
7. 3/8 + 1/2 + 1/4
8. Nina ran 1/3 mi then walked 1/4 mi. Total?
9. Pitcher had 2 1/2 c juice; 3/4 c poured out. Remaining?
10. Maya needs 1 1/2 c sugar; has 7/8 c. How much more?

Scoring: 10 problems · 8/10 = Meets.

15-problem quarter assessment on multiplication, division, and fractions.

1. 58 × 47
2. 326 × 18
3. 425 × 213
4. 672 ÷ 14
5. 3,234 ÷ 22
6. 4,851 ÷ 33
7. 1/3 + 1/4
8. 7/8 − 1/4
9. 2 1/2 + 1 3/4
10. 5 1/3 − 2 1/2
11. 24 shelves × 38 books each = ?
12. 2,016 marbles ÷ 18 per bag = ?
13. Pizza cut in 8: Liam ate 1/4, Mia ate 3/8. Combined?
14. Garden 12 ft: 3 1/4 ft tomatoes, 5 1/2 ft peppers. Unplanted?
15. Show the standard algorithm for 245 × 67. Find the product.

Scoring: 15 problems · 12/15 = Meets · keep result for portfolio.

Fraction × whole, fraction × fraction, mixed numbers, then word problems.

Multiply. Simplify when possible.

Part 1 — Fraction × whole number

1. 1/2 × 6
2. 2/3 × 9
3. 3/4 × 8
4. 5/6 × 12

Part 2 — Fraction × fraction

1. 1/2 × 1/3
2. 2/3 × 3/4
3. 3/5 × 5/6
4. 4/7 × 7/8

Part 3 — Mixed numbers

1. 2 × 1 1/2
2. 1 1/3 × 3/4
3. 2 1/2 × 1 2/3

Part 4 — Word problems

1. Recipe needs 2/3 c sugar; Carlos makes 1/2 the recipe. How much sugar?
2. Garden 4 1/2 ft × 2 1/3 ft. Area?
3. 24 students; 3/4 play a sport. How many?

Scoring: Practice — not scored.

Unit fraction ÷ whole, whole ÷ unit fraction, with five contextual problems.

Part 1 — Unit fraction ÷ whole number

1. 1/2 ÷ 4
2. 1/3 ÷ 2
3. 1/4 ÷ 3
4. 1/5 ÷ 4

Part 2 — Whole number ÷ unit fraction

1. 6 ÷ 1/2
2. 8 ÷ 1/4
3. 5 ÷ 1/3
4. 10 ÷ 1/5

Part 3 — Word problems

1. 1/2 yd ribbon cut into 4 equal pieces. Each =?
2. 6 c lemonade; glasses hold 1/2 c. How many glasses?
3. 1/4 lb cheese cut into 3 slices. Each slice =?
4. 8 yd rope cut into 1/4-yd pieces. How many pieces?
5. 1/3 lb chocolate split into 2 portions. Each portion =?

Scoring: Practice — not scored.

10-problem fluency quiz on fraction multiplication and unit-fraction division.

1. 1/3 × 6
2. 3/4 × 12
3. 2/3 × 1/4
4. 5/6 × 3/10
5. 1 1/2 × 4
6. 2 1/3 × 1 1/2
7. 1/4 ÷ 2
8. 8 ÷ 1/2
9. 6 ÷ 1/3
10. Class of 28; 3/4 absent. How many absent?

Scoring: 10 problems · 8/10 = Meets.

All four decimal operations to hundredths with money word problems.

Part 1 — Add and subtract

1. 3.45 + 2.67
2. 5.8 + 1.34
3. 7.92 − 3.45
4. 10.5 − 4.62

Part 2 — Multiplication

1. 0.6 × 0.4
2. 1.2 × 0.5
3. 2.3 × 4
4. 0.25 × 0.4

Part 3 — Division

1. 4.8 ÷ 4
2. 6.25 ÷ 5
3. 12.5 ÷ 2
4. 0.96 ÷ 4

Part 4 — Word problems

1. Jacket $24.99; with tax $26.74. Tax amount?
2. Ran 5.6 mi Mon, 4.85 mi Tue. Total?
3. Strawberry box 2.5 lb. 6 boxes weigh?
4. Marcus has $25.50. 5 markers × $1.45. Remaining?

Scoring: Practice — not scored.

10 problems across +, −, ×, ÷ of decimals to hundredths.

1. 2.45 + 3.67
2. 8.5 + 4.23
3. 9.81 − 3.45
4. 15.6 − 7.85
5. 0.4 × 0.5
6. 1.8 × 4
7. 0.36 × 0.5
8. 5.6 ÷ 4
9. 0.48 ÷ 6
10. Book $12.45; Maya pays $20. Change?

Scoring: 10 problems · 8/10 = Meets.

Single prisms, composite figures, and inverse problems (find missing dimension).

Part 1 — Find the volume

1. l=6, w=4, h=5
2. l=9, w=3, h=7
3. l=12, w=8, h=5
4. Cube with side 6

Part 2 — Composite figures

1. Prism A: 4 × 3 × 5; Prism B: 2 × 3 × 5. Total?
2. Stacked: bottom 6 × 4 × 3, top 6 × 4 × 2. Total?

Part 3 — Word problems

1. Tank 24 × 12 × 16 in. Volume?
2. Box 8 × 5 × ? = 200 cm³. Height?
3. Container 720 ft³, 12 × 10 × ?. Height?
4. Pool 20 × 10 × 5 ft. Volume?

Scoring: Practice — not scored.

10-problem quiz on volume formula, composites, and inverse problems.

1. Volume with l=5, w=4, h=3
2. Cube with side 4
3. Box vol 60, base 5 × 4. Height?
4. Prism vol 144, base 6 × 4. Height?
5. l=8, w=7, h=6
6. Two prisms 3×2×4 and 5×2×4. Combined?
7. Tank 18 × 10 × 12 in. Volume?
8. Pool 25 × 15 × 4 ft. Volume?
9. Box vol 240 in³, base 8 × 6. Height?
10. Why is volume measured in cubic units? Briefly explain.

Scoring: 10 problems · 8/10 = Meets.

15-problem assessment on fractions, decimals, and volume.

1. 2/3 × 9
2. 3/4 × 1/2
3. 1 1/4 × 2/3
4. 2 1/2 × 1 1/3
5. 1/3 ÷ 4
6. 5 ÷ 1/2
7. 12 ÷ 1/4
8. 6.34 + 2.89
9. 12.5 − 4.67
10. 0.4 × 0.6
11. 7.2 ÷ 4
12. Volume l=9, w=4, h=5
13. Box vol 168, base 7 × 4. Height?
14. Class of 32, 5/8 girls. How many girls?
15. Pitcher 4 c; glasses 1/2 c. How many glasses?

Scoring: 15 problems · 12/15 = Meets · keep for portfolio.

Identify, plot, and measure on the first-quadrant coordinate grid.

Use graph paper. Label the x- and y-axes 0–10. Plot accurately.

Part 1 — Identify ordered pairs

1. 4 right, 7 up. Pair?
2. 6 right, 2 up. Pair?
3. On the x-axis, 5 right of origin. Pair?
4. On the y-axis, 3 up. Pair?
5. Origin's pair?

Part 2 — Plot on graph paper

1. Plot A(3,5), B(7,2), C(0,8), D(5,0).
2. Plot E(2,3), F(8,3), G(8,7), H(2,7) and connect in order. What shape?

Part 3 — Distance on horizontal/vertical lines

1. (2,4) to (7,4): _____ units
2. (3,1) to (3,9): _____ units
3. (0,5) to (6,5): _____ units
4. (4,2) to (4,10): _____ units

Part 4 — Word problems

1. Treasure at (6,8); start at (2,8). How far and which direction?
2. Rectangle (1,2)(5,2)(5,6)(1,6). Length and width?
3. Square: vertices include (3,3) and (7,3), sides parallel to axes. Other two vertices?

Scoring: Practice — not scored.

10 problems on plotting and reading the first-quadrant grid.

1. Pair of the origin?
2. 5 right, 3 up: pair?
3. Plot (4,6). x-coord = ___, y-coord = ___.
4. Distance (1,3) to (8,3)?
5. Distance (2,1) to (2,9)?
6. Rectangle (1,1)(5,1)(5,4)(1,4). Length? Width?
7. On x-axis, 7 right. Coords?
8. On y-axis, 4 up. Coords?
9. A(2,5) to B(8,5) — how far?
10. Plot (3,2)(6,2)(6,5)(3,5). What shape?

Scoring: 10 problems · 8/10 = Meets.

True/false, attribute classification, and hierarchy reasoning for quadrilaterals.

Part 1 — True or false

1. All squares are rectangles.
2. All rectangles are squares.
3. All squares are parallelograms.
4. All parallelograms are quadrilaterals.
5. All rhombuses are parallelograms.
6. A trapezoid is always a parallelogram.

Part 2 — Classify by attributes

1. 4 right angles + 4 equal sides. All categories?
2. 4 right angles, sides NOT all equal. Name?
3. 4 equal sides, no right angles. Name?
4. Exactly 1 pair of parallel sides. Name?
5. Triangle with all sides + angles equal. Name?

Part 3 — Hierarchy

1. Why is every square also a rhombus?
2. Parallelogram → rectangle? Always/sometimes/never. Explain.
3. Rectangle → parallelogram? Always/sometimes/never. Explain.
4. Order most specific → most general: rectangle, polygon, square, quadrilateral, parallelogram.

Scoring: Practice — not scored.

10 problems on the quadrilateral hierarchy.

1. True/false: Every rectangle is a parallelogram.
2. True/false: Every parallelogram is a rectangle.
3. True/false: A square is a rhombus.
4. True/false: All quadrilaterals are polygons.
5. 4 equal sides + 4 right angles → ?
6. 4 sides, opposite sides parallel, no right angles → ?
7. Exactly one pair of parallel sides → ?
8. List all categories a square belongs to.
9. Every rhombus a square? always/sometimes/never.
10. Triangle with three equal sides → ?

Scoring: 10 problems · 8/10 = Meets.

15-problem Q4 assessment with full-year review folded in.

1. Pair: 5 right, 7 up.
2. Plot (2,4)(6,4)(6,8)(2,8). Shape? Length? Width?
3. Distance (1,2) to (9,2)?
4. Distance (5,1) to (5,7)?
5. T/F: Every square is a rectangle.
6. 4 equal sides + 4 right angles — name all categories.
7. Order most general → most specific: square, polygon, quadrilateral, rectangle.
8. 2 1/3 + 1 1/2
9. 4.56 − 1.89
10. 234 × 48
11. 1,728 ÷ 16
12. Volume l=7, w=5, h=3
13. 6 ÷ 1/3
14. Evaluate [(8 + 2) × 3] − 5
15. Round 4.378 to the nearest tenth.

Scoring: 15 problems · 12/15 = Meets.

25-problem cumulative final covering every Q1 + Q2 standard.

1. In 5,555, the 5 in the hundreds place is _____ times the 5 in the tens place.
2. Write 8.357 in word form.
3. Write 'two and forty-six thousandths' in standard form.
4. Compare: 0.6 ___ 0.060.
5. Round 7.892 to the nearest tenth.
6. Evaluate: (12 − 4) × (3 + 2) =
7. Evaluate: [(6 × 4) − 8] ÷ 4 =
8. Volume with l=8, w=3, h=4.
9. 67 × 48
10. 234 × 56
11. 418 × 137
12. 936 ÷ 12
13. 4,032 ÷ 24
14. 5,328 ÷ 18
15. 3/4 + 1/6
16. 5/6 − 1/4
17. 2 1/2 + 3 2/3
18. 6 1/4 − 2 1/2
19. 27 boxes × 64 crayons each = ?
20. 1,134 cookies in boxes of 18. How many boxes?
21. Garden 2 1/2 yd long; rows use 1/4 yd. How many rows? Show reasoning.
22. Maya had 3 1/3 c flour; used 1 1/2 c. Remaining?
23. Prism volume 60 with base 5 × 4. Height?
24. Round 0.0468 to the nearest hundredth.
25. Selena says (2 + 3) × 4 = 2 + 3 × 4. Is she right? Explain.

Scoring: 25 problems · 20/25 (80%) = Meets · keep for portfolio + parent conference.

25-problem cumulative final spanning every Grade 5 math standard.

1. In 7,000, the 7 in the thousands place is _____ times the 7 in the hundreds place.
2. Write 4.625 in word form.
3. Compare: 0.5 ___ 0.50.
4. Round 8.367 to the nearest tenth.
5. Evaluate: (15 − 3) ÷ (1 + 3)
6. Evaluate: [(7 × 3) − 6] × 2
7. 89 × 47
8. 358 × 24
9. 2,205 ÷ 15
10. 5,408 ÷ 26
11. 5/6 + 1/4
12. 4 1/3 − 2 1/2
13. 2/3 × 3/4
14. 1 1/2 × 2 1/3
15. 1/4 ÷ 3
16. 9 ÷ 1/3
17. 5.67 + 8.45
18. 12.4 − 4.85
19. 0.7 × 0.4
20. 8.4 ÷ 4
21. Volume l=10, w=4, h=6
22. Box vol 72, base 6 × 4. Height?
23. Plot (1,2)(5,2)(5,6)(1,6). Shape? Length? Width?
24. T/F: All squares are rectangles. All rectangles are squares.
25. Pizza place sells 234 pizzas/day. How many in 365 days?

Scoring: 25 problems · 20/25 (80%) = Meets · keep for portfolio + parent conference.