3B-REVIEW-0012 points
Find 6 × 8 by starting with five groups of eight. Explain the extra group.
Reveal worked explanation
Answer: 48
5 × 8 = 40. One additional group contains 8, giving 40 + 8 = 48.
Semester 3B · Original public practice · Internally reviewed; external trial pending
Cumulative semester review
74 original review questions spanning Chapters 8–15 with optional worked explanations.
Original cumulative review for Chapters 8–15: 74 questions worth 196 optional practice points. Untimed; work on paper and check each explanation only after trying the question. The review is grouped by topic to help identify gaps.
Chapter distribution
| Chapter | Questions | Points |
|---|---|---|
| Chapter 8: Multiplication and Division with 6–9 | 11 | 28 |
| Chapter 9: Fractions — Part 1 | 7 | 20 |
| Chapter 10: Fractions — Part 2 | 10 | 26 |
| Chapter 11: Measurement | 10 | 26 |
| Chapter 12: Geometry | 10 | 26 |
| Chapter 13: Area and Perimeter | 10 | 26 |
| Chapter 14: Time | 8 | 22 |
| Chapter 15: Money | 8 | 22 |
CHAPTER 8
Multiplication and Division with 6–9
11 questions; try each before revealing feedback.
3B-REVIEW-0022 points
Calculate 7 × 6 by breaking seven groups into 5 groups and 2 groups.
Reveal worked explanation
Answer: 42
(5 × 6) + (2 × 6) = 30 + 12 = 42. Both parts represent all seven groups.
3B-REVIEW-0032 points
Compute 6 × 9 in two different ways and explain why they agree.
Reveal worked explanation
Answer: 54
6 × (10 − 1) = 60 − 6 = 54; or (5 × 9) + 9 = 45 + 9 = 54. Both partition the same groups.
3B-REVIEW-0042 points
Share 84 counters equally among 7 groups. How many counters in each group?
Reveal worked explanation
Answer: 12
Because 7 × 12 = 84, each group contains 84 ÷ 7 = 12.
3B-REVIEW-0052 points
Find 8 × 7 by doubling 4 × 7.
Reveal worked explanation
Answer: 56
4 × 7 = 28. Doubling the number of groups doubles the total: 28 + 28 = 56.
3B-REVIEW-0062 points
Use 10 × 8 to calculate 9 × 8.
Reveal worked explanation
Answer: 72
10 × 8 = 80. Remove one group of 8: 80 − 8 = 72.
3B-REVIEW-0072 points
A shelf has 8 rows of 9 books. Determine the total using an area or equal-group model.
Reveal worked explanation
Answer: 72 books
Eight equal groups of nine give 8 × 9 = 72 books. An 8-by-9 array has the same 72 cells.
3B-REVIEW-0082 points
There are 75 pencils. Put 8 in each box. How many full boxes and how many remain?
Reveal worked explanation
Answer: 9 full boxes; 3 pencils remain
8 × 9 = 72, and 75 − 72 = 3. The remainder 3 is less than 8.
3B-REVIEW-0514 points
A theater has 8 rows of 7 seats. Six seats are empty. How many people are seated?
Reveal worked explanation
Answer: 50
The eight rows hold 8×7=56 seats in total. Six seats are empty, so 56−6=50 people are seated.
3B-REVIEW-0524 points
Find 9 × 12 using 10 × 12 and a subtraction.
Reveal worked explanation
Answer: 108
10×12=120; remove one twelve: 120−12=108.
3B-REVIEW-0534 points
83 students are arranged in groups of 8 for an activity. How many full groups and extras?
Reveal worked explanation
Answer: 10 groups and 3 extra
83 = 8×10 + 3; the remainder is less than 8.
CHAPTER 9
Fractions — Part 1
7 questions; try each before revealing feedback.
3B-REVIEW-0092 points
A rectangle is divided into 8 equal parts and 3 are shaded. What fraction is shaded? Explain the denominator.
Reveal worked explanation
Answer: 3/8
The whole has eight equal parts, so the denominator is 8; three are shaded, so the numerator is 3.
3B-REVIEW-0102 points
The interval from 0 to 1 is divided into 5 equal steps. What fraction is at the third tick after zero?
Reveal worked explanation
Answer: 3/5
Each step is 1/5 of the unit interval; three equal steps from zero reach 3/5.
3B-REVIEW-0112 points
Compare 5/9 and 7/9 with <, =, or >. Explain.
Reveal worked explanation
Answer: 5/9 < 7/9
Both fractions refer to ninths of the same-sized whole, and five ninths is less than seven ninths.
3B-REVIEW-0122 points
Which is larger, 3/5 or 3/8? Explain why a larger denominator does not mean a larger amount.
Reveal worked explanation
Answer: 3/5
If the whole is the same size, fifths are larger pieces than eighths. Three larger fifth-pieces make more than three eighth-pieces.
3B-REVIEW-0544 points
A shape is partitioned into 10 equal parts. Six are colored. Describe the fraction and why the word equal matters.
Reveal worked explanation
Answer: 6/10
Six of ten same-sized parts is six tenths; unequal pieces would not each be one tenth.
3B-REVIEW-0554 points
Compare 4/7 and 4/9. Explain using the same-sized whole.
Reveal worked explanation
Answer: 4/7 > 4/9
Sevenths are larger pieces than ninths, and both amounts have four pieces.
3B-REVIEW-0564 points
A unit interval is divided into 12 equal parts. Which is farther from zero, the fourth tick or the ninth tick? By what fraction of one unit?
Reveal worked explanation
Answer: Ninth tick; by 5/12
Positions are 4/12 and 9/12. Subtract 9/12−4/12=5/12 of the unit.
CHAPTER 10
Fractions — Part 2
10 questions; try each before revealing feedback.
3B-REVIEW-0132 points
Shade 1/2 of a strip divided into 6 equal cells. How many cells should be shaded?
Reveal worked explanation
Answer: 3 cells; 3/6
Half of six equal cells is three cells. Thus 1/2 and 3/6 describe the same portion of the same whole.
3B-REVIEW-0142 points
Complete 3/4 = __/12. Explain how the denominator changes.
Reveal worked explanation
Answer: 9/12
Multiply the denominator by 3, so also multiply the numerator by 3: 3 × 3 = 9. Same amount, smaller named parts.
3B-REVIEW-0152 points
Simplify 12/18 and identify the common factor used.
Reveal worked explanation
Answer: 2/3
Divide numerator and denominator by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3. No common factor greater than 1 remains.
3B-REVIEW-0162 points
Compare 3/4 and 5/8 using eighths.
Reveal worked explanation
Answer: 3/4 > 5/8
3/4 = 6/8. Six eighths is greater than five eighths.
3B-REVIEW-0172 points
Compare 5/6 and 7/9 using eighteenths.
Reveal worked explanation
Answer: 5/6 > 7/9
5/6 = 15/18 and 7/9 = 14/18. Therefore 5/6 is larger by 1/18.
3B-REVIEW-0182 points
Calculate 3/10 + 5/10. Express the answer in simplest form.
Reveal worked explanation
Answer: 4/5
3 tenths + 5 tenths = 8/10. Divide top and bottom by 2 to get 4/5.
3B-REVIEW-0192 points
Find 1/2 + 1/4 and draw or describe equal parts.
Reveal worked explanation
Answer: 3/4
Rename 1/2 as 2/4, then 2/4 + 1/4 = 3/4. The whole is divided consistently into fourths.
3B-REVIEW-0574 points
Find 3/6 + 2/6 and simplify if possible.
Reveal worked explanation
Answer: 5/6
Five of six equal parts are shaded. Five and six share no factor >1.
3B-REVIEW-0584 points
What fraction must be added to 5/8 to make one whole?
Reveal worked explanation
Answer: 3/8
One whole is 8/8. The missing part is 8/8−5/8 = 3/8, because the two amounts must combine to a whole.
3B-REVIEW-0594 points
Correct the claim 2/3 + 1/6 = 3/9.
Reveal worked explanation
Answer: 5/6
The parts need a common size: 2/3 = 4/6. Then 4/6+1/6=5/6. Adding denominators is invalid.
CHAPTER 11
Measurement
10 questions; try each before revealing feedback.
3B-REVIEW-0202 points
Convert 4 m 35 cm to centimeters.
Reveal worked explanation
Answer: 435 cm
Four meters is 4×100 = 400 cm. Add 35 cm to get 435 cm.
3B-REVIEW-0212 points
Find 5 m 12 cm − 75 cm. Show the exchange.
Reveal worked explanation
Answer: 4 m 37 cm
Exchange one meter for 100 cm: 5 m 12 cm = 4 m 112 cm. Subtract 75 cm to leave 4 m 37 cm.
3B-REVIEW-0222 points
Convert 3 km 450 m into meters.
Reveal worked explanation
Answer: 3,450 m
One kilometer is 1,000 m; 3,000 m + 450 m = 3,450 m.
3B-REVIEW-0232 points
Calculate 6 km 40 m − 785 m.
Reveal worked explanation
Answer: 5 km 255 m
Regroup 6 km 40 m as 5 km 1,040 m. Then 1,040−785=255 m, giving 5 km 255 m.
3B-REVIEW-0242 points
A pitcher has 2 L 350 mL. How many milliliters is that?
Reveal worked explanation
Answer: 2,350 mL
2 liters = 2,000 mL; add 350 mL to obtain 2,350 mL.
3B-REVIEW-0252 points
Express 4 kg 90 g in grams.
Reveal worked explanation
Answer: 4,090 g
Four kilograms = 4,000 g, and 4,000 + 90 = 4,090 g.
3B-REVIEW-0262 points
A pot has 3 L 200 mL of water. You pour out 850 mL. How much water remains?
Reveal worked explanation
Answer: 2 L 350 mL
3,200 mL − 850 mL = 2,350 mL = 2 L 350 mL. Convert to one unit before subtracting.
3B-REVIEW-0604 points
A tank has 5 L 150 mL, then 750 mL is removed. How much remains?
Reveal worked explanation
Answer: 4 L 400 mL
First convert 5 L 150 mL to 5,150 mL. Subtract 750 mL to get 4,400 mL, which is 4 L 400 mL.
3B-REVIEW-0614 points
What is the difference between 3 kg 25 g and 1 kg 800 g?
Reveal worked explanation
Answer: 1 kg 225 g
Convert both to grams: 3 kg 25 g = 3,025 g and 1 kg 800 g = 1,800 g. Their difference is 1,225 g = 1 kg 225 g.
3B-REVIEW-0624 points
A sign lists distances as 2 km 80 m and 1,350 m. How many meters in total?
Reveal worked explanation
Answer: 3,430 m
First distance is 2,080 m. Add 2,080+1,350=3,430 m.
CHAPTER 12
Geometry
10 questions; try each before revealing feedback.
3B-REVIEW-0272 points
A circle has radius 5 cm. What is its diameter, and why?
Reveal worked explanation
Answer: 10 cm
A diameter passes through the center between two boundary points, so it is twice the radius: 2×5=10 cm.
3B-REVIEW-0282 points
An angle measures 65°. Is it smaller or larger than a right angle? Explain.
Reveal worked explanation
Answer: Smaller (acute)
A right angle is 90°, and 65° < 90°. Ray length does not affect angle size.
3B-REVIEW-0292 points
Classify angles measuring 35°, 90°, and 130°.
Reveal worked explanation
Answer: Acute; right; obtuse
35° is less than 90°, 90° is exactly a right angle, and 130° is between 90° and 180°.
3B-REVIEW-0302 points
A triangle has sides 6 cm, 6 cm, and 4 cm. Classify it by side lengths.
Reveal worked explanation
Answer: Isosceles triangle
Exactly two lengths match (6 and 6), so the triangle is isosceles; the third side is different.
3B-REVIEW-0312 points
True or false: every equilateral triangle is also isosceles if “isosceles” means at least two equal sides. Explain.
Reveal worked explanation
Answer: True under that inclusive definition
An equilateral triangle has three equal sides, so it certainly has at least two equal sides. Naming conventions may distinguish “exactly two” in some classrooms.
3B-REVIEW-0322 points
Is every square also a rectangle? Explain using properties.
Reveal worked explanation
Answer: Yes
A rectangle has four right angles. A square has four right angles and four equal sides, so it satisfies the rectangle definition.
3B-REVIEW-0332 points
Set a compass opening to 3 cm, mark a center O, and draw a circle. Label a radius and write its length.
Reveal worked explanation
Answer: A circle centered at O, with a labeled 3 cm radius
Keep the compass point fixed at O and its opening at 3 cm. Every boundary point is 3 cm from O. Label one segment from O to the boundary as 3 cm.
3B-REVIEW-0634 points
A quadrilateral has four right angles and four equal sides. Give its most specific common name.
Reveal worked explanation
Answer: Square
A square satisfies both the rectangle condition (four right angles) and rhombus condition (four equal sides).
3B-REVIEW-0644 points
A triangle has sides 5 cm, 7 cm, and 9 cm. Classify it by its side lengths.
Reveal worked explanation
Answer: Scalene
All three side lengths differ, so it is scalene. The lengths also satisfy the triangle inequality, since 5+7>9.
3B-REVIEW-0654 points
A circle is drawn using a compass set to 4 cm. How long is a segment across the circle passing through the center?
Reveal worked explanation
Answer: 8 cm
That segment is a diameter, twice the 4 cm radius: 8 cm.
CHAPTER 13
Area and Perimeter
10 questions; try each before revealing feedback.
3B-REVIEW-0342 points
A rectangle covers 5 rows of 4 identical square tiles. Find its area in square tiles.
Reveal worked explanation
Answer: 20 square units
Each of 5 rows contains 4 tiles; 5×4=20 equal square units cover the region without gaps.
3B-REVIEW-0352 points
A rectangle is covered with 3 rows of 6 square-centimeter tiles. What is its area and unit?
Reveal worked explanation
Answer: 18 cm²
3×6=18 tiles, each measuring 1 square centimeter. Area is 18 cm², not 18 cm.
3B-REVIEW-0362 points
Find the area of a 9 cm by 4 cm rectangle.
Reveal worked explanation
Answer: 36 cm²
Nine columns of four square centimeters, or 9×4, give 36 cm².
3B-REVIEW-0372 points
An L-shape fits in an 8×6 square-unit rectangle with a 3×2 rectangle missing from one corner. Find its area.
Reveal worked explanation
Answer: 42 square units
Outer area 8×6 = 48. Remove the missing area 3×2 = 6. Result 48−6=42 square units.
3B-REVIEW-0382 points
A rectangle is 5 cm by 3 cm. Find its perimeter and explain what is measured.
Reveal worked explanation
Answer: 16 cm
Perimeter adds the outside edges: 5+3+5+3 = 16 cm. It is a length.
3B-REVIEW-0392 points
Calculate the perimeter of a rectangle 11 m long and 7 m wide.
Reveal worked explanation
Answer: 36 m
Perimeter = 2(11+7) = 2×18 = 36 m, adding all four sides.
3B-REVIEW-0402 points
Compare two rectangles of dimensions 3×8 and 4×6. Are their areas the same? Are their perimeters?
Reveal worked explanation
Answer: Same area 24; perimeters 22 and 20
Areas: 3×8=24 and 4×6=24. Perimeters: 2(3+8)=22 and 2(4+6)=20. Equal area need not give equal perimeter.
3B-REVIEW-0664 points
A rectangular garden 8 m by 5 m is surrounded by a fence. Find both planting area and fence length.
Reveal worked explanation
Answer: 40 m² and 26 m
Area=8×5=40 m². Perimeter=2(8+5)=26 m.
3B-REVIEW-0674 points
A rectangle is 9 units wide and 4 units high. One 2×3 corner rectangle is removed. Find remaining area.
Reveal worked explanation
Answer: 30 square units
Whole 9×4=36. Corner cutout 2×3=6. Remaining area=36−6=30.
3B-REVIEW-0684 points
A 5×5 square and a 3×9 rectangle both have integer side lengths. Compare their areas and perimeters.
Reveal worked explanation
Answer: Areas 25 and 27; perimeters 20 and 24
5×5=25; 3×9=27. Perimeters are 4×5=20 and 2(3+9)=24.
CHAPTER 14
Time
8 questions; try each before revealing feedback.
3B-REVIEW-0412 points
Convert 3 minutes 25 seconds into seconds.
Reveal worked explanation
Answer: 205 seconds
Three minutes is 3×60=180 seconds; add 25 to obtain 205 seconds.
3B-REVIEW-0422 points
How many minutes pass from 9:20 a.m. to 10:05 a.m.?
Reveal worked explanation
Answer: 45 minutes
From 9:20 to 10:00 is 40 min; from 10:00 to 10:05 is 5 min; total 45 min.
3B-REVIEW-0432 points
A movie starts at 4:15 p.m. and lasts 1 hour 35 minutes. What time does it end?
Reveal worked explanation
Answer: 5:50 p.m.
Add one hour to 5:15 p.m., then 35 minutes to 5:50 p.m.
3B-REVIEW-0442 points
How long is it from 11:50 a.m. to 12:30 p.m.?
Reveal worked explanation
Answer: 40 minutes
11:50 a.m. to noon is 10 min, and noon to 12:30 p.m. is 30 min. Total 40 min.
3B-REVIEW-0452 points
A student reads 25 minutes, rests 10 minutes, and reads another 30 minutes. How much time passes altogether?
Reveal worked explanation
Answer: 65 minutes (1 hour 5 minutes)
The complete schedule includes both reading periods and the rest: 25+10+30=65 minutes.
3B-REVIEW-0694 points
An event begins 10:55 a.m. and lasts 80 minutes. When does it end?
Reveal worked explanation
Answer: 12:15 p.m.
80 minutes is 1 h 20 min. 10:55 a.m. + 1 h =11:55 a.m.; +20 min reaches 12:15 p.m.
3B-REVIEW-0704 points
How many hours are in 2 days 6 hours?
Reveal worked explanation
Answer: 54 hours
Each day is 24 hours, so two days = 48 hours. Add another 6 hours: 48+6 = 54 hours.
3B-REVIEW-0714 points
A music class starts 3:40 p.m., lasts 35 min, rests 10 min, and studies 20 min. When does it finish?
Reveal worked explanation
Answer: 4:45 p.m.
35+10+20=65 minutes = 1 h 5 min. Start 3:40 p.m., finish 4:45 p.m.
CHAPTER 15
Money
8 questions; try each before revealing feedback.
3B-REVIEW-0462 points
Write 4 dollars and 7 cents as a money amount. Explain the zero.
Reveal worked explanation
Answer: $4.07
There are 100 cents in a dollar. Seven cents is 07 in the two cent places, so $4.07 rather than $4.70.
3B-REVIEW-0472 points
You have $6.85. How much more is needed to make $10.00?
Reveal worked explanation
Answer: $3.15
$6.85→$7.00 adds $0.15; $7.00→$10.00 adds $3.00, so total $3.15.
3B-REVIEW-0482 points
Find the total cost of $12.48 and $3.75.
Reveal worked explanation
Answer: $16.23
48 cents + 75 cents = 123 cents = $1.23. Dollars 12+3+1=16; total $16.23.
3B-REVIEW-0492 points
Find $20.00 − $7.86.
Reveal worked explanation
Answer: $12.14
Rename $20.00 as $19 and 100 cents. 100−86=14 cents, 19−7=12 dollars, giving $12.14.
3B-REVIEW-0502 points
You have $40.00. You buy a book for $13.45 and a pen for $2.75. How much remains?
Reveal worked explanation
Answer: $23.80
Total spent $13.45+$2.75=$16.20. Subtract $40.00−$16.20=$23.80.
3B-REVIEW-0724 points
You buy a notebook for $4.65 and a pencil for $1.90. You pay $10.00. Find your change.
Reveal worked explanation
Answer: $3.45
Total spent $6.55; subtract from $10.00 to obtain $3.45.
3B-REVIEW-0734 points
A toy costs $9.99. How many cents more than $9.00 is that?
Reveal worked explanation
Answer: 99 cents
The dollar amounts have the same whole-dollar part. Subtract $9.00 from $9.99 to get $0.99, which is 99 cents.
3B-REVIEW-0744 points
A family buys two sandwiches for $6.75 each and a juice for $2.40. Find the bill.
Reveal worked explanation
Answer: $15.90
2×$6.75=$13.50; add $2.40 to get $15.90.