64 original questions · eight chapters · all 48 lesson objectives referenced
Practice with feedback. This is an untimed cumulative review. Try each question independently before revealing its explanation. Drawings should be checked with a teacher or tutor.
Convert 4 km 85 m to meters, and 3,250 mL to liters and milliliters.
Each kilometer is 1,000 meters: 4,000+85=4,085. One liter is 1,000 mL, so 3,250 mL is 3 L plus 250 mL.
A path is 2 yd 2 ft long. How many feet is that? How many inches?
Two yards is 6 ft; add 2 ft to make 8 ft; multiply by 12 to obtain 96 inches.
A bag weighs 3 lb 7 oz. Express the weight in ounces. A second bag weighs 43 oz. Which is heavier?
3×16+7=55 oz, and 55−43=12 oz.
A jug holds 2 qt 1 pt. How many cups will it fill?
Each quart is 4 cups and each pint is 2 cups; 2×4+2=10 cups.
A science activity takes 2 min 35 s, then 95 s more. Give the total in minutes and seconds.
2 min 35 s =155 s; 155+95=250 s =4 min 10 s.
A ribbon is 3/4 m long. Find its length in centimeters. Explain what the whole is.
One whole meter is 100 cm. Three of its four equal quarters are 75 cm.
A tank contains 6 L of water. A quarter is used, then 750 mL more. How many mL remain?
A quarter of 6,000 mL is 1,500 mL. Subtract 1,500+750 from 6,000 to get 3,750 mL.
A 4 L tank is half full. You pour in 650 mL. How many milliliters are in it now?
Half of 4,000 mL is 2,000; add 650 to get 2,650.
Draw a rectangle 7 units by 4 units on the grid. Show why its area is 28 square units.
There are four rows of seven equal unit squares (or seven columns of four). 7×4=28.
A rectangular mat has an area of 54 cm² and a width of 6 cm. Find its length.
Area = length×width; 54÷6=9 cm.
A composite floor is a 9 m by 6 m rectangle with a 3 m by 2 m corner removed. Find its area.
The full rectangle is 54 m²; subtract the missing 6 m²: 48 m².
A rectangle is 11 cm long and 4 cm wide. Find the perimeter; identify the linear unit.
11+4+11+4=30 centimeters, not square centimeters.
An L-shaped path has clockwise boundary lengths 8 m, 2 m, 5 m, 3 m, 3 m, and 5 m. Find its perimeter.
Add all six exterior edges: 8+2+5+3+3+5=26 m.
A 12 m × 8 m rectangle has a 5 m × 3 m section removed. Find the remaining area.
12×8=96; 5×3=15; 96−15=81 m².
A rectangular fence surrounds a 13 m by 9 m plot. How many meters are required?
Perimeter=2(13+9)=44 m.
Shade 7 tenths of the strip. Write the value as a fraction and decimal.
Seven of ten equal parts represent 7/10 of one whole, written 0.7.
Place 0.4 and 0.9 on a 0-to-1 number line. Which lies farther right?
Divide the whole interval into ten equal steps; 0.9 is nine steps from 0, farther right.
Write 34/100 as a decimal. Describe how many full tenths and extra hundredths it contains.
34 hundredths can be grouped as 30 hundredths and 4 hundredths.
Explain why 0.6 and 0.60 name the same quantity.
Every tenth is 10 hundredths, so 6×10 = 60 hundredths. Appending zero does not change the value.
Express 0.45 as a fraction in simplest form.
0.45=45/100. Divide numerator and denominator by 5 to get 9/20.
Write 3/4 and 7/20 as decimals.
3/4=75/100=0.75; 7/20=35/100=0.35.
Order 0.8, 0.68, 0.75, and 0.7 from least to greatest.
Rename as hundredths: 68, 70, 75, 80 hundredths.
Round 6.47 to the nearest tenth and explain which two tenths surround it.
6.47 is 0.07 above 6.4 and 0.03 below 6.5; therefore it rounds to 6.5.
A student says 0.4 = 4/100. Explain and correct the claim.
The 4 occupies the tenths place, not the hundredths place.
Write an inequality comparing 0.72 and 0.7, and explain using hundredths.
0.7=0.70, and 72 hundredths >70 hundredths.
Compute 4.6+2.3 and 8.7−5.2. Explain the unit being combined.
Add or subtract ones and tenths: 46 tenths +23 tenths =69 tenths; 87−52 tenths=35 tenths.
Calculate 3.8+5.7. Where does the extra whole come from?
8 tenths+7 tenths=15 tenths; regroup 10 tenths as 1, then add the ones.
Calculate 8.2−3.6 using a place-value exchange.
Rename 8.2 as 7 ones and 12 tenths; 12−6=6 tenths and 7−3=4 ones.
Compute 7.48+3.67. Show why the result is greater than 11.
Hundredths 8+7=15; tenths 4+6+1=11; ones 7+3+1=11, giving 11.15.
Find 1−0.67 and 0.1−0.04.
Rewrite as 1.00−0.67 and 0.10−0.04 to align place values.
Compute 9.02−4.85. Show the exchange across the zero tenths.
Regroup 9.02 as 8 ones, 9 tenths, and 12 hundredths; subtract 4.85 to get 4.17.
A notebook costs $4.75 and a pencil costs $0.89. You pay $10. How much change do you receive?
Total is $5.64; subtract from $10.00 to get $4.36.
A student calculated 1.6+0.85=1.91. Explain the place-value mistake and find the correct result.
1.60+0.85=2.45; the tenths and hundredths must remain aligned.
Find the change from $15 after buying items costing $6.48 and $3.79.
6.48+3.79=10.27; 15.00−10.27=4.73.
Find 0.08×7. Explain using hundredths.
Eight hundredths taken seven times gives 56 hundredths, 0.56.
Find 2.4×6 using an equal-groups or repeated-addition model.
Six groups of 2 ones 4 tenths =12 ones+24 tenths=14.4.
A ribbon is 1.25 m long. Find the length of 24 identical ribbons; give a reasonable estimate.
1.25×(20+4)=25+5=30 m. An estimate such as 1.2×25≈30 checks the result.
Divide 0.72 equally among 8 groups; give the value in each group.
72 hundredths ÷8 =9 hundredths in each group.
Four equal bottles contain 9.6 L altogether. How much is in each?
9.6 L ÷4 =2.4 L. Multiply 2.4×4 to check 9.6.
Compute 5.16÷3. Explain any renaming of tenths as hundredths.
Divide 5 ones among 3; regroup remaining 2 ones into tenths, then regroup tenths as needed: 1.72.
A $23.40 fee is split equally among six students. How much does each pay?
2,340 cents divided by 6 is 390 cents, or $3.90.
A student says multiplying 0.45 by 10 gives 0.450 because a zero is appended. Explain and calculate.
Multiplication by 10 makes each digit worth ten times as much: 0.45×10=4.5.
A water tank has 18.6 L shared equally among three jugs. How much is in each?
18.6÷3=6.2 L; 6.2×3=18.6.
Two rays form the same opening even though one ray is extended. Does the angle get larger? Explain.
The turning amount between the rays stays unchanged when a ray is lengthened.
Use a protractor to measure the marked angle in the diagram. State the measure.
Center the protractor on the vertex, align 0° with the baseline, and read the matching scale at the slanted ray.
Draw a 115° angle with a protractor. Label the vertex and both rays.
Position the protractor at the vertex, mark 115° from the baseline and draw the ray; examiner checks within an agreed tolerance.
Two adjacent angles form a straight angle. One is 73°. Find the other.
Angles on a straight line sum to 180°. Compute 180−73=107°.
The smaller angle between two rays is 125°. What is the reflex angle between them?
A full rotation is 360°; 360−125=235°.
Sketch a 90° turn and a 45° turn. Which is larger, and by how much?
90−45=45; ray lengths do not affect the angle size.
Find x when a straight angle consists of adjacent angles x and 118°.
180−118=62°.
Are the horizontal and vertical grid lines perpendicular? Explain.
Their intersection forms a right angle; perpendicular lines meet at right angles.
Draw two distinct horizontal lines on the grid. Why are they parallel?
Parallel lines in a plane never intersect; these have constant distance apart.
Draw a vertical line n on the grid and a line m perpendicular to it. Then draw a different line p parallel to m.
Use the grid or a set square; the horizontal lines meet the vertical at 90° and remain parallel.
Name one property all rectangles (including squares) share. Explain one way a nonsquare rectangle differs from a square.
A square is a rectangle with all four sides equal; a general rectangle can have unequal adjacent sides.
How many reflection axes does a nonsquare rectangle have? Identify them.
Folding along either midline matches the halves; diagonals are not symmetry axes unless it is a square.
On the grid, draw a point 3 squares to the left of the vertical mirror line, then draw its reflected partner.
Reflect across the vertical axis by keeping equal perpendicular distances.
Explain why two lines that never meet on the page may not be parallel.
Parallel requires the complete extended lines to never meet, not just the visible segments.
Draw one pair of parallel lines and one perpendicular line on the grid. Label both relationships.
Perpendicular pair forms 90°; parallel pair have same direction.
A shape has one vertical mirror axis. A point is 4 grid squares left of it. Where is its image?
A reflection preserves perpendicular distance to the axis.
How many faces, edges, and vertices does a rectangular cuboid have?
There are three pairs of opposite rectangular faces, 12 edges, and eight corners.
Sketch (not to scale) a valid net for a 2 cm × 3 cm × 4 cm cuboid, labeling all six face dimensions.
Opposite faces match, and the six rectangles join along matching lengths with no overlap when folded.
A cuboid is 8 cm by 5 cm by 3 cm. State the area of each pair of opposite faces.
The face dimensions are 8×5, 8×3, and 5×3, with two of each.
A rectangular box has six faces. Are all six faces necessarily squares? Explain.
A 2×3×4 box has rectangular faces of three different shapes.
Why might six rectangles with the correct face sizes still be an invalid cuboid net?
Face count and dimensions are necessary, but a foldable arrangement is also required.