Semester 3B · Original public practice · Internally reviewed; external trial pending
Practice examination marking guide
58 scored practice items, 182 available points.
Practice examination only; this is an original proposed partial-credit rubric, not a standardized score conversion. Allow correct alternative representations or solution methods. Read each item independently before awarding full or partial credit.
Item-by-item criteria
3B-EXAM-001 — 3 points · 42 chairs
Criterion 1 (1 point): Use five groups of 7 to find 35 chairs. Criterion 2 (1 point): Add the sixth group of 7. Criterion 3 (1 point): Conclude 42 chairs.
Five groups of 7 give 35 chairs; another group adds 7, so 35 + 7 = 42.
3B-EXAM-002 — 3 points · 56 plants
Criterion 1 (1 point): Partition seven rows into four and three. Criterion 2 (1 point): Calculate 32 plants and 24 plants. Criterion 3 (1 point): Add to 56 plants.
Four rows have 4 × 8 = 32 plants; three rows have 3 × 8 = 24. Together 32 + 24 = 56.
3B-EXAM-003 — 3 points · No; 7 × 8 = 7 × 5 + 7 × 3 = 56
Criterion 1 (1 point): Identify that 8 × 3 is an invalid term. Criterion 2 (1 point): Correct to 7×5 + 7×3 or an equivalent partition. Criterion 3 (1 point): Calculate and justify 56.
The groups must have the same factor 7 in both pieces: 7 × (5+3) = 35+21 = 56. The proposed second term, 8 × 3, changes the quantity.
3B-EXAM-004 — 3 points · 13 stacks
Criterion 1 (1 point): Model 91 ÷ 7. Criterion 2 (1 point): Calculate 13 complete stacks. Criterion 3 (1 point): Verify 13×7=91.
91 ÷ 7 = 13; 13 × 7 = 91, with no books remaining.
3B-EXAM-005 — 3 points · 72
Criterion 1 (1 point): Recognize 2×9=18. Criterion 2 (1 point): Double to 4×9=36. Criterion 3 (1 point): Double to 8×9=72.
2 × 9 = 18; doubling gives 4 × 9 = 36; doubling again gives 8 × 9 = 72.
3B-EXAM-006 — 3 points · 63
Criterion 1 (1 point): Describe a correct strategy, such as 10×7 minus 7. Criterion 2 (1 point): Evaluate its intermediate product. Criterion 3 (1 point): Obtain 63 and justify the method.
Ten sevens is 70; remove one seven to make nine sevens: 70 − 7 = 63.
3B-EXAM-007 — 3 points · 8 × 6 is larger by 3
Criterion 1 (1 point): Evaluate 8×6=48. Criterion 2 (1 point): Evaluate 9×5=45. Criterion 3 (1 point): Conclude first is larger by 3.
Eight sixes is 48; nine fives is 45. Their difference is 48 − 45 = 3.
3B-EXAM-008 — 3 points · 9 minibuses
Criterion 1 (1 point): Divide 74 by 9, obtaining 8 remainder 2. Criterion 2 (1 point): Explain eight buses cannot carry all children. Criterion 3 (1 point): Conclude nine buses are required.
74 ÷ 9 = 8 remainder 2. Eight full minibuses carry 72 children; two remain, requiring a ninth minibus.
3B-EXAM-009 — 3 points · 4/6
Criterion 1 (1 point): Write 4/6. Criterion 2 (1 point): Explain six equal parts make the same whole. Criterion 3 (1 point): Explain one sixth is one such part.
Four of six equal pieces are colored. The unit fraction 1/6 is the amount in one of those six equal pieces.
3B-EXAM-010 — 3 points · 6/8 (equivalent to 3/4)
Criterion 1 (1 point): Recognize eight equal intervals make each interval 1/8. Criterion 2 (1 point): Label the sixth tick 6/8 or 3/4. Criterion 3 (1 point): Explain why 6/7 counts the intervals incorrectly.
Eight equal intervals span 0 to 1. Each tick adds 1/8, so the sixth tick is 6/8. Counting intervals—not just interior tick marks—sets the denominator.
3B-EXAM-011 — 3 points · 9/11, by 5/11
Criterion 1 (1 point): Identify 9/11 as greater. Criterion 2 (1 point): Compare numerators for equal denominators. Criterion 3 (1 point): Find the difference of 5/11.
With the same whole and denominator, compare numerators: 9 > 4. Difference = (9−4)/11 = 5/11.
3B-EXAM-012 — 3 points · 2/7 < 2/5 < 2/3
Criterion 1 (1 point): Identify 2/7 as smallest. Criterion 2 (1 point): Order 2/7 < 2/5 < 2/3. Criterion 3 (1 point): Explain that larger denominators mean smaller equal pieces.
All have numerator 2. Splitting the same whole into more equal parts makes each part smaller; sevenths are smallest and thirds largest.
3B-EXAM-013 — 3 points · Each equals the same quantity
Criterion 1 (1 point): Identify both fractions on the unit interval. Criterion 2 (1 point): Explain splitting thirds into sixths. Criterion 3 (1 point): Show 2/3=4/6 at the same location.
Dividing each of the three equal thirds into two equal parts creates six parts; four sixths covers the same interval as two thirds.
3B-EXAM-014 — 3 points · 10/16 and 15/24
Criterion 1 (1 point): Multiply both parts by 2 to obtain 10/16. Criterion 2 (1 point): Multiply both parts by 3 to obtain 15/24. Criterion 3 (1 point): Explain that both represent 5/8.
5/8 = (5×2)/(8×2) = 10/16, and (5×3)/(8×3) = 15/24. Multiplying by 1 in fractional form preserves the value.
3B-EXAM-015 — 3 points · 2/3
Criterion 1 (1 point): Identify subtracting five from both parts as invalid. Criterion 2 (1 point): Divide top and bottom by common factor five. Criterion 3 (1 point): Obtain 2/3 with an equivalence explanation.
Subtracting equal amounts does not preserve a fraction. Divide both by their common factor 5 instead: 10/15 = 2/3.
3B-EXAM-016 — 3 points · 3/4
Criterion 1 (1 point): Rename 4/6 as 8/12. Criterion 2 (1 point): Rename 3/4 as 9/12. Criterion 3 (1 point): Conclude 3/4 is larger.
4/6 = 8/12; 3/4 = 9/12. Nine twelfths is greater than eight twelfths.
3B-EXAM-017 — 3 points · No; 4/7 < 3/5
Criterion 1 (1 point): Reject the claim and establish thirty-fifths as common units. Criterion 2 (1 point): Convert 4/7 to 20/35 and 3/5 to 21/35. Criterion 3 (1 point): Conclude 4/7 < 3/5.
4/7 = 20/35; 3/5 = 21/35. Fractions are not ordered by denominator size alone.
3B-EXAM-018 — 3 points · 1/3 L
Criterion 1 (1 point): Represent the remainder as 9/12 minus 5/12. Criterion 2 (1 point): Obtain 4/12 L. Criterion 3 (1 point): Simplify to 1/3 L.
9/12 − 5/12 = 4/12 = 1/3 L; subtract like-sized twelfths.
3B-EXAM-019 — 3 points · 5/8 m
Criterion 1 (1 point): Rename 1/4 m to 2/8 m. Criterion 2 (1 point): Subtract 2/8 from 7/8. Criterion 3 (1 point): Obtain 5/8 m.
1/4 = 2/8; subtract 7/8 − 2/8 = 5/8 m. The fractions refer to the same-sized meter whole.
3B-EXAM-020 — 3 points · 2 m 78 cm
Criterion 1 (1 point): Recall 1 m = 100 cm. Criterion 2 (1 point): Decompose 278 cm into two hundreds and 78. Criterion 3 (1 point): Give 2 m 78 cm.
Two complete groups of 100 cm are 2 meters, leaving 78 cm.
3B-EXAM-021 — 3 points · 2 m 52 cm
Criterion 1 (1 point): Represent 3 m 8 cm as 308 cm or 2 m 108 cm. Criterion 2 (1 point): Subtract 56 cm to get 252 cm. Criterion 3 (1 point): Give 2 m 52 cm.
3 m 8 cm = 2 m 108 cm. Then 108−56=52 cm, so 2 m 52 cm remains.
3B-EXAM-022 — 3 points · 5 km 26 m
Criterion 1 (1 point): Recognize 1 km = 1,000 m. Criterion 2 (1 point): Separate 5,026 into 5,000 and 26. Criterion 3 (1 point): Give 5 km 26 m.
5 groups of 1,000 m make 5 km, with 26 m remaining.
3B-EXAM-023 — 3 points · 3 km 440 m
Criterion 1 (1 point): Convert 4 km 90 m to 4,090 m. Criterion 2 (1 point): Subtract 650 m to get 3,440 m. Criterion 3 (1 point): Express 3 km 440 m.
4 km 90 m = 3 km 1,090 m; 1,090−650=440 m, so 3 km 440 m remains.
3B-EXAM-024 — 3 points · 3 L 75 mL
Criterion 1 (1 point): Recognize 1 L = 1,000 mL. Criterion 2 (1 point): Split 3,075 mL into 3,000 and 75. Criterion 3 (1 point): Express 3 L 75 mL.
Three thousands of milliliters are 3 L, with 75 mL remaining.
3B-EXAM-025 — 3 points · 2 kg 640 g
Criterion 1 (1 point): Recognize 1 kg = 1,000 g. Criterion 2 (1 point): Split 2,640 g into 2,000 and 640. Criterion 3 (1 point): Express 2 kg 640 g.
Two complete 1,000 g units are 2 kg; 640 g remain.
3B-EXAM-026 — 3 points · 3 m 63 cm
Criterion 1 (1 point): Convert to consistent length units. Criterion 2 (1 point): Add 175 cm and 248 cm, then subtract 60 cm. Criterion 3 (1 point): Give 3 m 63 cm.
175 cm + 248 cm = 423 cm; 423−60=363 cm = 3 m 63 cm.
3B-EXAM-027 — 3 points · Radii 4 cm and 7 cm; second circle is larger
Criterion 1 (1 point): Use diameter = 2×radius. Criterion 2 (1 point): Calculate radii 4 cm and 7 cm. Criterion 3 (1 point): Identify the 14-cm-diameter circle as larger.
Each radius is half the diameter. The second radius is larger, so its circle is larger.
3B-EXAM-028 — 3 points · Yes, obtuse
Criterion 1 (1 point): Recognize angle size depends on turn, not ray length. Criterion 2 (1 point): Compare 120° with 90°. Criterion 3 (1 point): Identify the angle as obtuse.
Angle size is the amount of turn between rays. A 120° turn is greater than 90° and less than 180°, regardless of ray lengths.
3B-EXAM-029 — 3 points · Right angle, 90°
Criterion 1 (1 point): Identify the square corner as a right angle. Criterion 2 (1 point): State its measure is 90°. Criterion 3 (1 point): Explain the fit of the corner.
A square corner provides a right-angle reference, which is precisely a quarter turn of 360° or 90°.
3B-EXAM-030 — 3 points · Equilateral; three equal angles
Criterion 1 (1 point): Recognize all three side lengths are equal. Criterion 2 (1 point): Classify the triangle as equilateral. Criterion 3 (1 point): State its three interior angles are equal.
All three sides are equal, so it is equilateral. In Euclidean geometry its three interior angles are equal (each 60°).
3B-EXAM-031 — 3 points · Those two angles are equal
Criterion 1 (1 point): Identify the two equal sides. Criterion 2 (1 point): Identify the opposite angles. Criterion 3 (1 point): Conclude those two angles are equal.
In a triangle, equal sides face equal interior angles. This property is independent of the triangle’s orientation.
3B-EXAM-032 — 3 points · Rhombus yes; square no
Criterion 1 (1 point): Recognize four equal sides permit a rhombus. Criterion 2 (1 point): Recognize a square also requires four right angles. Criterion 3 (1 point): Conclude rhombus yes and square no.
A rhombus has four equal sides. A square also requires four right angles, which this quadrilateral lacks.
3B-EXAM-033 — 3 points · Two circles drawn around one center O; radii correctly labeled 2 cm and 4 cm
Criterion 1 (1 point): Draw both concentric circles with one marked center O. Criterion 2 (1 point): Draw and label radii measuring 2 cm and 4 cm (reasonable ruler tolerance). Criterion 3 (1 point): Explain maintaining the same compass center while changing its opening.
Mark O and keep the compass point fixed at O. Draw the first circle with a 2 cm opening, then draw the second with a 4 cm opening. Label radii from O to both boundaries. Both circles must share O.
3B-EXAM-034 — 3 points · No; tiles must cover the region without gaps or overlaps
Criterion 1 (1 point): Reject counting tiles if they overlap or leave gaps. Criterion 2 (1 point): Explain double-counted overlap and unmeasured gap. Criterion 3 (1 point): State that equal square tiles must cover exactly without gaps/overlaps.
An overlapping tile double-counts some area, while an uncovered corner is not measured at all. Arrange equal square tiles to cover the region exactly once, without gaps or overlaps, before counting.
3B-EXAM-035 — 3 points · 24 cm²
Criterion 1 (1 point): Identify a tiled area rather than linear length. Criterion 2 (1 point): Correct the numeric result to 24. Criterion 3 (1 point): Give and explain square-centimeter unit, cm².
The child counted two-dimensional squares, so the unit must be square centimeters (cm²), not a length unit.
3B-EXAM-036 — 3 points · 8 m
Criterion 1 (1 point): Use area = length × width, so 48 = 6×missing. Criterion 2 (1 point): Compute 48 ÷ 6 = 8. Criterion 3 (1 point): Give missing side as 8 m.
Rectangle area = length × width. Divide 48 m² by 6 m to get 8 m.
3B-EXAM-037 — 3 points · 38 m²
Criterion 1 (1 point): Find area of first nonoverlapping rectangle as 20 m². Criterion 2 (1 point): Find area of second as 18 m². Criterion 3 (1 point): Add to 38 m².
First region 5×4=20 m²; second 3×6=18 m². They do not overlap, so sum 20+18=38 m².
3B-EXAM-038 — 3 points · No; perimeter is 22 cm
Criterion 1 (1 point): Recognize 4×7=28 computes area, not perimeter. Criterion 2 (1 point): Set up 4+7+4+7 or 2(4+7). Criterion 3 (1 point): Compute 22 cm perimeter.
4×7=28 cm² is area. Perimeter = 4+7+4+7 = 22 cm around the boundary.
3B-EXAM-039 — 3 points · 9 cm
Criterion 1 (1 point): Use perimeter = 2(length + width). Criterion 2 (1 point): Find half-perimeter 15 cm. Criterion 3 (1 point): Subtract 6 cm to obtain 9 cm.
Half the perimeter is length + width = 15 cm; subtract width 6 cm to get length 9 cm.
3B-EXAM-040 — 3 points · 16 and 24 square units
Criterion 1 (1 point): Confirm both perimeters equal 20 units. Criterion 2 (1 point): Compute first rectangle area as 16 square units. Criterion 3 (1 point): Compute second area as 24 square units and explain the difference.
Both perimeters equal 2(2+8)=20 and 2(4+6)=20. Areas differ: 2×8=16 and 4×6=24. Equal perimeter need not give equal area.
3B-EXAM-041 — 3 points · 17 days
Criterion 1 (1 point): Convert 2 weeks to 14 days. Criterion 2 (1 point): Add 3 days. Criterion 3 (1 point): Obtain 17 days.
Two weeks equals 2×7=14 days; 14+3=17 days.
3B-EXAM-042 — 3 points · 47 minutes
Criterion 1 (1 point): Count 25 min from 2:35 to 3:00 p.m.. Criterion 2 (1 point): Count 22 min from 3:00 to 3:22 p.m.. Criterion 3 (1 point): Combine to 47 min.
2:35→3:00 takes 25 min; 3:00→3:22 takes 22 min; total 47 min.
3B-EXAM-043 — 3 points · 10:15 a.m.
Criterion 1 (1 point): Identify need to count backward 55 minutes. Criterion 2 (1 point): Regroup through 11:00 a.m.. Criterion 3 (1 point): Conclude 10:15 a.m..
Count backward 10 minutes to 11:00 a.m. and another 45 minutes to 10:15 a.m.
3B-EXAM-044 — 3 points · 45 minutes
Criterion 1 (1 point): Compute 25 min from 11:35 p.m. to midnight. Criterion 2 (1 point): Compute 20 min from midnight to 12:20 a.m.. Criterion 3 (1 point): Combine to 45 min.
11:35 p.m.→midnight takes 25 min; midnight→12:20 a.m. takes 20 min; total 45 min.
3B-EXAM-045 — 3 points · 3:15 p.m.
Criterion 1 (1 point): Add 40 + 15 + 35 = 90 minutes. Criterion 2 (1 point): Convert 90 min to 1 h 30 min. Criterion 3 (1 point): Find finish at 3:15 p.m..
Total duration = 40+15+35 = 90 min (1 h 30 min); 1:45 p.m. + 90 min = 3:15 p.m.
3B-EXAM-046 — 3 points · $6.35
Criterion 1 (1 point): Recognize 100 cents = $1. Criterion 2 (1 point): Convert 600 cents to six dollars. Criterion 3 (1 point): Give $6.35 including remaining 35 cents.
Six groups of 100 cents make $6, and 35 cents remain: $6.35.
3B-EXAM-047 — 3 points · $5.24
Criterion 1 (1 point): Set up $10.00 - $4.76. Criterion 2 (1 point): Compute $5.24. Criterion 3 (1 point): Check $4.76 + $5.24 = $10.00.
$10.00−$4.76=$5.24; check $4.76+$5.24=$10.00.
3B-EXAM-048 — 3 points · $15.63
Criterion 1 (1 point): Align dollars and cents in addition. Criterion 2 (1 point): Regroup 163 cents as $1.63. Criterion 3 (1 point): Obtain $15.63.
Align dollars and cents: 8.95+6.68=15.63. The cents total $1.63, so regroup one dollar.
3B-EXAM-049 — 3 points · $12.27
Criterion 1 (1 point): Set up $15.05 - $2.78. Criterion 2 (1 point): Regroup dollars/cents correctly. Criterion 3 (1 point): Compute $12.27.
In cents: 1,505−278 = 1,227 cents = $12.27. Exchange one dollar to handle the cents.
3B-EXAM-050 — 3 points · $12.50
Criterion 1 (1 point): Compute two-game cost $37.50. Criterion 2 (1 point): Subtract from $50.00. Criterion 3 (1 point): Give $12.50 change.
Cost = $18.75+$18.75=$37.50; $50.00−$37.50=$12.50 change.
3B-EXAM-051 — 4 points · 6 complete rows and 6 extra
Criterion 1 (1 point): Find 6×9=54 students. Criterion 2 (1 point): Divide 54 by 8 to obtain six full rows. Criterion 3 (1 point): Explain remainder six students cannot form a seventh full row. Criterion 4 (1 point): Give 6 complete rows and 6 extra.
6×9=54 students; 54 ÷ 8 = 6 remainder 6. The remainder cannot fill another complete row.
3B-EXAM-052 — 4 points · 5/6
Criterion 1 (1 point): Recognize equal numerator comparison requires same-sized whole. Criterion 2 (1 point): Explain sixths are larger than eighths. Criterion 3 (1 point): Correctly compare 5/6 > 5/8. Criterion 4 (1 point): Provide a valid verbal or visual justification.
With five pieces, sixth-pieces are larger than eighth-pieces; 5/6 > 5/8.
3B-EXAM-053 — 4 points · 7/8 L
Criterion 1 (1 point): Convert one-half to 4/8. Criterion 2 (1 point): Add 4/8 + 3/8. Criterion 3 (1 point): Express the result as 7/8 L. Criterion 4 (1 point): Explain equal denominators refer to equal units.
1/2 = 4/8. Add 4/8+3/8=7/8 L. The denominators represent consistent equal units.
3B-EXAM-054 — 4 points · 1 kg 375 g
Criterion 1 (1 point): Convert 4 kg to 4,000 g. Criterion 2 (1 point): Subtract first use 1,650 g. Criterion 3 (1 point): Subtract second use 975 g. Criterion 4 (1 point): Give 1 kg 375 g.
4,000 g−1,650 g−975 g=1,375 g=1 kg 375 g.
3B-EXAM-055 — 4 points · They are the same size
Criterion 1 (1 point): Convert a 10 cm diameter to radius 5 cm. Criterion 2 (1 point): Recognize second radius is 5 cm. Criterion 3 (1 point): Explain equal radii mean equal-sized circles. Criterion 4 (1 point): State the two circles have equal size.
The circle with 10 cm diameter has radius 5 cm, so both have the same radius. For circles, equal radius means equal size.
3B-EXAM-056 — 4 points · Same grass area; first needs more fencing
Criterion 1 (1 point): Compute both grass areas as 36 m². Criterion 2 (1 point): Compute first perimeter as 26 m. Criterion 3 (1 point): Compute second perimeter as 24 m. Criterion 4 (1 point): Conclude equal grass; first requires 2 m more fence.
Areas 36 m² for both. Perimeters 2(4+9)=26 m and 2(6+6)=24 m; first uses 2 more meters of fence.
3B-EXAM-057 — 4 points · 32 minutes
Criterion 1 (1 point): Find 12 min to midnight. Criterion 2 (1 point): Add 27 min after midnight for 39 total. Criterion 3 (1 point): Deduct 7 min stopped. Criterion 4 (1 point): Conclude moving time 32 min.
Total elapsed 12 minutes to midnight + 27 minutes after midnight =39 minutes; subtract 7 minutes stationary =32 minutes moving.
3B-EXAM-058 — 4 points · $11.95
Criterion 1 (1 point): Subtract $8.85 from $25.00. Criterion 2 (1 point): Subtract an additional $7.70 to obtain $8.45. Criterion 3 (1 point): Add $3.50 received. Criterion 4 (1 point): Conclude $11.95.
Start with $25.00; subtract $8.85 and $7.70 to get $8.45; add $3.50 to get $11.95.