Troy School District · Mathematics · Grade 3 · Form B
Standards Drill · 120 minutes · 100 points

Grade 3 Mathematics — Standards-Aligned Skills Examination

A calculation-focused, standards-walkthrough exam covering the CCSS-M Grade 3 standards (3.OA, 3.NBT, 3.NF, 3.MD, 3.G). Each problem cites the standard. Form B complements Form A.

Student Name
Proctor
Score

Instructions for the proctor and student

1. 3.OA.A,B,C · Multiplication and division facts within 100 12 points
  1. Find each multiplication fact (use what you know):

    (i) \(7 \times 8\)    (ii) \(6 \times 9\)    (iii) \(4 \times 7\)    (iv) \(5 \times 9\)    (v) \(8 \times 8\)    (vi) \(7 \times 7\)    (vii) \(3 \times 11\)    (viii) \(12 \times 4\)

  2. Find each division fact:

    (i) \(54 \div 6\)    (ii) \(48 \div 8\)    (iii) \(72 \div 9\)    (iv) \(81 \div 9\)    (v) \(36 \div 4\)    (vi) \(45 \div 5\)    (vii) \(63 \div 7\)    (viii) \(56 \div 8\)

  3. Find the missing number:

    (i) \(8 \times \square = 56\)    (ii) \(\square \times 7 = 42\)    (iii) \(63 \div \square = 9\)    (iv) \(\square \div 4 = 9\)

  4. Write a multiplication and a matching division sentence for the fact family with numbers 6, 9, and 54.
2. 3.OA.D · Word problems and multi-step 10 points
  1. A bookstore has 6 shelves with 8 books on each. How many books in all? Write a multiplication sentence.
  2. Mr. Patel had 48 crayons. He gives 6 crayons each to some students. How many students received crayons? Write a division sentence.
  3. Multistep: Mrs. Lee bought 4 packs of stickers. Each pack has 9 stickers. She gave 12 stickers to her son. How many stickers does Mrs. Lee have left? Solve in two steps with number sentences.
  4. Multistep: A baker made 5 trays of muffins, with 8 muffins per tray. She sold 27 muffins. How many remain? Solve in two steps.
  5. Multistep: A class of 24 students is divided into 4 equal groups. Each group has 3 boys. How many girls are in each group? Solve in two steps.
3. 3.NBT.A · Place value, rounding, +/− within 1000 12 points
  1. Round each to the nearest 10 and the nearest 100:

    (i) 384    (ii) 156    (iii) 745    (iv) 808    (v) 952

  2. Find (standard algorithm; show regrouping):

    (i) \(347 + 256\)    (ii) \(605 - 248\)    (iii) \(900 - 467\)    (iv) \(412 + 309 + 178\)    (v) \(528 + 296\)    (vi) \(812 - 379\)

  3. Multiply by a multiple of 10 (3.NBT.A.3):

    (i) \(8 \times 30\)    (ii) \(6 \times 90\)    (iii) \(5 \times 70\)    (iv) \(7 \times 80\)

4. 3.NF.A · Fractions — unit fractions, equivalence, on the number line 12 points
  1. Shade each fraction in a circle or rectangle:

    (i) \(\dfrac{3}{4}\) of a circle    (ii) \(\dfrac{2}{6}\) of a rectangle    (iii) \(\dfrac{5}{8}\) of a square

  2. On a number line drawn from 0 to 2 marked in fourths, locate \( \dfrac{1}{4},\ \dfrac{3}{4},\ \dfrac{5}{4},\ \dfrac{7}{4},\ \dfrac{8}{4} \). Label each.
  3. Identify equivalent fractions. For each pair, are they equivalent? Explain with a model or by reducing.

    (i) \(\dfrac{2}{4}\) and \(\dfrac{1}{2}\)    (ii) \(\dfrac{3}{6}\) and \(\dfrac{4}{8}\)    (iii) \(\dfrac{2}{3}\) and \(\dfrac{3}{4}\)

  4. Compare each pair using \(<,\ >,\ =\):

    (i) \(\dfrac{1}{4}\) ___ \(\dfrac{1}{6}\)    (ii) \(\dfrac{2}{3}\) ___ \(\dfrac{2}{5}\)    (iii) \(\dfrac{3}{4}\) ___ \(\dfrac{6}{8}\)    (iv) \(\dfrac{5}{8}\) ___ \(\dfrac{1}{2}\)

  5. Write each whole number as a fraction (with the named denominator):

    (i) 1 = ___ /4    (ii) 2 = ___ /3    (iii) 3 = ___ /5    (iv) 4 = ___ /1

5. 3.MD.A · Time and mass / liquid volume 10 points
  1. Tell the time on each clock (to the nearest minute; the proctor can sketch):

    (i) hour hand near 4, minute hand on 6 → ___:___    (ii) hour hand between 7 and 8, minute hand on 9 → ___:___

  2. Time elapsed:

    (i) Start 9:18 a.m., end 10:05 a.m. Elapsed = ___ min
    (ii) A movie starts at 2:35 p.m. and lasts 1 hr 47 min. End time = ___
    (iii) A class begins at 8:45 a.m. and lasts 50 min. End time = ___

  3. Mass and volume:

    (i) A bag of rice has mass 2 kg 350 g; another has 1 kg 875 g. Total = ___
    (ii) A pitcher holds 1 L 250 mL of juice. After pouring 4 cups (each 200 mL), how much juice is left? Convert to mL.
    (iii) A bottle holds 750 mL. Eight bottles hold ___ liters.

— You may take a 5-minute break here. —

6. 3.MD.B · Picture and bar graphs 8 points

The class voted on favorite season:

SeasonSpringSummerFallWinter
Votes91475
  1. How many students voted in all?
  2. How many more chose Summer than chose Winter?
  3. If you make a picture graph with key "★ = 2 votes," how many ★ will represent each season? (You may use half-stars for odd counts.)
  4. Sketch a bar graph with this data. Use a vertical scale of 2 (each y-axis unit = 2 votes). Label both axes.
7. 3.MD.C · Area 12 points
  1. Find the area of each rectangle (count squares or find with the formula):

    (i) 7 by 5    (ii) 8 by 4    (iii) 9 by 6    (iv) square, side 7

  2. List three different rectangles (with whole-number side lengths) with area 24.
  3. A rectangle has area 36 and one side of length 4. Find the other side. Set up the equation \(4 \times \square = 36\).
  4. Composite figure: rectangle A is 6 by 4 attached to rectangle B (3 by 4 along a 4-unit side). Sketch and find the total area.
  5. Apply the distributive property to find area: a 7-by-12 rectangle is split into a 7-by-10 and a 7-by-2 piece. Show: \(7 \times 12 = 7 \times (10 + 2) = 7 \times 10 + 7 \times 2 = ?\)
8. 3.MD.D · Perimeter 8 points
  1. Find the perimeter of each polygon:

    (i) rectangle 7 by 5    (ii) square, side 9    (iii) triangle, sides 8, 11, 14    (iv) regular hexagon, side 6

  2. A rectangle has perimeter 30 and length 11. Find the width.
  3. A rectangle has perimeter 26 and width 4. Find the length.
  4. List two different rectangles with perimeter 20 (whole-number sides). Find the area of each. Which has the greater area?
9. 3.G · Categories of shapes & partitioning 8 points
  1. Classify each polygon:

    (i) 4 sides, 4 right angles, all sides equal    (ii) 4 sides, two pairs of parallel sides, four right angles, but not all sides equal    (iii) 4 sides, exactly one pair of parallel sides    (iv) 4 sides, all equal, no right angles    (v) 3 sides, all equal

  2. Partition each shape into the named number of equal areas (sketch):

    (i) a rectangle into 4 equal areas    (ii) a circle into 6 equal areas    (iii) a triangle into 3 equal areas (along height)

  3. Each part of (b)(i) represents what fraction of the original rectangle? Of (b)(ii)? Of (b)(iii)?
10. 3.OA.A.7 · Multiplication fluency drill 8 points

The student must find each answer in 30 seconds or less (proctor times). Award 1 point for each correct, quick answer; 0.5 for correct but slow; 0 for incorrect.

  1. \(2 \times 8 = ?\)    (1 pt)
  2. \(6 \times 7 = ?\)    (1 pt)
  3. \(9 \times 4 = ?\)    (1 pt)
  4. \(7 \times 9 = ?\)    (1 pt)
  5. \(8 \times 6 = ?\)    (1 pt)
  6. \(56 \div 7 = ?\)    (1 pt)
  7. \(72 \div 8 = ?\)    (1 pt)
  8. \(45 \div 9 = ?\)    (1 pt)