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.
Instructions for the proctor and student
- Time limit: 120 minutes. Calculator is not permitted; rulers, fraction bars, and a clock face are. Take a 5-minute break after problem 5.
- Show all work. Drawings, equations, and short written explanations all count.
- Each problem header cites the CCSS-M code(s) the items target.
- 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) \(12 \times 4\)
- 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) \(56 \div 8\)
- Find the missing number:
(i) \(8 \times \square = 56\) (ii) \(\square \times 7 = 42\) (iii) \(63 \div \square = 9\) (iv) \(\square \div 4 = 9\)
- Write a multiplication and a matching division sentence for the fact family with numbers 6, 9, and 54.
- A bookstore has 6 shelves with 8 books on each. How many books in all? Write a multiplication sentence.
- Mr. Patel had 48 crayons. He gives 6 crayons each to some students. How many students received crayons? Write a division sentence.
- 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.
- Multistep: A baker made 5 trays of muffins, with 8 muffins per tray. She sold 27 muffins. How many remain? Solve in two steps.
- 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.
- Round each to the nearest 10 and the nearest 100:
(i) 384 (ii) 156 (iii) 745 (iv) 808 (v) 952
- Find (standard algorithm; show regrouping):
(i) \(347 + 256\) (ii) \(605 - 248\) (iii) \(900 - 467\) (iv) \(412 + 309 + 178\) (v) \(528 + 296\) (vi) \(812 - 379\)
- Multiply by a multiple of 10 (3.NBT.A.3):
(i) \(8 \times 30\) (ii) \(6 \times 90\) (iii) \(5 \times 70\) (iv) \(7 \times 80\)
- 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
- 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.
- 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 \(\dfrac{3}{4}\)
- 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) \(\dfrac{5}{8}\) ___ \(\dfrac{1}{2}\)
- Write each whole number as a fraction (with the named denominator):
(i) 1 = ___ /4 (ii) 2 = ___ /3 (iii) 3 = ___ /5 (iv) 4 = ___ /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 → ___:___
- 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 = ___ - 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. —
The class voted on favorite season:
| Season | Spring | Summer | Fall | Winter |
|---|---|---|---|---|
| Votes | 9 | 14 | 7 | 5 |
- How many students voted in all?
- How many more chose Summer than chose Winter?
- If you make a picture graph with key "★ = 2 votes," how many ★ will represent each season? (You may use half-stars for odd counts.)
- Sketch a bar graph with this data. Use a vertical scale of 2 (each y-axis unit = 2 votes). Label both axes.
- 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
- List three different rectangles (with whole-number side lengths) with area 24.
- A rectangle has area 36 and one side of length 4. Find the other side. Set up the equation \(4 \times \square = 36\).
- 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.
- 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: \(7 \times 12 = 7 \times (10 + 2) = 7 \times 10 + 7 \times 2 = ?\)
- 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
- A rectangle has perimeter 30 and length 11. Find the width.
- A rectangle has perimeter 26 and width 4. Find the length.
- List two different rectangles with perimeter 20 (whole-number sides). Find the area of each. Which has the greater area?
- 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
- 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)
- Each part of (b)(i) represents what fraction of the original rectangle? Of (b)(ii)? Of (b)(iii)?
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.
- \(2 \times 8 = ?\) (1 pt)
- \(6 \times 7 = ?\) (1 pt)
- \(9 \times 4 = ?\) (1 pt)
- \(7 \times 9 = ?\) (1 pt)
- \(8 \times 6 = ?\) (1 pt)
- \(56 \div 7 = ?\) (1 pt)
- \(72 \div 8 = ?\) (1 pt)
- \(45 \div 9 = ?\) (1 pt)