Troy School District · Mathematics · Grade 3
Form A · 120 minutes (with breaks) · 100 points

Grade 3 Mathematics — Testing-Out Examination

A student who passes this examination has demonstrated mastery of the Common Core Grade 3 standards (3.OA, 3.NBT, 3.NF, 3.MD, 3.G) and is eligible to advance directly to Grade 4 Mathematics.

Student Name
Proctor
Score

Instructions for the proctor and student

1. Multiplication and division within 100 10 points
  1. Find each answer (use what you know — no skip-counting on paper):

    (i) \(7 \times 8\)    (ii) \(6 \times 9\)    (iii) \(54 \div 6\)    (iv) \(48 \div 8\)    (v) \(7 \times 7\)    (vi) \(81 \div 9\)

  2. Find the missing number in each:

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

  3. Draw an array (rows and columns of dots) that shows \(4 \times 6 = 24\). Label the rows and columns.
  4. Write a multiplication sentence and a matching division sentence that describe the same fact family for the numbers 5, 8, and 40.
2. Properties of operations and word problems 8 points
  1. Show that \(3 \times 7 = 7 \times 3\) by drawing two different arrays — one with 3 rows of 7, the other with 7 rows of 3. State the property by name (commutative property of multiplication).
  2. Use the distributive property to find \(7 \times 12\) by breaking 12 into \(10 + 2\). Show your work as \(7 \times 10 + 7 \times 2\).
  3. Mr. Patel has 6 boxes of crayons. Each box contains 9 crayons. He gives 4 crayons to each of 12 students. How many crayons does Mr. Patel have left? Solve in two steps; write a number sentence for each step.
  4. List all the factor pairs of 24. (A factor pair is two whole numbers whose product is 24.)
3. Place value, rounding, and addition / subtraction within 1000 12 points
  1. Write 472 in expanded form (e.g., \(400 + 70 + 2\)).
  2. Round each number to the nearest 10 and the nearest 100:

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

  3. Use the standard way (the algorithm) to find each answer. Show regrouping clearly.

    (i) \(347 + 256\)     (ii) \(605 - 248\)     (iii) \(900 - 467\)     (iv) \(412 + 309 + 178\)

  4. Multiply by a multiple of 10:

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

4. Fractions — unit fractions, equivalence, on the number line 10 points
  1. Shade a circle to show \( \dfrac{3}{4} \). Then shade a rectangle to show \( \dfrac{2}{6} \). Label each part.
  2. On a number line drawn from 0 to 1, place tick marks for fourths and label \( \dfrac{1}{4}, \dfrac{2}{4}, \dfrac{3}{4} \). Then mark \( \dfrac{6}{8} \) on the same number line and explain why it lands at the same point as \( \dfrac{3}{4} \).
  3. Compare each pair using \(<\), \(>\), or \(=\). Explain with a fraction model or by reasoning about the size of pieces:

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

  4. A whole number can also be written as a fraction. Write each as a fraction with a denominator of 4: 1, 2, 3.
  5. Marisol ate \( \dfrac{2}{6} \) of a pizza. Her brother ate \( \dfrac{2}{4} \) of the same-size pizza. Who ate more? Explain with a drawing.
5. Multistep word problems 12 points
  1. A bookstore has 8 shelves. Each shelf holds 24 books. How many books can the store hold? Write a number sentence and solve.
  2. Mrs. Kim brings 145 stickers to class. She gives 8 stickers to each of the 16 students. How many stickers are left? Solve in two steps with number sentences.
  3. A bakery sells muffins in boxes of 6. The bakery sold 9 boxes on Monday and 7 boxes on Tuesday. How many muffins were sold in all? Solve in two steps.
  4. A school is planting trees. They plant 23 trees per row in 8 rows. How many trees in all?
  5. Sam saved $4 each week for 9 weeks. He spent $17 of his savings on a video game. How much money does Sam have left?

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

6. Area and perimeter 12 points
  1. A rectangle is 7 units long and 5 units wide. Find its area and its perimeter. Show how you found each.
  2. Find the area of a rectangle by tiling: a 4-by-6 rectangle is filled with 1-unit squares. How many squares fit? What multiplication sentence shows this?
  3. A rectangle has area 24 square units. List three different pairs of side lengths that give this area (using whole numbers).
  4. A rectangle has area 18 square units and one side length of 3 units. Find the other side length. Write the equation \(3 \times \square = 18\).
  5. A composite figure is made by joining a 5-by-3 rectangle to a 2-by-3 rectangle along a 3-unit side. Sketch the figure. Find its total area by adding the two parts. Then find its perimeter by tracing the outside.
7. Time, mass, and liquid volume 10 points
  1. A movie starts at 2:35 p.m. and lasts 1 hour 47 minutes. At what time does it end? Show your work — first hours, then minutes (regroup if needed).
  2. It is now 9:18 a.m. How long until 10:05 a.m.? Write in minutes.
  3. A bag of rice has a mass of 2 kg 350 g. A second bag has 1 kg 875 g. Find the total mass in kg and grams.
  4. A pitcher holds 1 L 250 mL of juice. After pouring 4 cups (each 200 mL), how much juice is left? Convert if needed and answer in mL.
  5. Sketch a clock face showing 7:45.
8. Data — bar graphs and picture graphs 10 points

A class voted on their favorite fruit. The bar graph shows the results.

FruitAppleBananaOrangeGrapeOther
Number of votes912584
  1. How many students voted in all?
  2. How many more students chose Banana than chose Orange?
  3. Which fruit got exactly 4 fewer votes than Banana?
  4. If you were to make a picture graph using a key of "★ = 2 votes," how many ★ would represent Banana?
  5. Make a small bar graph or picture graph showing this data, labeling axes and giving it a title.
9. Categories of shapes & equal partitioning 8 points
  1. Sort these shapes into the categories quadrilateral, parallelogram, rhombus, rectangle, square, trapezoid. (One shape may belong to several categories.) Explain each in one phrase using the defining property:

    (i) a 4-sided figure with all sides equal and four right angles    (ii) a 4-sided figure with two pairs of parallel sides and four right angles, but not all sides equal    (iii) a 4-sided figure with exactly one pair of parallel sides    (iv) a 4-sided figure with all sides equal but no right angles

  2. Partition each shape into 4 equal areas in two different ways. (Sketch each way.):

    (i) a square     (ii) a rectangle (non-square)

  3. What fraction of the original shape is each part in (b)?
10. Multistep problem — class garden 8 points

A 3rd-grade class is planting a small rectangular garden 6 ft long and 4 ft wide. Each plant needs a 1-foot-by-1-foot square space. The class plants tomatoes, peppers, and carrots.

  1. Find the area of the garden.
  2. How many plants can fit in the garden? Explain using the area.
  3. The class wants to plant equal numbers of tomatoes, peppers, and carrots in the 24 squares. Can they divide 24 into three equal groups? If so, how many of each?
  4. If a fence is to be built around the garden, how many feet of fence are needed? (Find the perimeter.)