3Rd Grade Diagnostic Math Assessment (1)

Name ______Date ______

3rd Grade Diagnostic Math Assessment (1)

The items in this assessment represent key mathematics standards from 3rd grade. The extent to which you can judge whether a student is actually proficient on the standards depends on the strategy they use to solve each problem. For example, in problem 1, if a student draws 3 pizzas with 6 pieces and counts all the pieces to get 18, they are not proficient on 3.OA.1 or 3.OA.3 as listed in the table below.

The second group of fluency items on p. 6 (below the line) are meant to be timed. Allow 30-45 seconds for students to complete these 15 items. Students are supposed to know all the products of one-digit numbers by the end of third grade, so you would want to do a complete fluency assessment (test all the combinations) several times after spring break, after students have mastered the concepts of multiplication and division and can solve these problems using strategies. A fluency assessment is included at the end of the two summative tests, along with a resource for helping students keep track of which combinations they know and which they have to work on.

There are two items on the computation page that are aligned to 3.OA.4, the ones with the missing divisor. The single digit multiplication combinations generally represent more difficult multiplications, while the related division problems represent some of the easier division combinations.

There are two versions of this test, so you can give it twice during the year. You can easily create additional versions by changing numbers or problem contexts.

Item Number / Common Core standard / Answer / Item Number / Common Core standard / Answer
1 / 3.OA.1 3.OA.3 / 18 / 10 / 3.MD.1 / 11:25 (words are acceptable)
2 / 3.OA.2 3.OA.3 / 3 / 11 / 3.MD.1 2.OA.1 / 25 minutes
3 / 3.OA.3 3.OA.8 3.NBT.3 / 46 / 12 / 3.NBT.2 / 565
4 / 3.OA.8 / b) 800 / 13 / 3.NF.1
3.G.2 / 16
5 / 2.OA.1 / 22 / 14 / 3.NF.3d /
Check student’s drawing
6 / 3.MD.1 2.OA.1 / 70 minutes / 15 / 3.NF.2a / See student’s number line – closer to 1/2 than 0.
7 / 3.OA.8 / 6 / 16 / 3.NF.3b /
8 / 3.OA.2 3.OA.3 / 6 / 17 / 3.MD.8 / 56
9 / 3.MD.7b 3.OA.7 / 72

1. Your class is having a pizza party. You buy 3 pizzas. Each pizza has 6 slices. How many slices is that altogether?

Answer: ______

Write this problem as a number sentence: ______

2. Ted has 15 candy bars. He wants to put them into 5 bags so there are the same number of candy bars in each bag. How many candy bars should go in each bag?

Answer: ______

Write this problem as a number sentence: ______

3. Beth has 4 packs of crayons. Each pack has 10 crayons in it. She also has 6 extra crayons. How many crayons does Beth have altogether?

Answer: ______

4. Estimate the answer: 317 + 495

a) 700 b) 800 c) 850

5. Ted has 65 shells in his collection. Pam gives him some more shells. Now he has 87 shells. How many shells did Pam give him?

Answer: ______

6. On Tuesday, you play soccer after school for 25 minutes. On Wednesday, you play soccer for 45 minutes. How much time did you play altogether on Tuesday and Wednesday?

Answer: ______

7. A baker puts 4 cupcakes in each box. She brings 6 boxes of cupcakes to school for a party. There are 18 people at the party. If each person gets 1 cupcake, how many are left over?

Answer: ______

8. You have 24 cookies. You want to give them to 4 friends so each friend has the same amount. How many cookies would each friend get?

Answer: ______

9. Tommy wants to put new carpet on his floor. He has to figure out how many square feet of carpet he will need. His room is 9 feet long and 8 feet wide, like the drawing below.

How much carpet will he need? Find the area of the floor.

square feet

10. What time is it on the clock? ______

11. You leave your house to go to school at 8:20 am. You get to school at 8:45 am. How long did it take you to get to school?

12. Two schools are getting together for an ice-cream party. One school has 245 children, the other school has 320 children. How many children are there altogether in the two schools?

13. There is one brownie left in this pan.
What fraction of the whole pan of brownies is that?

14. Circle the larger fraction or

Draw a picture to explain your answer.

15. Place a dot on the number line at .

16. Which fraction is the same as ?

a) b) c)

17. Your family is putting a fence around the outside of your garden, to keep out the rabbits. How much fence will you need to go around the whole garden? Find the perimeter of the garden.

62 78 256 178

+8 +16 +305 +532

42 86 563 603

-27 -7 -415 -351

2×8 _____ 5×4 _____ 7×3 _____

4×9 _____ 6×7 _____ 8×5 _____

5×7 _____ 3×9 _____ 5×6 _____

25÷5 _____ 18÷____=6 32÷8 _____

36÷9 _____ 20÷____=4 40÷8 _____

3rd Grade Diagnostic Math Assessment (2)

There are two versions of this test, so you can give it twice during the year. You can easily create additional versions by changing numbers or problem contexts.

Item Number / Common Core standard / Answer / Item Number / Common Core standard / Answer
1 / 3.OA.1 3.OA.3 / 32 / 10 / 3.MD.1 / 1:50 or ten to two (words are acceptable)
2 / 3.OA.2 3.OA.3 / 5 / 11 / 3.MD.1 2.OA.1 / 21 minutes
3 / 3.OA.3 3.OA.8 3.NBT.3 / 57 / 12 / 3.NBT.2 / 83
4 / 3.OA.8 / a) 700 / 13 / 3.NF.1
3.G.2 / 18
5 / 2.OA.1 / 23 / 14 / 3.NF.3d / Check student’s drawing
6 / 3.MD.1 2.OA.1 / 65 minutes / 15 / 3.NF.2a / See student’s number line – half way between 0 and 1/2.
7 / 3.OA.8 / 3 / 16 / 3.NF.3b /
8 / 3.OA.2 3.OA.3 / 7 / 17 / 3.MD.8 / 7
9 / 3.MD.7b 3.OA.7 / 40

1. Your class is having a party. There are 4 plates of brownies. Each plate has 8 brownies on it. How many brownies is that altogether?

Answer: ______

Write this problem as a number sentence: ______

2. Ted has 30 candy bars. He wants to put them into 6 bags so there are the same number of candy bars in each bag. How many candy bars should go in each bag?

Answer: ______

Write this problem as a number sentence: ______

3. Beth has 5 packs of crayons. Each pack has 10 crayons in it. She also has 7 extra crayons. How many crayons does Beth have altogether?

Answer: ______

4. Estimate the answer: 219 + 492

a) 700 b) 800 c) 850

5. Pam has 54 pencils. Justin gives her some more pencils. Now she has 77 pencils. How many pencils did Justin give to Pam?

Answer: ______

6. On Tuesday, you ride your bike after school for 20 minutes. On Wednesday, you ride your bike for 45 minutes. How much time did you spend riding your bike altogether on Tuesday and Wednesday?

Answer: ______

7. A store sells flowers in bunches. There are 5 flowers in each bunch. You buy 4 bunches to give to teachers at your school. There are 17 teachers in your school. You give one flower to each teacher. How many flowers will you have left over?

Answer: ______

8. You have 21 cookies. You want to put them into bags to sell at a bake sale. Each bag should have 3 cookies in it. How many bags will you need?

Answer: ______

9. Tommy wants to put tiles on his floor. He has to figure out how many tiles he will need. Each tile is 1 square foot. His room is 5 feet long and 8 feet wide, like the drawing below.

How many tiles will he need? ______

Write a multiplication equation to show this: ______

10. What time is it on the clock? ______

11. You leave school to walk home at 3:15 pm. You get home at 3:36 pm. How long did it take you to walk home?

12. A food store has 256 cans of soup. They sell 173 cans of soup in one week. How many cans of soup are left in the store?

13. There is one piece of pizza left in this pan.
What fraction of the whole pizza is that?

14. Circle the larger fraction or

Draw a picture to explain your answer.

15. Place a dot on the number line at .

16. Which fraction is the same as ?

a) b) c)

17. This 4-sided figure has a perimeter of 36 inches. Find the length of the missing side.

52 74 754 273

+9 +28 +105 +528

52 88 453 502

- 7 -73 -407 -341

2×8 _____ 5×4 _____ 7×3 _____

4×9 _____ 6×7 _____ 8×5 _____

5×7 _____ 3×9 _____ 5×6 _____

25÷5 _____ 18÷____=6 32÷8 _____

36÷9 _____ 20÷____=4 40÷8 _____

Multiplication fluency assessment

This fluency assessment has two sets of multiplication combinations. Give students 60 seconds to complete the first set of combinations. Ask them to work across the page, not to skip around, and to leave blank any combinations they don’t know. After 60 seconds, ask the students to mark with a slash where they ended, then give them 30 seconds more to finish any others that they can. Adjust these times as necessary as you gain experience with this assessment.

When the 60 second and 30 second time periods are over, ask the students to do problems 1 and 2. These are not timed.

Then repeat the 60 second and 30 second timings for the second set of multiplication combinations. Again, have them put a slash where they finish after 60 seconds.

When the time has elapsed for the second set of multiplication combinations, as students to do problems 3 and 4 plus the divisions at the bottom of that page.

After you have scored and recorded the results, pass the papers back and have students complete the chart of multiplication combinations. Have them circle the combinations that are hard for them to remember. These are the ones they need to work on. A few suggestions for fluency games are on the last two pages, but remember that students need to learn strategies, which lead to fluent retrieval of “math facts.” Most students who struggle with this have a hard time simply trying to memorize all the combinations (although there are a few that they may need to memorize.)

4 x 7 = / 3 x 6 = / 8 x 4 = / 3 x 8 =
3 x 9 = / 5 x 10 = / 7 x 5 = / 8 x 7 =
6 x 8 = / 7 x 6 = / 4 x 4 = / 6 x 5 =
4 x 9 = / 9 x 8 = / 6 x 10 = / 4 x 5 =
8 x 6 = / 5 x 9 = / 7 x 9 = / 9 x 4 =
6 x 3 = / 4 x 8 = / 9 x 6 = / 9 x 7 =
6 x 9 = / 5 x 6 = / 6 x 7 = / 8 x 5 =

1. Fill in the blank to finish each number pattern.

0, 6, 12, 18, ____, 30, ____

0, 9, 18, ____, ____

2. Find the number that makes each sentence true:

7 x ____ = 42 27 ÷ ____ = 3

7 x 3 = / 8 x 4 = / 9 x 5 = / 3 x 4 =
7 x 7 = / 8 x 3 = / 4 x 6 = / 2 x 9 =
8 x 2 = / 5 x 4 = / 7 x 4 = / 5 x 3 =
10 x 4 = / 3 x 2 = / 4 x 8 = / 7 x 8 =
5 x 8 = / 8 x 8 = / 6 x 6 = / 5 x 7 =
9 x 3 = / 5 x 5 = / 3 x 3 = / 8 x 9 =
6 x 2 = / 3 x 7 = / 6 x 9 = / 9 x 9 =