3rd Grade Diagnostic Math Assessment (1)
The items in this assessment represent key mathematics standards from 3 rd 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
5
2.OA.1
22
14
3.NF.3d
1
6
1
3
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
2
8
8
3.OA.2
3.OA.3
6
17
3.MD.8
56
9
3.MD.7b
3.OA.7
72
Name ____________________________________
Date ____________
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:
a) 700
b) 800
317 + 495
c) 850
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 1
Name ____________________________________
Date ____________
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: _____________
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 2
Name ____________________________________
Date ____________
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.
8 feet
9 feet
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?
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 3
Name ____________________________________
Date ____________
13. There is one brownie left in this pan.
What fraction of the whole pan of brownies is that?
14. Circle the larger fraction
1
3
or
1
6
Draw a picture to explain your answer.
15. Place a dot on the number line at
0
1
.
3
1
16. Which fraction is the same as
a)
4
1
b)
2
8
c)
2
1
?
4
2
5
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.
12 feet
16 feet
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 4
Name ____________________________________
Date ____________
62
+8
78
+16
256
+305
178
+532
42
-27
86
-7
563
-415
603
-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 _____
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 5
Name ____________________________________
Date ____________
3rd Grade Diagnostic Math Assessment (2)
The items in this assessment represent key mathematics standards from 3 rd 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
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
5
2.OA.1
23
14
3.NF.3d
1
8
2
Check student’s
6
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
2
6
8
3.OA.2
3.OA.3
7
17
3.MD.8
7
9
3.MD.7b
3.OA.7
40
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 6
Name ____________________________________
Date ____________
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:
a) 700
b) 800
219 + 492
c) 850
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 7
Name ____________________________________
Date ____________
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: _____________
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 8
Name ____________________________________
Date ____________
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.
5 feet
8 feet
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?
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 9
Name ____________________________________
Date ____________
13. There is one piece of pizza left in this pan.
What fraction of the whole pizza is that?
14. Circle the larger fraction
2
6
or
1
6
Draw a picture to explain your answer.
15. Place a dot on the number line at
0
1
.
4
1
16. Which fraction is the same as
a)
3
1
b)
2
6
c)
2
1
?
3
2
4
17. This 4-sided figure has a perimeter of 36 inches. Find the length of the
missing side.
8
?
10
11
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 10
Name ____________________________________
Date ____________
52
+9
74
+28
754
+105
273
+528
52
- 7
88
-73
453
-407
502
-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 _____
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 11
Name ____________________________________
Date ____________
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.)
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 12
Name ____________________________________
4x7=
3x6=
8x4=
3x8=
3x9=
5 x 10 =
7x5=
8x7=
6x8=
7x6=
4x4=
6x5=
4x9=
9x8=
6 x 10 =
4x5=
8x6=
5x9=
7x9=
9x4=
6x3=
4x8=
9x6=
9x7=
6x9=
5x6=
6x7=
8x5=
Date ____________
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
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 13
Name ____________________________________
7x3=
8x4=
9x5=
3x4=
7x7=
8x3=
4x6=
2x9=
8x2=
5x4=
7x4=
5x3=
10 x 4 =
3x2=
4x8=
7x8=
5x8=
8x8=
6x6=
5x7=
9x3=
5x5=
3x3=
8x9=
6x2=
3x7=
6x9=
9x9=
Date ____________
3. What multiplication fact can help you solve 56 ÷ 7 ? ____________
4. What multiplication fact can help you solve 28 ÷ 4 ? ____________
35 ÷ 7 = _____
54 ÷ 9 = _____
21 ÷ 7 = _____
64 ÷ 8 = _____
42 ÷ 6 = _____
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 14
Name ____________________________________
Date ____________
Fill out the multiplication chart below, then circle the number combinations that are hard
for you to remember.
x
2
2
4
3
4
5
6
7
8
9
10
3
4
5
6
7
8
9
10
Write a strategy or clue for remembering each combination that is hard for you.
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 15
Name ____________________________________
Date ____________
Some strategies for multiplying
x0
any number times zero is zero
x1
any number times 1 is itself
x2
doubles – skip count by 2’s – all the even
numbers
x3
skip count by 3’s
x4
double doubles
x5
times 10, then half (e.g. 6 x 5 is 6 x 10, then
half of that)
x 6, 7, 8 many of these are found by the commutative
property (e.g. 6 x 4 = 4 x 6. Then use the
strategy for 4’s)
squares
these are easy and fun to remember
near
square-1 (for any two numbers that are off
neighbors by two, take the square of the number
between them, then subtract 1, e.g. 7 x 5 = 6
x 6 - 1)
x9
the finger method, or remember that the sum
of all multiples of 9 is 9. (18 is 1+8, 27 is
2+7, 36 is 3+6 etc.)
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 16
Name ____________________________________
Date ____________
Fluency games
Multiplication war
Two students play this card game, sitting across from each other. Each student has half of the deck of
cards, which they hold face down. They each turn one card up and put it on the table at the same time,
then the first person who says the product of the two cards gets those cards. (Face cards count as 10.)
The play continues until one player has all the cards.
Be careful how you match kids up, or the game ends quickly!
Students who need work on adding can play this game by shouting out the sum of the two cards.
A good set of flash cards for younger ages is available here:
http://tumblehomelearning.com/product/mixing-in-math-card-games/
The Product Game and Factor Game
Two good online practice games:
http://illuminations.nctm.org/ActivityDetail.aspx?ID=29
http://illuminations.nctm.org/ActivityDetail.aspx?ID=64
You can easily make a board game out of the Product Game if getting online is not easy.
Rollette
Four students play this game, taking turns. The player whose turn it is rolls two dice – one is a standard
die with 1-6, the other is a number cube marked with 3-8. They then mark off the space on their game
board that corresponds to the product (see next page). The first person to mark out all facts on his or
her side of the board is the winner.
If another student thinks the player’s product is wrong, he or she can challenge. If the challenging player
wins, they can mark off any additional product on their board.
The game can be played with two number cubes marked 4-9 for more challenge. Create your own game
board for this.
There are lots of computer fluency games at http://multiplication.com
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 17
Name ____________________________________
Date ____________
From Teaching Learners Who Struggle with Mathematics: Systematic Intervention and Remediation, 2nd
Ed., by Sherman, Richardson and Yard. Published by Merrill/Pearson, 2009. Buy the book! It contains a
wealth of good suggestions for helping struggling learners.
Ingham Intermediate School District, Theron Blakeslee
9-10-13
p. 18