3rd Grade Number & Operations
Informal Assessment Tasks
M.O.3.1.1 read, write, order, and compare numbers to 10,000 using a variety of strategies (e.g.,
symbols, manipulatives, number line).
Third grade students at the above mastery level in mathematics read, write, order, and compare
whole numbers and decimals using manipulatives and number lines.
Third grade students at the distinguished level in mathematics read, write, order, and compare whole
numbers and decimals using symbolic representations.
Task 1
Students are presented word names of numbers. Students identify and/or write the names of the
numbers using numerals (e.g., five thousand eight hundred seventy-six; 5,876).
Task 2
Students are presented number values. Students identify and/or write the word names of the
numbers.
Task 3
Students are presented base-ten models of number values (1-10,000); Students identify and/or write
numerals and word names to identify the numbers represented by the models.
Task 4
Students are shown two or more number values (1-10,000). Students compare the place-values of
the digits in each of the number values. Students use the information obtained from the comparison
of place-values to write the numbers in order from greatest to least and/or least to greatest.
Task 5
Students are shown two number values (1-10,000). Students identify the number of greater and/or
lesser value. Students write a comparison statement (e.g., 6,221>4,156 or 4,156<6,221).
Revised April 2008
Name _________________________ Date __________
M.O.3.1.1 read, write, order, and compare numbers to 10,000 using a variety of strategies (e.g.,
symbols, manipulatives, number line).
1. Write numbers for the following number words.
a. six thousand five hundred ninety-eight
__________
b. two thousand seven hundred one
__________
c. nine thousand twenty-two
__________
d. five thousand four
__________
2. List the numbers above in order from least to greatest.
______________
______________
______________
______________
3. Write the number words for the following numbers.
a.
4,702 ___________________________________
____________________________________
b.
8,590 ___________________________________
____________________________________
c.
6,003 ___________________________________
____________________________________
4. Use the signs (< , >) and the three numbers above to make two comparisons.
__________ < __________ and __________ > __________
Revised April 2008
Name _________________________ Date __________
M.O.3.1.1 read, write, order, and compare numbers to 10,000 using a variety of strategies (e.g.,
symbols, manipulatives, number line).
The buffalo, elephant, rhino, lion and leopard are considered to be the “Big
5” in Africa. Using the chart below, list the animals in order from the
smallest to the largest animal.
Africa’s Big 5
Animal
Weight
Buffalo
1499 pounds
Elephant
13,200 pounds
Leopard
140 pounds
Lion
498 pounds
Rhino
2877 pounds
How did you determine which animal weighed the least?
How did you determine which animal weighed the most?
Revised April 2008
M.O.3.1.2 read, write, order, and compare decimals to hundredths, with manipulatives.
Task 1
Students are presented a base ten-model or diagram of a decimal value (up to hundredths).
a. Students write the decimal notation for the value.
b. Students identify the “face-value,” “place-value,” and “total-value” for each numeral in the
decimal notation of the number.
c. Students write the “word name” for the decimal numeral.
Task 2
Students are presented models for decimal numerals. Students use decimal notation to represent the
values and order them from least to greatest.
Task 3
Students will use the number line to order decimals.
Task 4
Students are presented a base ten-model or diagram of two decimal values (up to hundredths).
Students write a comparison statement for the decimal values (e.g. 3.42>1.13 or 1.13<3.42).
Task 5
Students are given money to make amounts given (e.g., $6.52 and $6.75). Students write comparison
statements.
Task
Students are presented models of a pair of mixed decimal values. Students write comparison
statements (e.g., given a mixed decimal pair 1.32 and 1.7, students write 1.32<1.7 or 1.7>1.32).
Task 7
Shade a hundred-square unit model to represent a decimal.
Revised April 2008
Name __________________________ Date __________
M.O.3.1.2 read, write, order, and compare decimals to hundredths, with manipulatives.
1.
Name the decimals for each shaded model.
a. _______
b. ________
c. ______
2. Use the decimals above to identify the digit and its value for each decimal place.
a.
b.
c.
hundredths place ______ value _______
tenths place
______
value _______
hundredths place
______
value _______
tenths place
______
value _______
hundredths place
______
value _______
tenths place
______
value _______
3. Write the word name for each decimal numeral above.
a.
_____________________________
b.
_____________________________
c.
_____________________________
4. Order the decimals above from greatest to least.
_______
_______
_______
Revised April 2008
Name __________________________ Date __________
M.O.3.1.2 read, write, order, and compare decimals to hundredths, with manipulatives.
You have been comparing the prices of video games at the local store. You
collected the following prices. List the video games from the greatest to the
least based on the price.
Video Game Prices
Video Game
Party Game
Price
$19.82
Puzzles
$14.83
Olympic Games
$34.82
Mystery of the Cave
$27.82
Go Kart
$35.88
How did you determine which game was the most expensive?
How did you determine which game was the least expensive?
Revised April 2008
M.O.3.1.3 identify place value of each digit utilizing standard and expanded form to 10,000.
Third grade students at the above mastery level in mathematics will identify place value of each digit
utilizing standard and expanded form to 100,000.
Third grade students at the distinguished level in mathematics will identify place value of each digit
utilizing standard and expanded form to 1,000,000.
Task 1
Students work in pairs. Each student writes three different 4-digit numbers.
a. The students each exchange one of their numbers with their pair partner. In turn, each pair
partner correctly reads the exchanged number, and identifies the “face-value,” “placevalue,” and “total-value” of each digit contained in the number.
b. The process of exchanging and reading numbers continues until all six of the 4-digit
numbers have been thoroughly read and discussed.
Task 2
Students work in pairs. Students take turns writing and discovering each others’ numbers.
a. One student (A) writes a 4-digit numeral and tells the pair partner the digits that were used
to write the numeral (e.g., “I used the digits 2-5.”)
b. b. The pair partner (B) may ask questions (limit ten) that can be answered with a “yes” or
“no” to try to discover the value and location of each digit in the 4-digit numeral.
c. A variation of this activity may have (A) give clues about their number.
Task 3
Students are presented a set of clues describing a 4-digit numeral. Students use the clues to write the
4-digit numeral.
For example:
a. All of the digits are even numbers greater than zero.
b. The tens-digit has a total-value of sixty.
c. The total-value of the whole number is less than four thousand.
d. The digit with the largest face-value is in the hundreds place.
e. The face-value of the units digit is double the face-value of the thousands digit.
Task 4
Students are presented a 4-digit numeral (e.g., 3,468).
a. Students generate clues to describe the “face-value,” “place-value,” and “total-value” of the
digits used to write the numeral.
b. Students play “guess my number” using clues similar to those described above to help
classmates discover their number.
Task 5
Students are given a set of 4-digit numbers (e.g., 2345, 4617, and 7926).
a. Students identify the number with the smallest total value.
Revised April 2008
b. Students identify the number having the greatest “face-value” and “total-value” in the
hundreds place.
c. Students identify the number with the largest “face-value” in the units place.
d. Students round each of the numbers to the nearest thousand; nearest hundred; and,
nearest ten.
Task 6
Use this group of numbers {8590, 1605, 4090, 5478} to answer the questions below.
a. Identify the number that has a zero in the “tens place.”
b. Identify the number that has a 5 in the “thousands place.”
c. Identify the number that has a 4 in the “hundreds place.” _____________
Task 7
Study this number 38,076. Complete the table provided below.
Numeral
0
3
6
7
8
Face Value
Place Value
Total Value
3
ten thousands
30,000
a. Write 38,076 in expanded form.
Revised April 2008
Name __________________________ Date __________
M.O.3.1.3 identify place value of each digit utilizing standard and expanded form to 10,000.
1. Given the number or expanded form, fill in the table below for the digit “4” in each number.
Number
Place
Value
Expanded form
3,497
4000+500+6
9,724
1000+800+40
4,108
Revised April 2008
M.O.3.1.4 apply estimation skills (rounding, benchmarks, compatible numbers) to solve and evaluate
reasonableness of an answer.
Task 1
Students are presented a table listing population totals for selected major cities across the United
States. Students round the population totals to the nearer thousand. Students answer questions
involving computation, using estimation.
Task 2
Students are presented a table listing mountain elevations around the world (or across the United
States). Students round the elevations to the nearest thousand feet. Students answer questions
involving computation, using estimation.
Revised April 2008
Name __________________________ Date __________
M.O.3.1.4 apply estimation skills (rounding, benchmarks, compatible numbers) to solve and evaluate
reasonableness of an answer.
The workmen are going to build new shelves for the biography section of the library. The library has
1487 biography books. Each shelf will hold 150 books. About how many shelves will the workmen
need to build? Show how your determined your answer.
Revised April 2008
Name __________________________ Date __________
M.O.3.1.4 apply estimation skills (rounding, benchmarks, compatible numbers) to solve and evaluate
reasonableness of an answer.
1. Round the 3,748 to nearer 10, 100, 1000.
To nearer 10:
3,748 is between 3,7_____ and 3,7_____.
3,748 is closer to _______________.
3,748 rounded to nearer 10 is ________________.
To nearer 100:
3,748 is between 3,_____ and 3,_____.
3,748 is closer to _________________.
3,748 rounded to nearer 100 is _______________.
To nearer 1000:
3,748 is between __________ and ___________.
3,748 is closer to _________________.
3,748 rounded to nearer 1000 is _________________.
2. Round each number to nearer 10, 100, 1000.
2,359 __________ __________ __________
8,071 __________ __________ __________
6,596 __________ __________ __________
Revised April 2008
M.O.3.1.5 demonstrate an understanding of fractions as part of a whole/one and as part of a
set/group using models and pictorial representations.
Third grade students at the above mastery level in mathematics will use pictorials and symbolic
representations to compare fractions as parts of a whole and part of a set.
Third grade students at the distinguished level in mathematics will use symbolic representations to
compare fractions as parts of a whole and part of a set.
Task 1
Students use drawings, unifix cubes, and paper folding to model examples of fractional parts of a
whole and/or a collection.
Task 2
Students use fraction towers and fraction circles to model and identify examples of fractional parts of
a whole.
Task 3
Students are presented diagrams of geometric shapes partitioned into fractional parts (e.g., circle or
rectangle divided into eight congruent parts). Students shade the diagram to represent specified
fractional parts of the whole.
Task 4
Students are presented sets of counters. Students determine the number of counters required to
represent a specified fractional part of the entire set (e.g., given twenty counters, students determine
how many counters are needed to represent a half, a fourth, a fifth, or a tenth of the set).
Task 5
Students are presented an “egg carton” or “cup cake pan.” Students discuss and describe situations
that would represent fractional parts of a whole carton or pan. (e.g., When would the carton or pan be
two-thirds full?)
Task 6
Students are presented pictures, diagrams, or groups of objects that depict fractional parts of a whole
and/or a group. Students identify the fractions depicted by the pictures and diagrams.
Task 7
Students are presented pictures, diagrams, and groups of objects that depict a whole. Students draw
lines or form groupings that represent specified fractional parts of the whole or group.
Task 8
Students are presented groups of objects representing a whole. Students identify the number of
objects that constitute a designated fraction of the group whole. (e.g., one-sixth of twelve is 2.)
Task 9
Revised April 2008
Place students in groups (10-24). Ask students to separate the group into two halves, three thirds,
and four fourths, five fifths, ten tenths, etc. (Teacher Note: Students should discuss why the fractional
parts of some groups cannot be formed.)
Revised April 2008
Name __________________________ Date __________
M.O.3.1.5 demonstrate an understanding of fractions as part of a whole/one and as part of a
set/group using models and pictorial representations.
You and 5 of your friends are going to share a pizza while you watch a movie. Your mother is going
to cut the pizza into five pieces. Sam decides that he doesn’t want any and says that he will give his
piece to you. Your mother said, “If Sam does not want any I’ll cut the pizza into five pieces.” What
fraction of pizza will each person get? Draw a picture to illustrate your answer.
Revised April 2008
Name __________________________ Date __________
M.O.3.1.5 demonstrate an understanding of fractions as part of a whole/one and as part of a
set/group using models and pictorial representations.
How many fractions are on a number line between 0 and 1? How do you know your answer is
correct? Use a number line to justify your response.
Revised April 2008
Name __________________________ Date __________
M.O.3.1.5 demonstrate an understanding of fractions as part of a whole/one and as part of a
set/group using models and pictorial representations.
Mrs. Baker asked her students what fractional part of these 16 circles is shaded.
Becky thinks the answer is 12/16.
Tom thinks the answer is 3/4.
Who is correct? How do you know?
Revised April 2008
Name __________________________ Date __________
M.O.3.1.5 demonstrate an understanding of fractions as part of a whole/one and as part of a
set/group using models and pictorial representations.
Name the fraction for the shaded part of each picture.
1.
_________
2.
_________
3.
_________
4.
_________
5.
_________
Revised April 2008
6. Divide the stars in thirds using circles and color 2/3 of the group.
7. Name the fraction for the number of rabbits.
_______ of the animals are rabbits.
Revised April 2008
M.O.3.1.6 create concrete models and pictorial representations to
 compare and order fractions with like and unlike denominators,
 add and subtract fractions with like denominators,
and verify results.
Third grade students at the above mastery level in mathematics will use pictorials and symbolic
representations to compare and order fractions and to add and subtract fractions with like
denominators.
Third grade students at the distinguished level in mathematics will use symbolic representations to
compare and order fractions and to add and subtract fractions with like denominators.
Task 1
Students are presented fraction models representing halves, thirds, fourths, etc. Students compare
the sizes of each fraction model and organize them in ascending and descending order according to
size. Students use fractional notation to represent each fractional model and list the representations
in ascending and/or descending order.
Task 2
Students use fraction models to compare and discuss fractions with like denominators (e.g., one-half
and two-halves, one-third and two-thirds, one-fourth and three-fourths, etc.) Students compare the
sizes of each fraction model and organize them in ascending and descending order according to size.
Students use fractional notation to represent each fractional model and list the representations in
ascending and/or descending order.
Task 3
Students are presented a group of congruent rectangles divided into halves, thirds, fourths, fifths, etc.
A fractional part of each rectangle is shaded. Students write a fraction to represent the shaded area
of each rectangle. Students list the fractions in ascending and/or descending order to represent a
comparison of the sizes of shaded rectangular areas. (Teacher Note: Students should compare and
discuss all of the rectangles, two at a time.)
Task 4
Use fraction bars, fraction circles, and/or other forms of fraction models to help order the fractions
listed below from least to greatest.
a. ⅞, ⅜, ⅛, and ⅝
b. 1¼, ½, ¾, and ¼
Revised April 2008
Name ____________________________ Date __________
M.O.3.1.6 create concrete models and pictorial representations to
 compare and order fractions with like and unlike denominators,
 add and subtract fractions with like denominators,
and verify results.
1. Name each fraction below, then order from least to greatest.







least to greatest
________
________
________
Revised April 2008
 Name __________________________ Date __________
M.O.3.1.6 create concrete models and pictorial representations to
 compare and order fractions with like and unlike denominators,
 add and subtract fractions with like denominators,
and verify results.





1. 5/8
+
2/8
=
______
2. 2/5
+
3/5
=
_____
3. 4/10
+
3/10
=
_____
Revised April 2008
4. 8/9
--
4/9
=
_____
5. 7/7
--
3/7
=
_____
6. 3/4
--
1/4
=
_____
Revised April 2008
Name __________________________ Date __________
M.O.3.1.6 create concrete models and pictorial representations to
 compare and order fractions with like and unlike denominators,
 add and subtract fractions with like denominators,
and verify results.
Use the picture of the blocks to answer the question.
There were 12 blocks on the floor. Denise picked up ½ of the 12
blocks. Nick picked up ¼ of the 12 marbles.
How many blocks were picked up?
What fraction of the 12 marbles was picked up?
Revised April 2008
M.O.3.1.7 use concrete models and pictorial representations to demonstrate an understanding of
equivalent fractions, proper and improper fractions, and mixed numbers.
Task 1
Students are presented fraction towers representing halves, thirds, fourths, etc. Students compare
fraction models to discover models that are equal (e.g. one-half, two-fourths, three-sixths). Students
use fractional notation to write statements of fractional equivalence (e.g., 2/3=4/6).
Task 2
Students are presented fraction circles representing halves, thirds, fourths, etc. Students compare
fraction models to discover models that are equal (e.g., one-half, two-fourths, three-sixths). Students
use fractional notation to write statements of fractional equivalence (e.g., 2/3=4/6).
Task 3
Students are presented a group of congruent rectangles or circles divided into halves, thirds, fourths,
fifths, etc. Students shade the rectangles or circles to model equivalent fractional relationships.
Students use fraction notation to indicate which pairs of rectangles or circles have equivalent shaded
areas.
Task 4
Students are presented a group of objects (e.g., 12, 18, or 24). Students are asked to determine how
many objects would be required to represent various fractional parts of the given group (e.g., halves,
thirds, fourths, sixths, etc.).
a. Students identify fractional parts of the designated group.
b. Students identify equivalent fractional parts of the designated group.
Task 5
Students are provided fraction towers and/or fraction circles. Students use materials to model and
identify proper and improper fractions and mixed numerals. Students use fraction notation to
represent the fractional value of each model.
Task 6
Students are presented an assortment of colored square tiles. Students use the tiles to model and
identify proper and improper fractions and mixed numerals. Students use fraction notation to
represent the fractional value of each model.
Task 7
Students are provided diagrams of rectangles and/or circles divided into fractional parts. Students
shade diagrams to model and identify proper and improper fractions and mixed numerals. Students
use fraction notation to represent the fractional value of each model.
Task 8
Students are presented fractional notation for proper and improper fractions and mixed numerals.
Students use manipulatives and/or draw diagrams to model the presented values.
Revised April 2008
Task 9
Students use models, manipulatives and/or diagrams to demonstrate that some improper fractions
and mixed numerals are equivalent.
Revised April 2008
Name ____________________________ Date __________
M.O.3.1.7 use concrete models and pictorial representations to demonstrate an understanding of
equivalent fractions, proper and improper fractions, and mixed numbers.
Use fraction models pictured below to help determine equivalent
fractional values.
1. 2/4 = n/6
n = ___


2. 6/8 = n/4
n = ___
3. ½ = 5/n
n = ___
Revised April 2008

NAME _________________________ Date _____________
M.O.3.1.7 use concrete models and pictorial representations to demonstrate an understanding of
equivalent fractions, proper and improper fractions, and mixed numbers.
1. Use a fraction manipulative to model the following proper fractions:
a.
3/8
b.
6/7
c.
7/10
d.
5/12
2. Use a fraction manipulative to model the following improper fractions:
a.
9/2
b.
8/3
c.
7/5
d.
11/4
3. Use a fraction manipulative to model the following mixed numbers:
a.
1 1/3
b.
4¾
c.
2½
d.
3 2/5
Revised April 2008
NAME _________________________ Date _____________
M.O.3.1.7 use concrete models and pictorial representations to demonstrate an understanding of
equivalent fractions, proper and improper fractions, and mixed numbers.
Which shaded region (s) show fractions equivalent to ¾?
Figure 1
Figure 2
A.
B.
C.
D.
Figure 1 only
Figure 2 only
Both figure 1 and figure 2
Neither figure 1 nor figure 2
How do you know?
Revised April 2008
M.O.3.1.8 add and subtract 2- and 3-digit whole numbers and money with and without regrouping.
Third grade students at the above mastery level explain procedures used to perform basic
computation with addition, subtraction, multiplication and division.
Third grade students at the distinguished level justify procedures used to perform basic computation
with addition, subtraction, multiplication and division.
Task 1
Students are presented pairs of 2-digit addends. Students estimate the sum and record their
estimate. Students compute the sum of the two addends.
Task 2
Students are presented a pair of 2-digit addends. Students estimate the difference and record their
estimate. Students compute the difference of the two addends.
Task 3
Students are presented a pair of 3-digit addends. Students estimate the sum and record their
estimate. Students compute the sum of the two addends.
Task 4
Students are presented a pair of 3-digit addends. Students estimate the difference and record their
estimate. Students compute the difference of the two addends.
Task 5
Students are presented a 3-digit and a 2-digit addend. Students estimate the sum and/or difference of
the two addends. Students compute the sum and/or difference of the two addends.
Task 6
Students are presented data tables containing 2- and 3-digit number values. Students use addition
and/or subtraction to answer questions related to number values presented in the table.
Task 7
Students are presented a menu price list. Students use the price list to determine the cost of a
selected meal. Students use the price list to determine the difference in cost for selected items.
Task 8
Students are presented price lists from toy or game catalogues. Students use the catalogue
information to determine the sums and/or differences of prices for two or more items listed in the
catalogue.
Revised April 2008
Name __________________________ Date __________
M.O.3.1.8 add and subtract 2- and 3-digit whole numbers and money with and without regrouping.
1. Determine the sums.
a.
423 + 75 = _____
b.
369 + 438 = _____
c.
819 + 125 = _____
d.
$1.22 + $.89 + $1.40 = _____
e.
$2.38 + $1.52 + $4.17 = _____
f.
$7.05 + $0.81 + $1.28 = _____
2. Determine the differences.
a.
78 -- 31 = _____
b.
504 -- 96 = _____
c.
567 -- 325 = _____
d.
800 – 157 = _____
e.
$1.95 -- $0.38 = _____
f.
$7.11 – $6.87 = _____
g.
$2.01 -- $0.99 = _____
Revised April 2008
M.O.3.1.9 demonstrate and model multiplication (repeated addition, arrays) and division (repeated
subtraction, partitioning).
Third grade students at the above mastery level explain procedures used to perform basic
computation with addition, subtraction, multiplication and division.
Third grade students at the distinguished level justify procedures used to perform basic computation
with addition, subtraction, multiplication and division.
Task 1
Students are presented an assortment of colored square tiles or unifix cubes.
a. Students use the tiles or cubes to build “stack models” to represent repeated addition (“two
groups of one,” “three groups of two,” four groups of three,” “five groups of four,” etc.).
Students draw a diagram and write an addition statement to represent each model.
b. Students combine the “stack models” representing a repeated addition to form a
“rectangular model” representing a multiplication (e.g., a “stack model” of four groups of
three would become a 4 by 3 “rectangular model”) Students draw and label a diagram and
write a multiplication statement to represent each “rectangular model.”
Task 2
Students are presented grid paper. Students draw and label diagrams for different “rectangular
models” of the product twelve. (Teacher Note: Use any product that can be represented in more
than one way.)
a. Students write two multiplication sentences related to each diagram.
b. Students write two repeated addition sentences related to each diagram.
c. Students write two division sentences related to each diagram.
d. Students write two repeated subtraction sentences related to each diagram.
Task 3
Students are presented a multiplication fact (e.g., 6 X 8 = 48).
a. Students build “stack models” and “rectangular models” to represent each fact.
b. Students write repeated addition and multiplication sentences to represent each fact.
c. Students write two division statements related to each multiplication fact statement.
Task 4
Students are presented a product which is not a prime number. Students build or draw and label at
least three “rectangular models” that can be used to represent the product. Students use the model to
identify repeated addition facts, multiplication facts, and division facts appropriately associated with
the model.
Revised April 2008
Name ___________________________ Date ___________
M.O.3.1.9 demonstrate and model multiplication (repeated addition, arrays) and division (repeated
subtraction, partitioning).
1.
2.
3.
Write the multiplication fact for each expression. Solve.
a.
5 + 5 + 5 + 5 = _________________________
b.
2 + 2 + 2 + 2 + 2 = ______________________
c.
8 + 8 = _______________________________
Write the multiplication sentence for each addition sentence.
a
45 + 45 = _____________________________
b.
77 + 77 + 77 + 77 + 77 + 77 = _____________
c.
68 + 68 + 68 = _________________________
Write the division fact for each expression. Solve.
a.
27 – 9 = 18, 18 – 9 = 9, 9 – 9 = 0 ________________
b.
18 – 3 = 15, 15 – 3 = 12, 12 – 3 = 9, 9 – 3 = 6, 6 – 3 = 3,
3–3=0
___________________
4.
Write the division sentence for each subtraction sentence.
a.
144 – 24 = 120 – 24 = 96 – 24 = 72 – 24 = 48 – 24 = 24 – 24= 0
____________________
b.
100 – 50 = 50 – 50 = 0
____________________
Revised April 2008
Name ___________________________ Date ___________
M.O.3.1.9 demonstrate and model multiplication (repeated addition, arrays) and division (repeated
subtraction, partitioning).
Sue and Pattie have a bag of 180 gumballs. They want to find the greatest number of gumballs to put
into 12 bags so that each bag will have the same amount.
Sue says they should see how many times they can subtract 12 from 156.
Pattie says they should divide 180 by 12.
Who is correct? Sue, Pattie, both, or neither?
How do you know?
How many gumballs will they put in each bag? Show how you solved the problem.
Revised April 2008
M.O.3.1.10 use and explain the operations of multiplication and division including the properties (e.g.,
identity element of multiplication, commutative property, property of zero, associative property,
inverse operations).
Third grade students at the above mastery level explain procedures used to perform basic
computation with addition, subtraction, multiplication and division.
Third grade students at the distinguished level justify procedures used to perform basic computation
with addition, subtraction, multiplication and division.
Task 1
Students are presented a rectangular model of a product. Students describe how the “a X b”
orientation of the model differs from the “b X a” orientation of the model and determine if the
differences affect the product represented by the model.
Task 2
Students are presented a three dimensional model of the product “a X b X c.” Students describe if
and how the orientation of the model affects the product represented by the model.
Task 3
Write a division statement and a different multiplication statement that are based on this multiplication
statement: 4 x 5 = 20.
____________________
____________________
Task 4
Write a division statement and a different multiplication statement that are based on this multiplication
statement: 8 x 13 = 104.
____________________
_____________________
Task 5
Describe what happens when you multiply zero by any number value.
Task 6
Describe what happens when you multiply a number value by one.
Task 7
Describe why you think the product of 4 X 5 = 2 X 10. Hint: Look at the sentence when it is written in
this form. (2 X 2) X 5 = 2 X (2 X 5).
Revised April 2008
Name __________________________ Date ____________
M.O.3.1.10 use and explain the operations of multiplication and division including the properties (e.g.,
identity element of multiplication, commutative property, property of zero, associative property,
inverse operations).
1.
a.
1 x 6 = ____
b.
234 x 1 = ____
c.
n x 1 = ____
2.
a.
5 x 0 = ____
b.
0 x 78 = _____
c.
n x 0 = ____
3.
Fill in the missing number.
a. 4 X 5 = ___ X 4
c. 2 X ___ = 7 X 2
b. 6 X 3 = 3 X ___
d. ___ X 9 = 9 X 8
4. Fill in the missing number.
a. 2 X (3 X 5) = (2 X __ ) X 5
c. 1 X (6 X 7) = (1 X 6) X __
b. ( __ X 4) X 2 = 6 X (4 X 2)
d. (8 X 5) X __ = (8 X 5) X 9
Revised April 2008
M.O.3.1.11 recall basic multiplication facts and the corresponding division facts.
Task 1
Students work in groups (2-4). Students are provided a spinner or cards with number values
( 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 25). Students take turns using the spinner or randomly
drawing a card. A student spins or draws a number. The student correctly states as many basic
division facts related to the number as he/she can (e.g., student draws or lands on 8; student states:
8 divided by 1 is 8, 8 divided by 8 is 1, 8 divided by 4 is 2, and 8 divided by 2 is 4). The group
monitors the statements for accuracy. The student scores one point for each correctly stated division
fact (e.g., in the example provided, the student would score four points). The game is continued until
each student has had four turns (using the spinner) or all of the cards have been used. (Teacher
Note: the game can be expanded by adding more basic fact products to the spinner and/or cards.)
Task 2
Students work in pairs for this activity. Students are given two number cubes (each with sides 0, 1, 2,
3, 4, 5). Students take turns rolling the cubes and naming/recording the product of the top faces. After
each student has had five turns, the students each determine the sum of their five products. The
student with the greater sum wins that round. The game is repeated.
Revised April 2008
M.O.3.1.12 model the distributive property in multiplication of 2- and 3-digit numbers by a 1-digit
number.
Task 1
Students work in pairs. Students are presented an assortment of base ten blocks and a (2-digit by 1digit) multiplication problem (e.g., 35 X 4). Students represent the multiplication with a base-ten model
of the 2-digit number value X the 1-digit value (e.g., 3 ten-strips and 5 units cubes X 4).
a. Students represent the product using base-ten blocks (e.g., 12 ten-strips and 20 unit
cubes).
b. Students trade base-ten blocks to simplify the model (e.g., 12 ten-strips traded for
hundreds-square and two ten-strips; 20 units cubes traded for 2 ten-strips.
c. Students determine the value of the base-ten model and report a numerical answer for the
multiplication problem (e.g., 140).
d. Students verify the answer by constructing a rectangular model of the product on grid paper
and determining the number of squares in the model (e.g., students draw a 4 X 35
rectangle on grid paper; the rectangle can be partitioned into 12 groups of ten and 4 groups
of five; this is equivalent to 14 groups of ten or 140).
Task 2
Students are presented grid paper and a (3-digit by 1-digit) multiplication problem (e.g., 354 X 2.)
a. Students represent the multiplication with a base-ten diagram of the 3-digit number value X
the 1-digit numeral (e.g., 3 hundreds-squares, 5 ten-strips and 4 units cubes X 2).
b. Students represent the product using base-ten diagrams and numerals (e.g., 6 hundredssquares, 10 ten-strips, and 8 unit cubes).
c. Students simplify the base-ten representation of the product (e.g., replace 10 ten-strips to
get a new diagram of 7 hundreds-squares and 8 unit cubes).
d. Students determine the value of their base-ten diagram and report a numerical answer for
the multiplication problem.
e. Students verify the answer using repeated addition (e.g., 354 + 354 = 708).
Task 3
Students are presented a place-column table and (2-digit by 1-digit) multiplication problem (e.g., 54 X
Students use the place-column table and represent the multiplication problem as the product of an
expanded 2-digit numeral times a 1-digit number (e.g., [5 (10) + 4 (1)] X 3 (1)).
a. Students represent the product using the place-column table (e.g., 15 (10) and 12 (1)).
b. Students rename the base-ten representation of the product (e.g., replace 15 (10) with
1(100) and 5(10) and replace 12 (1) with 1(10) and 2 (1)).
c. Students determine the value of their place-column representations and report a numerical
answer for the multiplication problem (e.g., 162).
d. Students verify the answer using repeated addition (e.g., 54 + 54 + 54 = 162).
Task 4
Students are presented a place-column table and a (3-digit by 1-digit) multiplication problem (e.g.,
245 X 3).
a. Students create a place-column heading and represent the multiplication problem as the
product of an expanded 3-digit numeral times a 1-digit number (e.g., [2 (100) + 4 (10) + 5
(1)] X 3 (1)).
Revised April 2008
b. Students represent the product using the place-column table (e.g., 6 (100), 12 (10), and 15
(1)).
c. Students rename the base-ten representation of the product (e.g., replace 12 (10) with
1(100) and 2(10) and replace 15 (1) with 1(10) and 5 (1)).
d. Students determine the value of their place-column representations and report a numerical
answer for the multiplication problem (e.g., 735).
e. Students verify the answer using repeated addition (e.g., 245 + 245 + 245 = 735).
Revised April 2008
M.O.3.1.13 use models to demonstrate division of 2- and 3-digit numbers by a 1-digit number.
Task 1
Students work in pairs. Students are presented an assortment of base ten blocks and a (2-digit by 1digit) division problem (e.g., 35 ÷ 3)
a. Students represent the division with a base-ten model of the 2-digit number value divided
by the 1-digit value (e.g., 3 ten-strips and 5 unit cubes ÷ 3)
b. Students represent the quotient using base-ten blocks (e.g., 1 ten-strip and 1 unit cube with
2 cubes left over).
c. Students determine the value of the base-ten model and report a numerical answer for the
multiplication problem (e.g., 11 R 2).
d. Students verify the answer using repeated subtraction (e.g., 35-11-11-11 leaves 2).
Task 2
Students are presented a place-column table and (2-digit by 1-digit) division problem (e.g., 53 ÷ 4)
a. Students use the place-column table and represent the division problem as the quotient of
an expanded 2-digit numeral divided by a 1-digit number (e.g., [5 (10) + 3 (1)] ÷ 4 (1)).
b. Students represent the quotient using the place-column table (e.g., 1(10) + R [10 + 3] ÷
4(1)).
c. Students rename the base-ten representation of the product (e.g., replace 1(10) + R [10 +
3] ( 4 with 1(10) + 3 (1) + R 1.
d. Students determine the total value of the place-column representation of the quotient and
report a numerical answer for the multiplication problem (e.g., 13 R 1).
e. Students verify the answer using repeated subtraction (e.g., 53-13-13-13-13 = 1).
Task 3
Students work in pairs. Students are presented assortment of base ten blocks and a (3-digit by 1digit) division problem (e.g., 435 ÷ 2).
a. Students represent the division with a base-ten model of the 3-digit number value divided
by the 1-digit value (e.g., 4 hundred-squares 3 ten-strips and 5 units cube ÷ 2.
b. Students represent the quotient using base-ten blocks (e.g., 2 hundred-squares + 1 tenstrip + 7 unit cubes R 1).
c. Students determine the value of the base-ten model and report a numerical answer for the
multiplication problem (e.g., 217 R 1).
d. Students verify the answer using repeated subtraction (e.g., 435-217-217 = 1).
Task 4
Students are presented a place-column table and a (3-digit by 1-digit) division problem (e.g., 245 ÷ 3)
a. Students create a place-column heading and represent the division problem as the quotient
of an expanded 3-digit numeral divided by a 1-digit number (e.g., [2 (100) + 4 (10) + 5 (1)] ÷
3 (1)).
b. Students represent the partial quotients using the place-column table (e.g., 6(10) + 2 (10)
+1 (1) + R 2).
c. Students rename the base-ten representation of the product (e.g., replace 6 (10) + 2 (10) +
1(1) + R 2 with 8 (10) + 1(1) + R 2.
d. Students determine the value of their place-column representations and report a numerical
answer for the division problem (e.g., 81 R 2).
e. Students verify the answer using repeated subtraction (e.g., 245-81-81- 81=2).
Revised April 2008
Name _______________________ Date _______________
M.O.3.1.13 use models to demonstrate division of 2- and 3-digit numbers by a 1-digit number.
Use a place value mat and place value blocks to solve the following division problems.
1.
32 ÷ 2 = _____
6. 96 ÷ 4 = _____
2.
47 ÷ 3 = _____
7. 80 ÷ 8 = _____
3.
615 ÷ 5 = _____
8. 96 ÷ 3 = _____
4.
408 ÷ 7 _____
9. 828 ÷ 4 _____
5.
600 ÷ 6 _____
10. 563 ÷ 2 = _____
Revised April 2008
M.O.3.1.14 create grade-appropriate real-world problems involving any of the four operations using
multiple strategies, explain the reasoning used, and justify the procedures selected when presenting
solutions.
Third grade students at the distinguished level in mathematics will create and analyze gradeappropriate real-world problems justifying the solution and processes in clear, concise manner.
Name___________________________ Date____________
The Surprise Party
You are planning a surprise birthday party for your mother. The local party store has
the following items for sale:
Plates
packages of 10 for $3.00
Cups
packages of 20 for $5.09
Napkins
packages of 50 for $3.20
Balloons 1 balloon for $4.05
Birthday Cake
$12.53
Create a problem to help you determine how much it will cost for your mother’s party.
After you have written the problem, show how someone might solve the problem.
Explain their reasoning and justify the procedures they selected to use.
Rubric
The Surprise Party
Distinguished Level
Above Mastery Level
Mastery Level
Partial Mastery Level
Novice
Exceeds the objects of this task. Demonstrates a
high level of understanding. Student is able to
justify solution and processes in a clear, concise
manner.
Meets the objectives of this task. Student is able
to justify the procedures used.
Meets the objectives of this task.
Partially meets the objectives of the task. The
student is able to solve the problem, but has
difficulty explaining the solution.
The student has difficulty creating the word
problem.
Revised April 2008