MADISON PUBLIC SCHOOL DISTRICT
Grade 3 Mathematics
Authored by: Beverly DeFabiis
Updated by: Kathryn Lemerich
Reviewed by: Lee Nittel
Director of Curriculum and Instruction
Updated with Common Core State Standards: Fall 2012
Members of the Board of Education:
Lisa Ellis, President
Patrick Rowe, Vice-President
David Arthur
Kevin Blair
Shade Grahling
Linda Gilbert
Thomas Haralampoudis
James Novotny
Superintendent : Dr. Michael Rossi
Madison Public Schools
359 Woodland Road, Madison, NJ 07940
www.madisonpublicschools.org
I. OVERVIEW
The K-5 mathematics curriculum is to provide students with a strong content base in mathematics while
promoting and instilling the skills of problem solving, communication in mathematics, making mathematical
connections, and reasoning. Throughout the delivery of the K-5 mathematics program, various tools and
technology are employed, including manipulatives, calculators, software, websites, and computers. A strong
focus of the program in on promoting high levels of mathematical thought through experiences which extend
beyond traditional computation. The program is directly correlated to the Common Core State Standards
and is designed to adequately prepare students for the NJ state assessments.
II. RATIONALE
The K-5 mathematics program mission is to provide students with content-specific skills and concepts while
developing problem-solving skills and strategies, communication, and reasoning. Lessons are prepared and
implemented developmentally, sequentially and with the understanding that learning proceeds from concrete
to abstract levels.
III. STUDENT OUTCOMES (Linked to the Common Core State Standards for Mathematics)
Unit 2 Money and Time
Measurement and Data (3.MD)
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of
objects.
3.MD.1: Tell and write time to the nearest minute and measure time intervals in minutes. Solve word
problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on
a number line diagram.
Unit 1 Place Value
Number and Operations in Base Ten (3.NBT)
Use place value understanding and properties of operations to perform multi-digit arithmetic.4
4
A range of algorithms may be used.
3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
Unit 3 Addition and Subtraction
Operations and Algebraic Thinking (3.OA)
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations
with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental
computation and estimation strategies including rounding.3 3This standard is limited to problems posed with
whole numbers and having whole number answers; students should know how to perform operations in the
conventional order when there are no parentheses to specify a particular order (Order of Operations).
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and
explain them using properties of operations. For example, observe that 4 times a number is always even, and explain
why 4 times a number can be decomposed into two equal addends.
Number and Operations in Base Ten (3.NBT)
Use place value understanding and properties of operations to perform multi-digit arithmetic.4
4
A range of algorithms may be used.
3.NBT.2: Fluently add and subtract within 1000 using strategies and algorithms based on place value,
properties of operations, and/or the relationship between addition and subtraction.
Measurement and Data 3.MD
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of
objects.
3.MD.1: Tell and write time to the nearest minute and measure time intervals in minutes. Solve word
problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on
a number line diagram.
Unit 5 Multiplication Concepts
Operations and Algebraic Thinking (3.OA)
Represent and solve problems involving multiplication and division.
3.OA.1: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups
of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal
groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.1 1See Glossary, Table 2.
3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole
numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48,
5 = ÷ 3, 6 × 6 = ?.
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.5: Apply properties of operations as strategies to multiply and divide.2 2Students need not use formal
terms for these properties.
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication) 3 × 5 × 2 can
be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication)
Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56.
(Distributive property)
Multiply and divide within 100.
3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.
By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations
with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental
computation and estimation strategies including rounding.3 3This standard is limited to problems posed with
whole numbers and having whole number answers; students should know how to perform operations in the
conventional order when there are no parentheses to specify a particular order (Order of Operations).
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and
explain them using properties of operations. For example, observe that 4 times a number is always even, and explain
why 4 times a number can be decomposed into two equal addends.
Number and Operations in Base Ten (3.NBT)
Use place value understanding and properties of operations to perform multi-digit arithmetic.4
4
A range of algorithms may be used.
3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using
strategies based on place value and properties of operations.
Unit 6 Multiplication Facts
Operations and Algebraic Thinking (3.OA)
Represent and solve problems involving multiplication and division.
3.OA.1: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups
of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal
groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.1 1See Glossary, Table 2.
3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole
numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48,
5 = ÷ 3, 6 × 6 = ?.
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.5: Apply properties of operations as strategies to multiply and divide.2 2Students need not use formal
terms for these properties.
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication) 3 × 5 × 2 can
be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication)
Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56.
(Distributive property)
Multiply and divide within 100.
3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.
By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations
with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental
computation and estimation strategies including rounding.3 3This standard is limited to problems posed with
whole numbers and having whole number answers; students should know how to perform operations in the
conventional order when there are no parentheses to specify a particular order (Order of Operations).
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and
explain them using properties of operations. For example, observe that 4 times a number is always even, and explain
why 4 times a number can be decomposed into two equal addends.
Number and Operations in Base Ten (3.NBT)
Use place value understanding and properties of operations to perform multi-digit arithmetic.4
4
A range of algorithms may be used.
3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using
strategies based on place value and properties of operations.
Unit 8 Division Concepts
Operations and Algebraic Thinking (3.OA)
Represent and solve problems involving multiplication and division.
3.OA.2: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects
in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects
are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a
number of groups can be expressed as 56 ÷ 8.
3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal
groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.1 1See Glossary, Table 2.
3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole
numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48,
5 = ÷ 3, 6 × 6 = ?.
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.5: Apply properties of operations as strategies to multiply and divide.2 2Students need not use formal
terms for these properties.
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication) 3 × 5 × 2 can
be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication)
Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56.
(Distributive property)
3.OA.6: Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that
makes 32 when multiplied by 8.
Multiply and divide within 100.
3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.
By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations
with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental
computation and estimation strategies including rounding.3 3This standard is limited to problems posed with
whole numbers and having whole number answers; students should know how to perform operations in the
conventional order when there are no parentheses to specify a particular order (Order of Operations).
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and
explain them using properties of operations. For example, observe that 4 times a number is always even, and explain
why 4 times a number can be decomposed into two equal addends.
Unit 9 Division Facts
Operations and Algebraic Thinking (3.OA)
Represent and solve problems involving multiplication and division.
3.OA.2: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects
in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects
are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a
number of groups can be expressed as 56 ÷ 8.
3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal
groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.1 1See Glossary, Table 2.
3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole
numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48,
5 = ÷ 3, 6 × 6 = ?.
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.5: Apply properties of operations as strategies to multiply and divide.2 2Students need not use formal
terms for these properties.
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication) 3 × 5 × 2 can
be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication)
Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56.
(Distributive property)
3.OA.6: Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that
makes 32 when multiplied by 8.
Multiply and divide within 100.
3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.
By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations
with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental
computation and estimation strategies including rounding.3 3This standard is limited to problems posed with
whole numbers and having whole number answers; students should know how to perform operations in the
conventional order when there are no parentheses to specify a particular order (Order of Operations).
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and
explain them using properties of operations. For example, observe that 4 times a number is always even, and explain
why 4 times a number can be decomposed into two equal addends.
Unit 4 Measurement
Measurement and Data 3.MD
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of
objects.
3.MD.2: Measure and estimate liquid volumes and masses of objects using standard units of grams (g),
kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving
masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a
measurement scale) to represent the problem.7
6
Excludes compound units such as cm3 and finding the geometric volume of a container.
7
Excludes multiplicative comparison problems (problems involving notions of “times as much”
Represent and interpret data.
3.MD.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an
inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—
whole numbers, halves, or quarters.
Unit 11 Fractions and Decimals
Number and Operations—Fractions5 (3.NF)
5
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
Develop understanding of fractions as numbers.
3.NF.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal
parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
3.NF.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole
and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of
the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize
that the resulting interval has size a/b and that its endpoint locates the number a/b on the number
line.
3.NF.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a
number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the
fractions are equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number
line diagram.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their
size. Recognize that comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by
using a visual fraction model.
Unit 7 Geometry and Measurement
Measurement and Data (3.MD)
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
3.MD.5: Recognize area as an attribute of plane figures and understand concepts of area measurement.
a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area,
and can be used to measure area.
b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an
area of n square units.
3.MD.6: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised
units).
3.MD.7: Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is
the same as would be found by multiplying the side lengths.
b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of
solving real world and mathematical problems, and represent whole-number products as rectangular
areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a
and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in
mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to
solve real world problems.
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between
linear and area measures.
3.MD.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the
perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same
perimeter and different areas or with the same area and different perimeters.
Geometry (3.G)
Reason with shapes and their attributes.
3.G.1: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share
attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g.,
quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw
examples of quadrilaterals that do not belong to any of these subcategories.
3.G.2: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the
whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of
the shape.
Unit 10 Data and Probability
Measurement and Data (3.MD)
Represent and interpret data.
3.MD.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories.
Solve one- and two-step “how many more” and “how many less” problems using information presented in
scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
Unit 12 Multiplying and Dividing
Operations and Algebraic Thinking (3.OA)
Represent and solve problems involving multiplication and division.
3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal
groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem.1 1See Glossary, Table 2.
3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole
numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48,
5 = ÷ 3, 6 × 6 = ?.
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.5: Apply properties of operations as strategies to multiply and divide.2 2Students need not use formal
terms for these properties.
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication) 3 × 5 × 2 can
be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication)
Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56.
(Distributive property)
3.OA.6: Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that
makes 32 when multiplied by 8.
Multiply and divide within 100.
3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.
By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.8: Solve two-step word problems using the four operations. Represent these problems using equations
with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental
computation and estimation strategies including rounding.3 3This standard is limited to problems posed with
whole numbers and having whole number answers; students should know how to perform operations in the
conventional order when there are no parentheses to specify a particular order (Order of Operations).
3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and
explain them using properties of operations. For example, observe that 4 times a number is always even, and explain
why 4 times a number can be decomposed into two equal addends.
Number and Operations in Base Ten (3.NBT)
Use place value understanding and properties of operations to perform multi-digit arithmetic.4
4
A range of algorithms may be used.
3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using
strategies based on place value and properties of operations.
IV. ESSENTIAL QUESTIONS AND CONTENT
Unit 2: Money and Time
1. Count and compare amounts of money
2. Read and write time to the minute
3. Determine elapsed time using clocks and calendars
4. Analyze and solve problems using skills and strategies
Unit 1: Place Value
1. Read, write, and identify place values of digits in whole numbers through hundred thousands
2. Round numbers through four digits
3 . Compare and order numbers
4. Analyze and solve problems using skills and strategies
Unit 3: Addition and Subtraction
1. Add two-, three-, and four-digit numbers and estimate sums
2. Use addition and subtraction properties
3. Subtract two-, three-, and four-digit numbers and estimate differences
4. Analyze and solve problems using skills and strategies~
Unit 5: Multiplication Concepts
1. Use the Commutative Property of Multiplication
2. Multiply with 0, 1, 2, 3, 4, 5, and 10
3. Analyze and solve problems using skills and strategies
Unit 6: Multiplication Facts
1. Multiply with 6, 7, 8, and 9
2. Use the Associative Property for Multiplication
3. Analyze and solve problems using skills and strategies
Unit 8: Division Concepts
1. Relate multiplication and division
2. Divide by 2, 3, 4, and 5
3. Use zero and 1 in division
4. Analyze and solve problems using skills and strategies
Unit 9: Division Facts
1. Identify fact families
2. Divide by 6, 7, 8, 9, and 10
3. Analyze and solve problems using skills and strategies
Unit 4: Measurement
1. Estimate and measure lengths and convert customary units of length
2. Estimate and convert customary units of capacity and weight
3. Estimate and convert among metric units of length
4. Convert among metric units of capacity and mass
5. Read a thermometer
6. Analyze and solve problems using skills and strategies
Unit 11: Fractions and Decimals
1. Identify parts of regions and groups; write mixed numbers
2. Compare and order fractions
3. Add and subtract fractions and decimals
4. Use and compare decimals: tenths, hundredths, and decimals greater than 1
5. Analyze and solve problems using skills and strategies
Unit 7: Geometry and Measurement
1. Identify plane and solid geometric figures
2. Identify congruent figures and a line of symmetry
3. Find perimeter, area, and volume
4. Analyze and solve problems using skills and strategies
Unit 10: Data and Probability
1. Use line plots to find range and mode
2. Make and interpret a pictograph and a bar graph
3. Graph ordered pairs
4. Determine a likelihood of an occurrence and make predictions
5. Analyze and solve problems using skills and strategies
Unit 12: Multiplying and Dividing
1. Multiply two- and three-digit numbers by a one-digit number
2. Multiply and divide money
3. Divide two- and three-digit numbers by 2, 3, 4, and 5
4. Analyze and solve problems using skills and strategies
V. STRATEGIES
Students will be involved in cooperative learning and individual study throughout mathematics instruction.
Much of the instruction will incorporate problem-based learning, including hands-on activities,
manipulatives, projects, and class discussions, as well as other strategies determined by the teacher.
▪ Given a group of individual problem-solving situation, students will use a variety of mathematical
perceptions such as seeing patterns, making comparisons, estimating amounts, etc. to deduce a
solution.
▪ Given a set of oral or written problems, students will understand the mathematical context,
recognize the operative significance of the symbols, and calculate the solutions.
▪ Given manipulatives, games, models, calculators, and other technology, students will solve
problems appropriate to the unit or skill being studied.
▪ Differentiated Instruction is a key component to mathematics instruction. See Appendix A (to be
developed in summer 2009) for grade specific activities and lessons.
VI. EVALUATION
Students’ learning will be evaluated regularly in the following manner:
▪ Teacher observation
▪ Homework assignments
▪ End of chapter tests
▪ Anecdotal records
▪ Student projects
▪ District math assessments: Open Ended Problem Solving Assessment (October and May),
Cumulative Math Assessment (May)
VII. REQUIRED RESOURCES:
Houghton Mifflin Mathematics, Volume One and Volume Two (2002)
The Problem Solver 3: Activities for Learning Problem-Solving Strategies
Wright Group / McGraw-Hill (1989)
www.creativepublications.com
VIII. SCOPE AND SEQUENCE
It is important to follow the Scope and Sequence as written, even though the chapters may seem out of order.
There are mathematical items on the state assessments that must be taught prior to the spring administration
of the test and this sequence addresses this.
The Problem Solver Book is designed to be utilized throughout the units once per week Be attentive to the
mathematic content level in each of the problem solving lessons in this resource. The strategy Logical
Reasoning is a skill that is applicable to a variety of situations. Consideration should be given when looking
at the mathematic developmental level of students relative to mathematical concepts in The Problem Solver
lessons. Use professional discretion when introducing problem solving lessons in The Problem Solver book.
Although the strategy may match the strategy in the Houghton Mifflin Textbook, the mathematical concepts
may be too difficult to use to solve the problems if they were not introduced.
Houghton Mifflin Mathematics Textbook: Utilize Fast Facts, Quick Checks, Chapter Review/Test Prep,
Spiral Review, Pre and Post Tests, and Activity/Enrichment Centers.
Note: Before the start of each unit of study, it is suggested that mini lessons reviewing reading in mathematics
be embedded into lesson preparations. These lessons include Reading Mathematics – Reviewing Vocabulary;
Reading Words and Symbols. Ideas are found in the beginning of each chapter of the mathematics textbook.
Unit 2: Money and Time
(approximately 2 weeks)
2.1
Value of Money
2.2
Count Coins and Bills
2.3
Equivalent Amounts …………. *Activity: Count it Up!
2.4
Count Change
2.5
*Problem Solving Skill: Choose the Operation
2.6
Hour, Half-Hour, Quarter Hour (Algebra)
2.7
2.8
2.9
2.10
2.12
Time to Five Minutes …………. *Activity: Using a Time Line
Time to Minute
*Problem-Solving Strategy: Use Logical Thinking
Elapsed Time 2.11 Use a Calendar
*Problem-Solving Application: Use a Schedule
Resource Book: The Problem Solver/Related Lessons for Unit 2
Problems 1, 2
(T.1 – T.4)
Logical Reasoning
Problems 3, 4
(T.5 – T.8)
Make an Organized List
Problems 7, 8
(T.13 – T.16) Make an Organized List
Problems 19, 20
(T. 37 – T.40) Use or Make a Table
Unit 1: Place Value
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
(approximately 3 weeks)
Numbers Through 999
Round Two-Digit Numbers (Algebra)
Round Three-Digit Numbers …………. *Activity: What's My Number?
*Problem-Solving Skill: Estimated or Exact Amounts
Modeling One Thousand Activity
Place Value to Thousands
Compare Numbers (Algebra)
Ordering Numbers
Round Four-Digit Numbers
*Problem-Solving Strategy: Find a Pattern
Place Value to Ten Thousands
Place Value to Hundred Thousands
*Problem-Solving Application: Read a Graph
Resource Book: The Problem Solver/Related Lessons for Unit 1
Problems 21, 22
(T.41 – T. 44) Use or Look for a Pattern
Problems 25, 26
(T.49 - T.52) Use or Look for a Pattern
Unit 3: Addition and Subtraction
(approximately 3 weeks)
3.1
Addition Properties (Algebra)
3.2
Regroup Ones (Algebra); Number Sense: Adding in Different Ways (Algebra)
3.3
Regroup Ones and Tens
3.4
Estimate Sums
3.5
*Problem-Solving Skill: Exact Answer or Estimate
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
Column Addition (Algebra) …………. *Activity: Add it Up!
Add Greater Numbers (Algebra)
*Problem-Solving Strategy: Guess and Check
Subtraction Strategies and Properties (Algebra)
Regroup Tens (Algebra) Number Sense: Subtracting in Different Ways
Regroup Tens and Hundreds
Estimate Differences
Subtract Greater Numbers
Subtract Across Zeros
*Problem-Solving Application: Use Operations
Resource Book: The Problem Solver/Related Lessons for Unit 3
Problems 13, 14
(T.25 – T.26) Guess and Check
Problems 5, 6
(T.9 – T. 12)
Use or Make a Table
Unit 5: Multiplication Concepts
(approximately 3 weeks)
5.1
Modeling Multiplication
5.2
Arrays and Multiplication
5.3
Multiply with 2
5.4
Multiply with 5
5.5
Multiply with 10
5.6
*Problem Solving Skill: Too Much Information
5.7
Multiply with 1 and 0
5.8
Multiply with 3…………Multiplication Practice Game-Multiplying Dots
5.9
*Problem-Solving Strategy: Use Models to Act it Out
5.10
Multiply with 4
5.11
*Problem-Solving Application: Use a Pictograph
Resource Book: The Problem Solver/Related Lessons for Unit 5
Problems 15, 16
(T.15 - T. 32) Act Out or Use Objects
Problems 23, 24
(T. 45 – T.48) Act Out or Use Objects
Problems 17, 18
(T. 33 – T.36) Make a Picture or Diagram
Unit 6: Multiplication Facts
(approximately 3 weeks)
6.1
Using a Multiplication Table………….Hands-On Activity
6.2
Multiply with 6
6.3
Multiply with 8……..Practice Activity: Coloring Counts
6.4
*Problem-Solving Skill: Multistep Problems
6.5
Multiply with 7
6.6
Multiply with 9
6.7
*Problem-Solving Strategy: Choose a Strategy
6.8
Patterns on a Multiplication Table……..Hands-On Activity
6.9
Multiply Three Numbers
6.10
*Problem-Solving Application: Use Operations
Resource Book: The Problem Solver/Related Lessons for Unit 6
Problems 47, 48
(T.93 – T.96) Brainstorm
Unit 8: Division Concepts (approximately 3 weeks)
8.1
Modeling Division……………Hands-On Activity
8.2
Relate Multiplication and Division
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
Divide by 2
Divide by 5
*Problem-Solving Skill: Choose the Operation
Division Rules
Divide by 3
*Problem-Solving Strategy: Draw a Picture
Divide by 4……………………Division Facts
Practice Activity: Make a Match*Problem-Solving Application: Find a Unit Cost
Resource Book: the Problem Solver/Related Lessons for Unit 8
Problems 9, 10
(T.17 – T.20) Make a Picture or Diagram
Problems 31, 32
(T. 61 - T. 64) Make a Picture or Diagram
Unit 9: Division Facts
(approximately 3 weeks)
9.1
Using a Multiplication table to Divide……………..Hands-On Activity
9.2
Fact Families
9.3
Divide by 10
9.4
*Problem-Solving Skill: Too Much or Too Little Information
9.5
Divide by 6
9.6
Divide by 7
9.7
*Problem-Solving Strategy: Write a Number Sentence
9.8
Divide by 8
9.9
Divide by 9……………Division Facts Practice Activity: Math Scramble
9.10
*Problem-Solving Application: Use Money
Resource Book: The Problem Solver/Related Lessons for Unit 9
Problems 11, 12
(T.21 – T.24) Make an Organized List
Unit 4: Measurement
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
(May teach in tandem with parts of the Fraction Unit 11) (approx. 3 weeks)
Measuring Length……………….Hands-On Activity
Measure to the Nearest Half Inch
Customary Units of Length
Estimating and Measuring Capacity……….Hands-On Activity
Customary Units of Capacity
Customary Units of Weight……………Practice Activity: Match the Measure
Temperature: Degrees in Fahrenheit
*Problem-Solving Strategy: Work Backward
Centimeter and Decimeter
Meter and Kilometer
Metric Units of Capacity
*Problem-Solving Skill: Choose a Computation Method
Metric Units of Mass
Temperature: Degrees Celsius
*Problem-Solving Application: Use Measurement
Resource Book: The Problem Solver/Related Lessons for Unit 4
Problems 29, 30
(T.57 – T.60) Work Backwards
Problems 43, 44
(T.85 – T.88) Work Backwards
Unit 11: Fractions and Decimals
(approximately 3 weeks)
11.1
Fractions and Regions
11.2
Fractions and Groups
11.3
Compare Fractions
11.4
Order Fractions
11.5
Modeling Equivalent Fractions………….Hands-On Activity
11.6
Find Equivalent Fractions
11.7
*Problem-Solving Strategy: Choose a Strategy
11.8
Fractional Parts of a Group
11.9
Mixed Numbers
11.10
Add and Subtract Fractions…………Practice Activity: Fraction Bingo
11.11
*Problem-Solving Skill: Multistep Problems
11.12
Tenths
11.13
Hundredths
11.14
Decimals Greater Than 1
11.15
Compare and Order Fractions and Decimals
11.16
Add and Subtract Decimals
11.17
Decimals, Fractions, and Money
11.18
*Problem-Solving Application: Use Money
Resource Book: The Problem Solver/Related Lessons for Unit 11
Problems 41, 42
(T.81 – T.84) Guess and Check
Unit 7: Geometry and Measurement
(approximately 4 weeks)
7.1
Lines, Line Segments, Rays, and Angles
7.2
Plane Figures
7.3
Quadrilaterals
7.4
Triangles
7.5
*Problem-Solving Skill: Visual Thinking
7.6
Congruent Figures/Similar Figures
7.7
Line of Symmetry
7.8
Perimeter
7.9
Find Area
7.10
Estimating Area………..Hands-On Activity
7.11
*Problem-Solving Strategy: Find a Pattern
7.12
Solid Figures……………Practice Activity: Meet Your Match
7.13
Estimating Volume…….Hands-On Activity
7.14
Find Volume
7.15
*Problem-Solving Application: Use Measurement
Resource Book: The Problem Solver/Related Lessons for Unit 7
Problems 37, 38
(T.73 – T.76) Use or Look for a Pattern
Unit 10: Data and Probability
(approximately 4 weeks)
10.1
Collecting and Organizing Data………………Hands-On Activity
10.2
Use Line Plots
10.3
Make a Pictograph
10.4
*Problem-Solving Skill: Use a Bar Graph
10.5
Make a Bar Graph
10.6
Graph Ordered Pairs
10.7
*Problem-Solving Strategy: Make a Table
10.8
Probability
10.9
10.10
10.11
Recording Outcomes……......Hands-On Activity; Practice Activity: Pick and Predict
Make Predictions
*Problem-Solving Application: Use Probability
Resource Book: the Problem Solver/Related Lessons for Unit 10
Problems 27, 28
(T.53 – T.56) Make a Table
Problems 35, 36
(T.69 – T.72) Make an Organized List
Problems 33, 34
(T. 65 – T.68) Make a Picture or Diagram
Unit 12: Multiplying and Dividing
(approximately 3 weeks)
12.1
Mental Math: Multiply Multiples of 10, 100, and 1,000
12.2
Modeling Multiplication………………………….Hands-On Activity
12.3
Two-Digit Numbers
12.4
Three Digit Numbers
12.5
Regrouping Twice
12.6
Multiply Money
12.7
*Problem-Solving Strategy: Solve a Simpler Problem
12.8
Modeling Division with Remainders…………….Hands-On Activity
12.9
Two-Digit Quotients…………….Practice Activity: Remainder Race
12.10
*Problem-Solving Skill: Interpret Remainders
12.11
Regrouping in Division
12.12
Three-Digit Quotients
12.13
Divide Money
12.14
Placing the First Digit
12.15
*Problem-Solving Application: Use Operations
Resource Book: The Problem Solver/Related Lessons for Unit 12
Problems 45, 46
(T.89 – T.92) Make it Simpler
Problems 39, 40
(T.77 – T.80) Use Logical Reasoning
MADISON PUBLIC SCHOOL DISTRICT
Grade 3 Math Enrichment Addendum
Below are suggested projects and materials for each unit of study in the third grade textbook. These projects
are only suggestions and can be replaced by another project that might better suit a child’s learning style. At
the end of this document is a list of other product ideas. Feel free to interchange a project with any of the
other product ideas.
Chapter 1: Place Value
Project: Cross word puzzle
Chapter 2: Money and Time
Project: Make a clock using compass and ruler
Money word problem
Chapter 3: Addition and Subtraction
Math TV How to Problem Solve with Practice:
http://www.mathplayground.com/thinkingblocks.html
Project: Brochure on the process of addition and subtraction
Chapter 4: Measurement
Project: Take a recipe and convert the measurements to metric.
Have students measure the classroom and calculate the square footage and area of the room.
Compare this to a classroom next door to see which is bigger and by how much.
Chapters 5-6: Multiplication
Math TV How to Problem Solve with Practice:
http://www.mathplayground.com/thinkingblocks.html
Project: Create a multiplication chart
Write a fictional story using multiplication
Chapter 7: Geometry and Measurement
Math TV How to Problem Solving:
http://www.mathplayground.com/mathtv.html
Chapters 8-9: Division
Math TV How to Problem Solve with Practice:
http://www.mathplayground.com/thinkingblocks.html
Project: Create an illustrated dictionary and how to textbook
Create a word problem book
Chapter 10: Data and Probability
Recommended reading, Murphy, Stuart. Lemonade for Sale. NY: HarperCollins, 1998. (found at
CAS and KRS)
Project: *After reading the story, the children create a graph story in a flipbook.
*Solve how much money the children earned for the book and in student created story
Chapter 11: Fractions and Decimals
Math TV How to Problem Solving:
http://www.mathplayground.com/mathtv.html
Recommended reading:
Leedy, Loreen. Fraction Action. NY: Holiday House, 1994. (found at CAS)
McGrath, Barbara. More M&M Math. Mass.: Charlesbridge, 1998. (found at KRS)
Project: *Create picture book showing 1/3,1/4,1/5, and 1/6. Include addition
*Create number sentences for addition and subtraction from the book or child created picture book.
Chapter 12: Multiplication and Division
Math TV How to Problem Solve with Practice:
http://www.mathplayground.com/thinkingblocks.html
Recommended reading:
McGrath, Barbara. More M&M Math. Mass.: Charlesbridge, 1998. (found at KRS)
Project: Create multiplication and division project using colored stickers/coloring
Books in our Schools:
Leedy, Loreen. Fraction Action. NY: Holiday House, 1994. (found at CAS)
Lewis, J. Patrick. Arithme-tickle. NY: Harcourt Inc. (found at CAS)
McGrath, Barbara. More M&M Math. Mass.: Charlesbridge, 1998. (found at KRS)
Murphy, Stuart. Lemonade for Sale. NY: HarperCollins, 1998. (found at CAS and KRS)
Product Ideas
Spoken Products
Debate
Advertisement
Poems for 2 voices
Newscast
Mock Trial
Simulation
Eulogy
Auction
D.J. Show
Narration
Weather
Report
Guided tours
Chronicles
Plays
Speeches
Poetry readings
Interviews
Teaching a lesson
Songs
Demonstration
Announcements
Comedy routines
Panel discussion
Sermon
Rap
Oral report
Forum
Sign language
Radio plays
Story telling
Oral histories
Lecture
Sales promotion
Committee meetings
Master of ceremonies
Town crier
Book talks public
address book review
Dramatic dialogue
Written Products
Pamphlets
Brochures
Books
Speech
Survey
Captions
Charts
Debates
Radio programs
Instructions
Interview questions
Simulation
Ballad
Legend
Advertisement
Magazine
Diary
Editorial
Haiku
Journal
Bibliography
Rhyme
Limerick
Parable
Ethnography
Article
Poetry
Marketing plan
Comic strip
Jokes/riddles
Slogan
Questionnaire
Invitations
Storyboard
Greeting cards
Grant
Analysis
Epic
Melody
Homepage
Autobiography
Tall tale
E-mail message
Law
Banners
Plays/skits
Letters/postcard
Crossword puzzle
Jingles
Summaries
Consumer report
Lists
Note taking
Budget
Blueprint
Criteria listing
Census report
Folk tale tune
Flow chart
Story problem
Announcement
Family tree
Amendment
Visual Products
Video
Slide show
Powerpoint
presentation
Sculpture
advertisement
Puppet
Calendar
Musical score
Book jacket
Layouts
Model
Pottery timeline
Diagram/chart
Sketch
Graph
Collage
Ice sculpture
Blueprints
Lists
Graphic design
Painting
Map
Mobile
Set design
Experiment
Caricature
Silkscreen
Graphic organizer
Photos
Clothing
Documentary
Animation
Costume
Charcoal sketch
Landscape design
Museum exhibit
Photo essay
Stitchery
Batik
Etching
Construction Project
Scenery for a play
Sculpture
Relief map
Habitat
Bridges
Inventions food
Fitness trail
Terrarium
Greenhouse gardens
Diorama
Shelter
Collection ceremony
Learning center
Pottery
Working model
Building
Toys
Games
Legos
Birdhouse
Bulletin board
Circuit boards
Theater
Exhibition
3 D figures
Furniture
Instruments
Robots
Machine
Rockets
Quilts
Multimedia
presentation
Mask
Prototype
Catalogue
Maze
Leadership Products
Persuasive speech
Plan
School patrol
Leading a rally
Consensus building
Role playing
Musical performance
Election
campaign
Protest
Speech
Open forum
Fund raising