Bay Math Course of Study Gr 3 FINAL
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Whole group discussion of what the 8 mathematical practices will look like for the content statement.AssessmentComments, questions and ideasTier 3 Vocab (Content specific words)Literature ConnectionsScience ConnectionsSocial Studies Connection
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Operations & Algebraic Thinking
Represent and solve problems involving
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.
I can show multiplication in a real life problem by using groups with equal objects in each group.Quarter 1
Quarter 2
Quarter 3
Quarter 4
Unit 2: Operations and Algebraic Thinking: the Relationship Between Multiplication and Divisionproduct
factors
equal groups
multiplication
equation
number model
fact families
skip counting
3
Operations & Algebraic Thinking
Represent and solve problems involving
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 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.
I can show division by putting numbers into equal groups.(How many groups can I make?)

I can show division by knowing the number of equal groups and putting numbers into groups. (How many in each group?)

Quarter 1
Quarter 2
Quarter 3
Quarter 4

Unit 2: Operations and Algebraic Thinking: the Relationship Between Multiplication and Divisiondivision
divisor
quotient
repeated subtraction
equal shares
4
Operations & Algebraic Thinking
Represent and solve problems involving
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.
I can show multiplication by using drawings, jumps on the number line, and arrays for solving multiplication problems up to 100.
I can use drawings or jumps on the number line to show the number of groups in solving a division problem up to 100.
Quarter 1
Quarter 2
Quarter 3
Quarter 4

Unit 2: Operations and Algebraic Thinking: the Relationship Between Multiplication and Divisionarrays
equal groups
jumps on a number line
5
Operations & Algebraic Thinking
Represent and solve problems involving
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 the equation 8 x ? = 48.I can solve for the missing factor or product in a multiplication problem.

I can solve a division problem when the size of the group is unknown.

I can solve a division problem when the number of groups is unknown.

Quarter 1
Quarter 2
Quarter 3
Quarter 4
Unit 2: Operations and Algebraic Thinking: the Relationship Between Multiplication and Divisionunknown factor
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Operations & Algebraic Thinking
Understand properties of multiplication and the
relationship between multiplication and division.
5. Apply properties of operations as strategies to
multiply and divide. 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.)
I can explain that the product of a multiplication problem stays the same when the factors are reversed. (Associative)

I can explain that the order of factors does not matter when multiplying.
(Commutative)

I can multiply by breaking apart one of the factors into smaller numbers and then multiplying each one by the other factor

Quarter 1
Quarter 2
Quarter 3
Quarter 4
Unit 2: Operations and Algebraic Thinking: the Relationship Between Multiplication and DivisionFormal vocabulary to be introduced:
Commutative property
Associative property
Distributive property
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Operations & Algebraic Thinking
Understand properties of multiplication and the
relationship between multiplication and division.
6. Understand division as an unknown-factor
problem. For example, find 32 ÷ 8 by finding the
number that makes 32 when multiplied by 8.
I can solve a division problem by using multiplication.Quarter 1
Quarter 2
Quarter 3
Quarter 4
Unit 2: Operations and Algebraic Thinking: the Relationship Between Multiplication and Divisioninverse operations (multiplication and division)
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Operations & Algebraic Thinking
Multiply and divide within 100
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
I can multiply basic facts to 100 with accuracy.

I can divide basic facts to 100 with accuracy.

Quarter 1
Quarter 2
Quarter 3
Quarter 4
Unit 2: Operations and Algebraic Thinking: the Relationship Between Multiplication and Division
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Operations & Algebraic Thinking
Solve problems involving the four operations, and
identify and explain patterns in arithmetic.
8. Solve 2-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.
I can solve a two part problem by deciding which of the operations, multiplication, division, addition and subtraction to use.

I can solve a two part problem using a letter for the unknown in an equation.

I can determine if my answer makes sense by using estimation to show the reasonableness of my answer.

I can use mental math to determine the reasonableness of my answer.

Quarter 1
Quarter 2
Quarter 3
Quarter 4
Unit 3: Operations and Algebraic Thinking: Patterns in Addition and Multiplicationone-step problem
two-step problem
reasonableness
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Operations & Algebraic Thinking
Solve problems involving the four operations, and
identify and explain patterns in arithmetic.
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

I can find patterns in addition and explain how the pattern works.

I can find patterns in multiplication and explain how the pattern works.

Quarter 1
Quarter 2
Unit 3: Operations and Algebraic Thinking: Patterns in Addition and Multiplicationarithmetic patterns
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Numbers & Operations in Base 10
Use place value understanding and properties of operations to perform multi-digit arithmetic.
1. Use place value understanding to round whole
numbers to the nearest 10 or 100.
I can round numbers to the nearest 10 and explain my reasoning.

I can round numbers to the nearest 100 and explain my reasoning.

Quarter 1
Quarter 2
1.11, 2.7, 2.8Unit 1: Numbers and Operations in Base Tenrounding
estimating
place value
base ten numberal form
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Numbers & Operations in Base 10
Use place value understanding and properties of operations to perform multi-digit arithmetic.
2. Fluently add and subtract within 1000 using
strategies and algorithms based on place value,
properties of operations, and/or the relationship
I can add numbers within 1000 and explain how I solved the problem.
I can subtract numbers up to the thousands place and explain my reasoning in solving the problem.
Quarter 1
Quarter 2
1.4, 1.8, 1.9, 1.10, 1.11, 1.13, 2.1, 2.2,
2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.5, 4.5

Unit 1: Numbers and Operations in Base Tenaddition
subtraction
sum
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Numbers & Operations in Base 10
Use place value understanding and properties of operations to perform multi-digit arithmetic.
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.
I can explain the meaning of multiples of 10.

I can use basic facts when multiplying multiples of 10.

Quarter 1
Quarter 2
1.4, 1.8, 1.9, 1.10, 1.11, 1.13, 2.1, 2.2,
2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.5, 4.5

Unit 1: Numbers and Operations in Base Tenmultiple
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Number & Operations - Fractions
Develop understanding of fractions as numbers
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. I can show a fraction as equal parts of a whole using area (parts of a whole), models (circles, rectangles, squares), and number lines.

Quarter 3
Quarter 4
Unit 5: Representing and Comparing Fractionsnumerator
denominator
fraction
partition
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Number & Operations - Fractions
Develop understanding of fractions as numbers
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 a/b on the number line.
I can divide a number line from 0 to 1 into equal parts and explain that each part represents the same length.

I can label each fractional part on a number line based on how far it is from 0 to the endpoint.

Quarter 3
Quarter 4
Unit 5: Representing and Comparing Fractionsnumber line
interval
endpoint
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Number & Operations - Fractions
Develop understanding of fractions as numbers
3. Explain equivalence of fractions in special cases, and compare frations 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 fraction, 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 fraction 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 fraction with the same numerator or the same denominator by reasoning about their size. Recognize that comparison are valid only when the two fractions refer to the same whole. Record the results of comparison with the symbols >, =, or <, and justifyl the conclusions, e.g. by using a visual fraction model.
I can show and explain that two fractions are equivalent by comparing them on a number line.

I can write whole numbers as fractions and show them at the same point on a number lne.

I can compare two fractions with the same numerator and explain why they are different using fraction models.

I can compare two fractions with the same denominator and explain why they are different using fraction models.
Quarter 3
Quarter 4
Unit 5: Representing and Comparing Fractionsequivalent fractions
equivalency
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Measurement & Data
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
1. Tell and write time to the nearest minute and
measure time intervals in minutes. Solve word
of time intervals in minutes, e.g., by representing the
problem on a number line diagram.
I can tell time using an analog clock to the nearest minute.

I can solve word problems using addition and subtraction of time intervals in minutes.
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Unit 6: Measurementanalog clock
time intervals
digital clock
minute hand
hour hand
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2. Measure and estimate liquid volumes and
masses of objects using standard units of grams
(g), kilograms (kg), and liters (l). Add, subtract,
multiply, or divide to solve 1-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.
I can estimate the volume of liquids in liters.
I can determine th volume of liquids in liters by reading the scales on measuring tools.
I can estimate the mass of an object in grams and kilograms.
I can determine the mass of an object by using measuring tools in intervals of grams and kilograms.
I can solve 1-step word problems involving volume of liquids using addition, subtraction, multiplication, or division.
I can solve 1-step word problems involving masses of objects using addition, subtraction, multiplication, or division.

Quarter 3
Quarter 4
Unit 6: Measurementliquid volume
mass
gram
kilogram
liter
metric system
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Measurement & Data
Represent & Interpret Data
3. Draw a scaled picture graph and a scaled bar
graph to represent a data set with several
categories. Solve one- and 2-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.
I can read and solve problems using a scaled bar graph including both horizontal and vertical bar graphs.
I can draw a scaled bar graph representing a data set.
I can solve one and two step problems (how many more and how many less) from information presented in a bar graph.
I can read and solve problems using a scaled picture graph that include symbols that represent multiple data.
I can draw a scaled picture graph representing a data set.
I can solve one and two step problems (how many more and how many less) from information presented in a picture graph.
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Unit 6: Measurementvertical bar graph
horizontal bar graph
graph intervals
picture graph
less than
greater than
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Measurement & Data
Represent & Interpret Data
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.
I can measure lengths using rulers marked with halves and fourths of an inch.
I can show a data set of length measurement in fourths, halves, and wholes by making a line plot.
Quarter 2
Quarter 3
Unit 6: Measurementcustomary measurement
line plot
inch
foot
yard
21
Measurement & Data
Geometric measurement: understand concepts
of area and relate area to multiplication and to
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.
I can explain area as an attribute of a plane figure.

I can show that area is measured in square units.

I can determine the area of a plane figure by covering it with square units that do not overlap.
Quarter 3
Quarter 4
Unit 3: Operations and Algebraic Thinking: Patterns in Addition and Multiplication
Unit 6: Measurement
area
plane figure
two-dimensional shape
unit
square units
22
Measurement & Data
Geometric measurement: understand concepts
of area and relate area to multiplication and to
6. Measure areas by counting unit squares (square
cm, square m, square in, square ft., and
improvised units)
I can measure areas by counting unit squares ( square cm, square m, square in, square ft, square yds).
Quarter 3
Quarter 4
Unit 6: Measurementsquare cm
square m
square in
square ft
square yd
tile/tiling
23
Measurement & Data
Geometric measurement: understand concepts
of area and relate area to multiplication and to
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 representwhole-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 non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
I can find the area of a rectangle using tiles and relate it to multiplying using arrays (width x length).

Given the side lengths of rectangles in a real world problem, I can multiply the length x width to determine the area.

I can use tiles to show that that area of a retangle axb can be chunked (distributive property) into two smaller rectangles that when combined has the same area as axb.

I can decompose a rectilinear figure ito different rectangles, find the area of each, and add them together to determine the area of the entire figure.
Quarter 3
Quarter 4
Unit 6: Measurementlength of rectangle
width of rectangle
area model
24
Measurement & Data
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
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.
I can explain that perimeter is an attribute of a plane figure.

I can find the perimeter of a variety of polygons when given the side lengths.

I can find an unknown side length when given the perimeter of a polygon.

I can compare different rectangles that have the same perimeter but different areas.

I can compare different rectangles that have the same area by different perimeters.
Quarter 3
Quarter 4
Unit 6: Measurementperimeter
25
Geometry
Reason with shapes and their attributes
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
rectangles, and squares as examples of
quadrilaterals that do not belong to any of these
subcategories
I can classify 4-sided shapes according to their attributes.

I can compare (how are they alike? how are they different?) 4-sided shapes according to their attributes.

Quarter 3
Quarter 4
Unit 4: Geometryattributes
polygon
closed shape
rectangles
rhombus
square
parallelogram
trapezoid
26
Geometry
Reason with shapes and their attributes
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.
I can divide shapes into equal parts and describe each part as a fraction of the whole.
Quarter 3
Quarter 4
Unit 4: Geometryequal areas
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