Bay Grade 5 Math Course of Study FINAL
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DomainStrandStandardLearning Target (I can statements) You can have multiple learning targets for one content statement. Put them all in the box. Use CTRL+ENTER to move to a second line within one box.Month Taught (units taught)Tier 3 Vocab (Content specific words)Everyday Math Alignment
Central Resources for course - textbooks, workbooks
Supplemental Resources/Lesson Ideas
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Formative/Summative Assessment - Please note any common unit assessments. Please share what assessment methods might be used to gather evidence for this standard.
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Numbers and Operations Base 10Understand the place value system1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.I can recognize that each place to the left is 10 times
larger in a multi-digit number.
I can recognize that each place to the right is 1/10 as
much in a multi-digit number.
September-October
Unit 1 Number Theory
Unit 2 Estimation/Computation
3
Numbers and Operations Base 10Understand the place value system2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.I can express powers of ten using whole number
exponents.
I can illustrate and explain a pattern for how the number
of zeros of a product-when multiplying a whole
number by power of 10-relates to the power of 10(e.g.
500-which is 5 x 100.)
I can illustrate and explain a pattern for how
multiplying or dividing any decimal by a power of 10
relates to the placement of the decimal point.
September-October
powers of ten, exponent, decimalUnit 1 Number Theory
Unit 2 Estimation/Computation
4
Numbers and Operations Base 10Understand the place value system3. Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
I can read and write decimals to the thousandths in
word form, base-ten numerals, and expanded form.
I can compare two decimals to the thousandths
using place value and record the comparison using
symbols <, >, =.
September-October
decimal, decimal placeUnit 1 Number Theory
Unit 2 Estimation/Computation
5
Numbers and Operations Base 10Understand the place value system4. Use place value understanding to round decimals to any place.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
I can explain how to use place value and what digits
to look at to round decimals to any place.
I can use the value of the digit to the right of the place
to be rounded to determine whether to round up or down.
I can round decimals to any place.
September-October
decimal placeUnit 1 Number Theory
Unit 2 Estimation/Computation
6
Numbers and Operations Base 10Understand the place value system5. Fluently multiply multi-digit whole numbers using the standard algorithm.I can explain the standard algorithm for multi-digit whole
number multiplication.
I can use the standard algorithm to multiply multi-digit
whole numbers with ease.
Period
November
standard algorithmUnit 2 Estimation/Computation
7
Numbers and Operations Base 10Understand the place value system6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.I can demonstrate division of whole numbers with four-
digit dividends and two-digit divisors using place
value, rectangular arrays, area model, and other
strategies.
I can solve division of a whole number with four-digit
dividends and two-digit divisors using properties
of operations and equations.
I can explain my chosen strategy.
Period
November
rectangular arrays, area modelUnit 4 Division
8
Numbers and Operations Base 10Understand the place value system7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Foundation for Grade 6 The Number System.
I can add, subtract, multiply and divide decimals to
hundredths using strategies based on place value,
properties of operations, or other strategies.
I can explain and illustrate strategies using concrete
models or drawings when adding, subtracting,
multiplying, and dividing decimals to hundredths.
September-October
decimalUnit 2 Estimation/Computation
Unit 4 Division
9
Numbers and Operations - FractionsUse equivalent fractions as a strategy to add and subtract fractions.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
I can determine common multiples of unlike
denominators.
I can create equivalent fractions using common
multiples.
I can add and subtract fractions with unlike
denominators (including mixed numbers) using
equivalent fractions.
Period
November/December/
January
mixed numbers, equivalent fractionsUnit 5 Fractions/Decimals/Percents
10
Numbers and Operations - FractionsUse equivalent fractions as a strategy to add and subtract fractions.2. Solve word problems involving addition and subtraction of fractions
referring to the same whole, including cases of unlike denominators,
e.g., by using visual fraction models or equations to represent the
problem. Use benchmark fractions and number sense of fractions to
estimate mentally and assess the reasonableness of answers. For
example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing
that 3/7 < 1/2.
I can solve addition and subtraction word problems
involving fractions using visual models or equations.
I can use estimation strategies, benchmark fractions
and number sense to check if my answer is
reasonable.
Period
November/December/
January
Unit 5 Fractions/Decimals/Percents
11
Numbers and Operations - FractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions3. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
I can explain that fractions can be represented as a
division of the numerator by the denominator, and
illustrate why a*b can be reperesented by the
fraction a/b.
I can solve word problems involving the division of whole numbers
and interpret the quotient-which could be a whole number,
mixed number, or fraction-in the context of the problem.
I can explain or illustrate my solution strategy using visual
fraction models or equations that represent the problem.
Period
November/December/
January
Unit 5 Fractions/Decimals/Percents
12
Numbers and Operations - FractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.equivalently, as the result of a sequence of operations a × q ÷ b.
For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
I can create story contexts for problems involving
multiplication of a fraction and a whole number or
multiplication of two fractions by interpreting
multiplication with fractions in the same way that I
would interpret multiplication of whole numbers. (e.g.
2/3 x 4 can be interpreted as, "If I need 2/3 cups of
sugar for 1 batch of cookies, how much sugar do I
need to make 4 batches of cookies?")
Second and Third
January
Unit 8 Fractions/Multiplication/Division
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Numbers and Operations - FractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions5. Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b =(n×a)/(n×b) to the effect of multiplying a/b by 1.
I can interpret the relationship between the size of the
factors to the size of the product.
I can explain why multiplying a given number by a
number or fraction greater than 1 results in a product
greater than the given number.
I can explain why multiplying a given number by a
fraction less than 1 results in a product less than the
given number.
I can explain multiplication as scaling (to enlarge or
reduce) using a visual model.
I can multiply a given fraction by 1 to find an
equivalent fraction.
Second and Third
January
Unit 8 Fractions/Multiplication/Division
14
Numbers and Operations - FractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.I can solve real-world problems involving multiplication
of fractions and mixed numbers and interpret the
product in the context of the problem.
I can explain or illustrate my solution strategy using
visual fraction models or equations that represent
the problem.
Period
November/December/
January
benchmark fractionsUnit 8 Fractions/Multiplication/Division
15
Numbers and Operations - FractionsApply and extend previous understandings of multiplication and division to multiply and divide fractions7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
b. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
I can create story contexts for problems involving
division of a unit fraction by a whole number or division
of a whole number by a unit fraction.
Second and Third
January
mixed numberUnit 8 Fractions/Multiplication/Division
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Operations and Algebraic ThinkingWrite and interpret numerical expressions1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.I can use parentheses, brackets or braces to group
an expression within a multi-step numerical
expression.
I can evaluate numerical expressions with parentheses,
brackets, or braces.
February
numerical expression, evaluateUnit 7 Exponents/Notations/Order
of Operations
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Operations and Algebraic ThinkingWrite and interpret numerical expressions2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7).Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
I can represent a calculation expressed verbally
with a numerical expression.
I can analyze expressions without solving.
February
expression, numerical expressionUnit 7 Exponents/Notations/Order
of Operations
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Operations and Algebraic ThinkingAnalyze patterns and relationships.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
I can generate two numerical patterns with the same
starting number for two given rules.
I can explain the relationship between two numerical
patterns by comparing how each pattern grows or by
comparing the relationship between each of the
corresponding terms from each pattern.
I can form ordered pairs out of corresponding terms from
each pattern and graph them on a coordinate plane.
February
numerical pattern, corresponding terms, ordered pair,
coordinate plane
Unit 9 Coordinate Grids/ Graphing/
Perimeter/Area/Volume
19
GeometryGraph points on the coordinate plane to solve real-world and mathematical problems.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).I can construct a coordinate system with two
intersecting perpendicular lines and recognize that the
intersection is called the origin and it is the point where
0 lies on each of the lines.
I can recognize that the horizontal axis is generally
labeled as the x-axis and the vertical axis is generally
labeled as the y-axis.
I can identify and ordered pair as an x-coordinate
followed by a y-coordinate.
I can explain the relationship between the ordered pair
and the location on the coordinate plane.
February
Unit 9 Coordinate Grids/ Graphing/
Perimeter/Area/Volume
20
GeometryGraph points on the coordinate plane to solve real-world and mathematical problems.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.I can determine when a mathematical problem has a
set of ordered pairs.
I can graph points in the first quadrant of a coordinate
plane using a set of ordered pairs.
I can relate the coordinate values of any graphed point
to the context of the problem.
February
ordered pair, quadrant, coordinate planeUnit 9 Coordinate Grids/ Graphing/
Perimeter/Area/Volume
21
GeometryClassify two-dimensional figures into categories based on their properties.3. Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category.
For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
I can classify two-dimensional figures by their
attributes.
I can explain two-dimensional attributes can belong to
several two-dimensional figures.
I can identify subcategories using two dimensional
attributes.
October
Unit 3 Geometry
22
GeometryClassify two-dimensional figures into categories based on their properties.4. Classify two-dimensional figures in a hierarchy based on properties.
I can group together all shapes that share a single
property, and then among these shapes, group
together those that share a second property, and then
among these, group together those that share a third
property.
October
Unit 3 Geometry
23
Measurement and DataConvert like measurement units within a given measurement system.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.I can convert measurement units within the same
measurement system.
I can solve multi-step measurement conversions.
Period
March/April
convert, conversionGeorgia Math and Teacher Generated
Supplements
24
Measurement and DataRepresent and interpret data.2. Make a line plot to display a set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
I can create a line plot with a given set of unit fraction
measurements.
I can solve problems using data on line plots.
Period
March/April
line plot, unit fractionGeorgia Math and Teacher Generated
Supplements
25
Measurement and DataGeometric measurement: understand concepts of volume and relate volume to multiplication and to addition.3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
I can identify volume as an attribute of a solid figure.
I can recognize that a cube with 1 unit side length
is "one cubic unit" of volume.
I can explain a process for finding the volume of a
solid figure by filling it with unit cubes without gaps and
overlaps.
Period
March/April
volume, unit cube, cubic unitUnit 9 Coordinate Grids/ Graphing/
Perimeter/Area/Volume
26
Measurement and DataGeometric measurement: understand concepts of volume and relate volume to multiplication and to addition.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.I can measure the volume of a hollow three-
dimensional figure by filling it with unit cubes without
gaps and counting the number of unit squares.
Period
March/April
volume, unit cube, cubic unitUnit 9 Coordinate Grids/ Graphing/
Perimeter/Area/Volume
27
Measurement and DataGeometric measurement: understand concepts of volume and relate volume to multiplication and to addition.5. Relate volume to the operations of multiplication and addition and
solve real world and mathematical problems involving volume.
 Find the volume of a right rectangular prism with whole-number side
lengths by packing it with unit cubes, and show that the volume is
the same as would be found by multiplying the edge lengths,
equivalently by multiplying the height by the area of the base.
Represent threefold whole-number products as volumes, e.g., to
represent the associative property of multiplication.
 Apply the formulas V = l × w × h and V = b × h for rectangular
prisms to find volumes of right rectangular prisms with wholenumber
edge lengths in the context of solving real world and
mathematical problems.
 Recognize volume as additive. Find volumes of solid figures
composed of two non-overlapping right rectangular prisms by
adding the volumes of the non-overlapping parts, applying this
technique to solve real world problems.
I can use unit cubes to determine the volume of a
rectangular prism.
I can explain multiplication of the area of the base by the
height will result in the volume.
I can relate finding the product of three numbers to
finding the volume and relate both to the
associative property of multiplication.
I can use the formulas to determine the volume of
rectangular prisms.
I can decompose an irregular figure into non-overlapping
rectangular prisms and find the volume of the irregular
figure by finding the su of the volumes of each of the
decomposed prisms.
I can solve real-world problems involving volume.
Period
March/April
volume, right rectangular prism, additiveUnit 9 Coordinate Grids/ Graphing/
Perimeter/Area/Volume
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