s3.amazonaws.com€¦ · web view2013-12-11 · goddard public schools, usd 265. grade 5 math...

Goddard Public Schools, USD 265Grade 5 Math Pacing-Curriculum Guide 2013-2014

First Nine Weeks

CC Strand Cluster Standard Essential Question(s) Textbook Correlation: Lessons/Units Length Vocabulary

Emphasized

Resources:Technology,

websites, apps

A=Assess

1 2 3 4

Operations and Algebraic

Thinking

Write and interpret numerical

expressions.

5.OA.2Write 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 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

• Can you use mathematical

symbols (parenthesis, brackets, and braces)

to create and evaluate a numerical

expression?

Topic 8—Really Cover this standard in the

2nd Nine Weeks.

•

Parenthesis: a pair of symbols used to

enclose sections of a mathematical

expression• Brackets:

a pair of symbols used to enclose sections of

a mathematical expression

• Braces: a pair of symbols used to enclose sections of


• Numerical Expression: an expression that contains only numbers and

operations• Symbols: mathematical signs

PEMDASD www.brainpop.com

A A


Thinking

Analyze pattern and

relationships.

5.OA.3Generate 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

• Given two rules, can you describe the

numerical patterns?

• Can you plot points on a

coordinate plane, making a graph of those points, and then interpret the

graph identifiying the relationships?

Topic 16—Really Cover this standard in

the 4th Nine Weeks.

• numerical patterns: recurring or repeated sequence of

numbers; Note: sequence means

there is a constant ratio or progression

between the numbers

• rules: the method used for

finding the pattern, sequence

•

relationships: the set

http://mathvids.com/lesson/mathhelp/

1294-plotting-pointshttp://mathvids.com/lesson/mathhelp/750-

graphing-ordered-pairs-in-the-

coordinate-planehttp://

www.helpingwithmath.com/by_subject/

algebra/alg_patterns_4oa5.ht

m

A A

Goddard CCSS Math Pacing Curriculum Guide – Grade 5 1 Last Revised November 2013


observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

of ordered pairs (EX: {(1,3), (2,5), (3, 7)} is a

relation.

•

corresponding terms: the feature that is

situated in the same position/way but may have different values,

objects.

• ordered pairs: a pair of

numbers where order is important, for example, (3,5)) is

different to (5,3). The ordered pair is

typically used to indicate a point on a

coordinate plane, graph or map.

Number and Operations in

Base Ten

Understand the place value

system.

5.NBT.1Recognize 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.

• What does it mean if I move one

place to the left or one place to the

right?

Topic 1 in Textbook • Multi-digit number- a number with more than one

digit• Place-

ones, tens, hundreds, etc.

Money- pennies, dime, dollars, ten dollars, hundred

dollars, etcPlace Value Mats and

other modelsBase Ten Blocks

A A A A


Base Ten


system.

5.NBT.2Explain 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.

• Is there a pattern? Do I

understand the pattern?

• When using an exponent,

what does that mean?

Topic 3 in Textbook • patterns- place value, decimal,

model, repeating process

• product- answer to a

multiplication problem

• powers of ten- numbers that are formed by multiplying ten by itself a certain

number of times (10^3=1000)

• exponents-

Place value mat A A A A



a small number placed to the upper right of the number

saying how many times the number is multiplied by itself


Base Ten


system.

5.NBT.3Read, write, and compare decimals to thousandths.

• Write the number on a place value mat, line the

digits into the proper place value.

• Can I read this decimal number correctly? Can I write

a given decimal number correctly?• Explain

how you know which decimal is larger or

smaller.

Topic 1 in Textbook • Decimals to thousandths- a piece of a whole

number including digits to the right of the decimal point,

tenths, hundredths, and thousandths

Place value matFraction & Decimal

TilesNumber Line

Kim Sutton Place Value Resources

A


Base Ten


system.

5.NBT.3Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000).

• Can I write a number using expanded form? Standard form? Numeral form?

Topic 1 in Textbook • Decimals to thousandths- see

prior definition• Base-ten numerals- standard

form• Number names- writing the number in words

• Expanded form-347.392 = 3 x

100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x

(1/1000).

Place value matFraction & Decimal

TilesNumber Line

Word Wall for number words

A


Base Ten


system.

5.NBT.3bCompare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

• What does this symbol mean?

• How do I know which decimal

is bigger than another decimal?

Topic 1 in Textbook • Decimals to thousandths-see

prior definition• Greater than- bigger than

another• Equal-

same• Less than- smaller than another

Place value matNumber line

A


Base Ten


system.

5.NBT.4Use place value understanding to round

• How do I know which way to

round (up or down)?

Topic 2 in Textbook • Place value- see prior

definition

Place value matNumber line

Kim Sutton “Up the

A



decimals to any place. • Which place do I round to?

• Round decimals to ANY place- change a

number to an easier number to manipulate

Hill”


Base Ten

Perform operations with

multi-digit whole numbers and

with decimals to hundredths.

5.NBT.5Fluently multiply multi-digit whole numbers using the standard algorithm.

• What two numbers do I

multiply?• What

order do I multiply in?• Do you

know what standard algorithm means?

Show me how to use it.

Topic 3 in Textbook • Multi-digit whole numbers- see

prior definition• Standard algorithm- carrying

numbers, regrouping, conventional multiplication

Models-array, area model, etc

Alternative algorithmsLattice model

distributive property (Singapore Math)

A


Base Ten




5.NBT.6Find 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.

• What is the divisor? What is

the dividend? What is a quotient?

• How will I show my answer?

Topic 4 for 1-Digit Divisors; Topic 5 for 2-Digit Divisors; We

may cover this standard in the 1st

Nine Weeks but most likely we will cover this standard in the

2nd Nine Weeks.

• Whole-number quotients- answer to division

problem• Dividend- number to be divided

• Divisor- number dividend is

divided by• strategies based on place value-

powers of ten, rounding

• properties of operations- communative,

distributive, associative, zero

property, etc.•

relationship between multiplication and division- inverse

operations• calculation

by using equations, rectangular arrays,

and/or area models-using visual models to

solve problems

Money, Base Ten Blocks

Picture DrawingModels-array, area

model, etcAlternative algorithms

•

http://illuminations.nctm.org/ActivityDetail

.aspx?ID=64

A A

Number and Perform 5.NBT.7 • What Topic 2 for Adding • Decimals Models-array, area A



Operations in Base Ten

operations with multi-digit whole

numbers and with decimals to

hundredths.

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.

strategy did I use? Why did it work?

• Can I add, subtract, multiply,

and divide decimals?

and Subtracting Decimals; Topic 6 for Multiplying Decimals;

Topic 7 for Dividing Decimals

to hundredths- a piece of a whole

number including digits to the right of the decimal point,

tenths, and hundredths

• Concrete models or drawings-

manipulatives, graphs, arrays, etc

• strategies based on place value-

see prior definition• properties

of operations- see prior definition

•

relationship between addition and

subtraction- inverse operations

model, etc.Number line



Second Nine Weeks


Emphasized


websites, apps

A=Assess

1 2 3 4


Thinking

Write and interpret numerical

expressions.

5,OA.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

• Can you use mathematical

symbols (parenthesis, brackets, and braces)

to create and evaluate a numerical

expression?

Topic 8: Numerical Expressions, Patterns,

and Relationships

•

Parenthesis: a pair of symbols used to

enclose sections of a mathematical

expression• Brackets:

a pair of symbols used to enclose sections of


• Braces: a pair of symbols used to enclose sections of


• Numerical Expression: an expression that contains only numbers and

operations• Symbols: mathematical signs

A


Base Ten




5.NBT.6Find 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.

• What is the divisor? What is

the dividend? What is a quotient?

• How will I show my answer?

Topic 6 and 7—Multiplying and

Dividing Decimals

• find-locate• illustrate• explain

Models-array, area model, etc

Alternative algorithms•

http://illuminations.nctm.org/ActivityDetail

.aspx?ID=64

A


Base Ten



5.NBT.7Add, subtract, multiply, and divide decimals to hundredths, using concrete

• What strategy did I use? Why did it work?

• Can I add,

Topic 6 and 7—Multiplying and

Dividing Decimals

• Decimals to hundredths- a piece of a whole

number including

Models-array, area model, etc.

Number line

A




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.

subtract, multiply, and divide decimals?

digits to the right of the decimal point,

tenths, and hundredths

• Concrete models or drawings-

manipulatives, graphs, arrays, etc

• strategies based on place value-

see prior definition• properties

of operations- see prior definition

•

relationship between addition and

subtraction- inverse operations

Number and Operations –

Fractions

Use equivalent fractions as a

strategy to add and subtract

fractions.

5.NF.1Add 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.)

• Can the student recognize

unlike denominators?• Can the student calculate

equivalent fractions before adding or

subtracting fractions?

Topic 9—Adding and Subtracting Fractions

• Fraction – a number which

represents a part of a whole; usually

expressed as a/b•

Denominator – the part of the fraction

that is below the line & functions as the

divisor of the numerator

• Unlike Denominator – when 2 or more fractions

are present, the divisors are different

• Like Denominator – when 2 or more fractions

are present, the divisors are the same• Equivalent

fraction – fractions that have the same value even though

they may look



different (eg..1/2 and 2/4 – they both equal

half)• Equivalent sum – the total (add)

of the combined fractions will have the

same value• Equivalent

difference – the difference (subtract)

between the fractions will have the same

value• Mixed

number – a number consisting a whole

number and a fraction or decimal (eg.. 4 ½ or

4.5)Number and Operations –

Fractions

Use equivalent fractions as a

strategy to add and subtract

fractions.

5.NF.2Solve 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.

• Can the student create

equivalent fractions when faced with

unlike denominators?• Can the

student choose relevant information

to solved the problem?

• Can the student check for

reasonableness of the answer?

Topic 9—Adding and Subtracting Fractions

• Word problem – a type of

problem designed to help students apply

abstract mathematical

concepts to “real-world” situations

• Fraction - a number which


expressed as a/b• Whole – the amount or total

• Unlike denominator - when 2 or more fractions are present, the divisors

are different• Equation –

consist of the expressions that have

to be equal on opposite sides of an

equal sign• Visual fraction model –

A



representation of a fraction without using

numbersNumber and Operations –

Fractions

Apply and extend previous understandings of multiplication and division to multiply and

divide fractions.

5.NF.3Interpret 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?

• Can the student choose

relevant information to solve the problem?

• Can the student divide the

parts of the fraction?• Can the student change a

fraction into a mixed number or a mixed

number into a fraction?

Topic 11—Multiplying and Dividing Fractions and Mixed Numbers



expressed as a/b• Numerator

– the part of the fraction that is above the line & functions as

the dividend of the denominator

•

Denominator - the part of the fraction

that is below the line & functions as the

divisor of the numerator

• Word problem - a type of

problem designed to help students apply

abstract mathematical

concepts to “real-world” situations

• Equation – consist of the

expressions that have to be equal on

opposite sides of an equal sign

• Visual fraction model –


numbers

A


Fractions


divide fractions.

5.NF.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

• Can the student apply

multiplication to fractions?

Topic 11—Multiplying and Dividing Fractions and Mixed Numbers



expressed as a/b• Whole

Number – a number

A



which doesn’t contain a fraction or a

decimalNumber and Operations –

Fractions


divide fractions.

5.NF.4aInterpret the product (a/b) xq as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations axq ÷ b. For example, use a visual fraction model to show (2/3) x4 = 8/3, and create a story context for this equation. Do the same with (2/3) x(4/5) = 8/15. (In general, (a/b) x(c/d) = ac/bd.)

• Can the student apply the

order of operations to fractions?

• Can the student multiply & divide fractions?

Topic 11 • Partition - division

• Product – answer to a

multiplication problem

• Sequence of operations – the

order in which numbers are

computed

A


Fractions


divide fractions.

5.NF.4bFind 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.

• Can the student apply the

formula for finding the area of rectangle?

• Can the student find the area of a rectangle using fractional units of

measure?• Can the

student create a model using tiles that

demonstrates the answer?

Topic 11 • Area of Rectangle – surface measurement (eg..

length x width)Rectangle – a four-sided polygon that has 4 right angles &

each pair of opposite sides are parallel and

of the same length• Unit – a

standard of measurement

(eg..cm, m, in, etc)

A


Fractions


divide fractions.

5.NF.5bExplaining 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 = (nxa)/(nxb) to the effect of multiplying a/b by 1.

• Can the student explain how a

number changes when multiplied by a

fraction?• Can the fraction reduce a fraction to lowest terms? (simplify a

fraction)

Topic 11 • Fraction - a number which


expressed as a/b• Product –

the answer to a multiplication

problem• Principle

of Fraction Equivalence –

reducing the fraction to lowest terms; simplify; simplest

form

A

Number and Apply and 5.NF.6 • Can the Topic 11 • Real world A



Operations – Fractions

extend previous understandings of multiplication and division to multiply and

divide fractions.

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

student determine the relevant

information that is required to solve the

problem?• Can the

student multiply fraction & mixed

numbers?

problems – word problems that relate

to “real world” situations

• Visual fraction model -


numbers• Equations -

consist of the expressions that have

to be equal on opposite sides of an

equal sign

Geometry Graph points on the coordinate plane to solve real-world and mathematical

problems.

5.G.1Use 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).

• Can I find the origin of the coordinate grid?• Can I

locate an ordered pair on the coordinate

grid?• Can I give the ordered pair for a specific point given on the coordinate grid?

• Do I understand what the x & y axes are and am

I using them in the correct order?

Topic 16—Coordinate Geometry—This will actually be assessed during the 4th Nine

Weeks

•

Perpendicular Number Lines – Two lines that are at right angles to each other• X Axis –

Horizontal line used as a reference line• Y Axis –

Vertical line used as a reference line

• Coordinate System – system used to pinpoint where a location is on a map

or graph•

Intersection (origin) – point where two lines

cross over• Point – an

exact location• Ordered Pair (coordinates) –

two numbers written in a certain order, usually written in

parentheses, with the x value first and the y value second ex. (2,3)

http://www.math-aids.com/Geometry/

Coordinate/http://

www.oswego.org/ocsd-web/games/

BillyBug/bugcoord.html

http://www.mathwire.com/games/gridlock2.pdf

http://www.purplemath.co

m/modules/plane2.htm

http://www.smarterbalanced.org/wordpress/wp-

content/uploads/2012/05/

TaskItemSpecifications/Guidelines/StyleGuide/

StyleGuide.pdfwww.eduplace.com/math/mathsteps/4/c/4.coord.tips.html

http://teachingimage.com/

coordinates.phpwww.math-

aids.com/Geometry/

A



used to identify a point on a coordinate

grid

Coordinate/Angry_Birds_Graphin

g_Puzzle.htmlGeometry Graph points on

the coordinate plane to solve real-world and mathematical

problems.

5.G.2Represent 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.

• How does geometry better describe objects?

• Can you plot points on a

coordinate plane, making a graph on those points, and

interpret the geometric attributes

of the figure created?

Topic 16—Coordinate Geometry

• Ordered pair: a pair of

numbers where order is important, for example, (3,5) is

different to (5,3). The ordered pair is

typically used to indicate a point on a

coordinate plane, graph, or map.

• Quadrant: One of the quarters of

the plane of the Cartesian coordinate

system• Coordinate

plane: The plane determined by a

horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each

point in the coordinate plane can

be specified by an ordered pair of

numbers.

www.math-play.comwww.ixl.com

A A



Third Nine Weeks


Emphasized


websites, apps

A=Assess

1 2 3 4


Fractions


divide fractions.

5.NF.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.24

24 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

A


Fractions


divide fractions.

5.NF.7aInterpret 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) x4 = 1/3.

A


Fractions


divide fractions.

5.NF.7bInterpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x(1/5) = 4.

A

Number and Apply and 5.NF.7c A



Operations – Fractions

extend previous understandings of multiplication and division to multiply and

divide fractions.

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?

Measurement and Data

Convert like measurement units within a

given measurement

system.

5.MD.1Convert 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.

A

Geometry Classify two-dimensional figures into

categories based on their

properties.

5.G.3Understand 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.

A

Geometry Classify two-dimensional figures into

categories based on their

properties.

5.G.4Classify two-dimensional figures in a hierarchy based on properties.

A



Fourth Nine Weeks


Emphasized


websites, apps

A=Assess

1 2 3 4


Represent and interpret data.

5.MD.2Make a line plot to display a data 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.

A


Geometric measurement:

understand concepts of volume and

relate volume to multiplication

and to addition.

5.MD.3Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

A





and to addition.

5.MD.3aA 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.

A





and to addition.

5.MD.3bA solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

A

Measurement Geometric 5.MD.4 A



and Data measurement: understand concepts of volume and


and to addition.

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.





and to addition.

5.MD.5Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

A





and to addition.

5.MD.5aFind 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.

A





and to addition.

5.MD.5bApply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

A





and to addition.

5.MD.5cRecognize 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

A



world problems.


s3.amazonaws.com€¦ · web view2013-12-11 · goddard public schools, usd 265. grade 5 math...

Documents