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APS District Curriculum Map Grade Level: 8 _Course /Subject: Math

8th Grade Math September 1, 2009-10 Final 1

ESSE�TIAL

COMPO�E�TS

Month: August Moving Straight Ahead

1. Big Ideas

Student answers to EQs that

lead them to the Big Ideas

A relationship is linear if there is a constant rate of change between variables. The pattern of change in a linear

relationship will show up in a table through observing a constant increase or decrease in the dependent variable as the

independent variable increases by a constant amount. In a graph, the linear pattern of change shows up as a straight

line. In an equation, the linear relationship shows up if it looks like y=2x or y= 100 + 10x. There is a number in front

of the x variable and there may be a number that you add to give you the starting value.

2. Essential Questions

Questions that lead students to

Big Ideas.

What patterns in a problem suggest that it is linear? How can the linear pattern be represented in a problem, in a table,

in a graph, or with an equation?

3. Performance Standards

PROCESS STA�DARDS:

Problem Solving

• Build new mathematical knowledge through problem solving

• Solve problems that arise in mathematics and other contexts

• Apply and adapt a variety of appropriate strategies to solve pro

• blems, and

• Monitor and reflect on the process of problem solving.

Reasoning and Proof

• Recognize reasoning and proof as fundamental aspects of mathematics,

• Make and investigate mathematical conjectures,

• Develop and evaluate mathematical arguments and proofs, and

• Select and use various types of reasoning and methods of proof.

Communication

• Organize and consolidate their thinking through communication,

• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others,

• Analyze and evaluate the mathematical thinking and strategies of others,

• Use the language of mathematics to express mathematical ideas precisely, and

• Describe mathematical concepts using developmentally appropriate definitions.

Connections

• Recognize and use connections among mathematical ideas,

• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole, and

• Recognize and apply mathematics in contexts outside of mathematics.

Representation

• Create and use representations to organize, record, and communicate mathematical ideas,

• Select, apply, and translate among mathematical representations to solve problems, and




(Continued)

• Use representations to model and interpret physical, social, and mathematical phenomena.

CO�TE�T STA�DARDS:

Strand: �UMBER A�D OPERATIO�S Students will understand numerical concepts and mathematical operations.

5-8 Benchmark �.3 Compute fluently and make reasonable estimates.

�.3.1 Formulate algebraic expressions that include real numbers to describe and solve real-world problems.

�.3.2 Use a variety of computational methods to estimate quantities involving real numbers.

�.3.4 Use real number properties to perform various computational procedures and explain how they were used.

�.3.5 Perform and explain computations with rational numbers, pi, and first degree algebraic expressions in one

variable in a variety of situations.

�.3.6 Select and use appropriate forms of rational numbers to solve real world problems including those involving

proportional relationships.

�.3.7 Approximate, mentally and with calculators, the value of irrational numbers as they arise from problem

situations.

Strand: ALGEBRA Students will understand algebraic concepts and applications.

5-8 Benchmark A.1 Understand patterns, relations, and functions.

A.1.1 Move between numerical, tabular, and graphical representations of linear relationships.

A.1.2 Use variables to generalize patterns and information presented in tables , charts, and graphs:

A.1.2.a graph linear functions noting that the vertical change per unit of horizontal change (the slope of the graph) is

always the same.

A.1.2.b plot the values of quantities whose ratios are always the same, fit a line to the plot, and understand that the

slope of the line equals the quantities.

5-8 Benchmark A.2 Represent and analyze mathematical situations and structures using algebraic symbols.

A.2.5 Graph solution sets of linear equations in two variables on the coordinate plane.

A.2.6 Formulate and solve problems involving simple linear relationships, find percents of a given number, variable

situations, and unknown quantities.

5-8 Benchmark A.3 Use mathematical models to represent and understand quantitative relationships.

A.3.1 Generate different representations to model a specific numerical relationship given one representation of data

(e.g., a table, a graph, an equation, a verbal description).

5-8 Benchmark A.4 Analyze changes in various contexts.

A.4.1 Use graphs, tables, and algebraic representations to make predictions and solve problems that involve change.

A.4.2 Estimate, find, and justify solutions to problems that involve change using tables, graphs, and algebraic

expressions.

A.4.3 Use appropriate problem-solving strategies (e.g., drawing a picture, looking for a pattern, systematic guessing

and checking, acting it out, making a table or graph, working a simpler problem, writing an algebraic expression, or

working backward) to solve problems that involve change.



A.4.4 Solve multiple-step problems that involve changes in rate, ,average speed, distance, and time

A.4.5 Analyze problems that involve change by identifying relationships, distinguishing relevant from irrelevant

information, identify missing information, sequencing, and observing patterns.

A.4.6 Generalize a pattern of change using algebra and show the relationship among the equation, graph, and table of

values.

A.4.7 Recognize the same general pattern of change presented in different representations.

Strand: MEASUREME�T Students will understand measurement systems and applications.

5-8 Benchmark M.2 Apply appropriate techniques, tools, and formulas to determine measurements.

M.2.5 Perform conversions with multiple terms between metric and U.S. standard measurement systems.

M.2.7 Solve simple problems involving rates and derived measurements for such properties as velocity and density.

4. Assessments Fall DBA standards & (items): A.1.1(7) – (1), A.1.2(7) – (2), A.1.3(7) – (1), A.1.6(7) – (1), A.2.1(7) – (3), A.2..2(7) –

(1), A.2.6(7) – (1), A.3.2(7) – (1), A.4.1(7) – (1), D.1.3(7) – (1), D.1.11(7) – (1), D.2.1(7) – (1), D.3.2(7) – (2),

G.3.1(7) – (1), G.1.4 (7) – (1), G.4.2(7) – (1), M.1.1(7) – (1), M.1.2(7) – (1), M.2.2(7) – (1), M.2.3(7) – (2), N.1.3(7) –

(3), N.2.1(7) – (8), N.2.3(7) – (2), N.2.7(7) – (1), N.2.8(7) – (2). Total items = 41.

* (7) – Out of grade level standard to be used as baseline for 09-10 school year

Recommendations for the Content (What students need to know – nouns), Skills (What students need to be able to do – verbs), Vocabulary List

(Words students need to know to understand concepts), Learning Activities/Lesson Plans (Essential Experiences or Guided Practice),

and Resources are provided below and should be used at teachers’ discretion. Refer to OPD, C&A, and RDA Websites for additional resources

5. Content

�ouns (What students need

to know)

8.N.3.1: algebraic expression, real number, real-world problem

8.N.3.2: computational method, quantity, real number

8.N.3.4: real number properties, computational procedure

8.N.3.5: computation, rational number, variable

8.N.3.6: forms of rational number, proportional relationship

8.A.1.1: representation, linear relationship

8.A.1.2: variable, pattern, table, graph, chart, linear function, vertical change, horizontal change, slope, value ratio, line

8.A.2.1: equation, expression

8.A.2.5: solution set, linear equation, variable, coordinate plane

8.A.2.6: problem, linear relationship, percent, variable situation, unknown quantity

8.A.3.1: representation, numerical relationship, table, graph, equation, verbal description

8.A.4.1: graph, table, algebraic representation, prediction, change

8.A.4.2: solution, change, table, graph, algebraic expression

8.A.4.4: multiple-step problems, rate, average speed, distance, time

8.A.4.3: problem-solving strategy, change

8.A.4.5: change, relationship, relevant information, irrelevant information, missing information, sequencing, patters

8.A.4.6: pattern, change, equation, graph, table of values

8.A.4.7: pattern, change, representation

8.M.2.5: conversion, multiple terms, US standard measurement system

8.M.2.7: problem, rates, derived measurement, property

6. Skills

Verbs (What students need to

be able to do)

8.N.3.1: formulate, describe

8.N.3.2: use computational method, estimate

8.N.3.4: use properties, explain

8.N.3.5: perform, explain



8.N.3.6: select, use forms of rational numbers

8.A.1.1: move between representations

8.A.1.2: use variables, graph, plot

8.A.2.1: demonstrate difference

8.A.2.5: graph

8.A.2.6: formulate, solve

8.A.3.1: generate representations

8.A.4.1: use representations

8.A.4.2: estimate, find, justify solutions

8.A.4.3: use strategies

8.A.4.4: solve

8.A.4.5: analyze, identify, distinguish,

8.A.4.6: generalize, show relationship

8.A.4.7: recognize

8.M.2.5: perform conversion

8.M.2.7: solve

7. Vocabulary List (Words

students need to know to

understand concepts)

Coefficient, constant term, linear relationship, y-intercept, constant rate of change, equation of a line, linear function, solving and equation, x-intercept,

function, dependent variable, independent variable, ratio/rate, scale, graph/coordinate graph, origin

Equation and expression

8. Learning

Activities/Lesson Plans (Essential Experiences or

Guided Practices)

Review concepts involving addition, subtraction, multiplication, and division of fractions (CM2, Bits and Pieces II, Additional Practice, Investigation 2 p.49-

50, Investigation 3 p.53-54,

Investigation 4, p.57-58) *

Review concepts involving addition, subtraction, multiplication, and division of integers (CM2, Accentuate the Negative, Additional Practice, Investigation 2

p.70-72, Investigation 3 p.76-78, Investigation 4 p.81) *

Determine walking rates, answer questions about time and distance using walking rates, write equations representing distance traveled over time (CM2,

Moving Straight Ahead, 1.1)

Describe patterns of change between independent and dependent variables for linear relationships in tables, and construct tables, graphs and equations to

represent linear patterns of change (CM2, Moving Straight Ahead, 1.2).

Construct graphs and tables to model problem situations, and translate information about linear relations given in a table, a graph, or an equation to one of the

other forms (CM2, Moving Straight Ahead, 1.3)

Understand negative rates of change and how they are represented in equations, tables, and graphs, explore y-intercept, describe information the

variables and numbers in an equation represent (CM2, Moving Straight Ahead, 1.4)

9. Assessments: Formative Assessments

How will students and teacher

know what students have

learned so far? Differentiated

Rubric Links / Attached

Summative Assessments

How will students show that

they have mastered the

standard? Differentiated


Quiz: Identify linear relationships from tables, write equations of linear relationships, describe what happens to the y value as x increases (CM2, Moving

Straight Ahead, Check-Up 1)

Essay: Describe how the pattern of change for a linear relationship shows up in a table, a graph, and an equation of the relationship (CM2, Moving Straight

Ahead, Mathematical Reflections 1)

Essay: Describe how the dependent variable changes as the independent variable changes in a linear relationship. Give examples (CM2, Moving Straight

Ahead, Mathematical Reflections 1)

No unit summative Assessment this month because only part of the unit is completed.

10. Resources 8th Grade Teacher CD, http://www.phschool.com, http://connectedmath.msu.edu



ESSE�TIAL

COMPO�E�TS

Month: September MSA (continued)

1. Big Ideas



Any ordered pair (point) on a line or a table for a linear relationship can be used to find a solution to a problem. You

could also use the equation by substituting values of given in the problem into the equation and figuring out the

unknown. A linear relationship in an equation is represented by the form y= mx + b where “m” controls the slope of

the line and “b” gives the y-intercept.



Big Ideas.

How can tables, graphs, and equations of linear relationships be used to express and answer questions? How can a

linear relationship be represented by an equation?



Problem Solving



• Apply and adapt a variety of appropriate strategies to solve problems, and


Reasoning and Proof





Communication






Connections




Representation







(Continued)












situations.


5-8 Benchmark A.1 Understand patterns, relations, and functions.




always the same.




A.2.1 Demonstrate the difference between an equation and an expression

A.2.2 Solve two-step linear equations and inequalities in one variable with rational solutions










expressions.








A.4.6 Generalize a pattern of change using algebra and show the relationship among the equation, graph, and table of values.






4. Assessments Fall DBA standards & (items): A.1.1(7) – (1), A.1.2(7) – (2), A.1.3(7) – (1), A.1.6(7) – (1), A.2.1(7) – (3), A.2..2(7) –

(1), A.2.6(7) – (1), A.3.2(7) – (1), A.4.1(7) – (1), D.1.3(7) – (1), D.1.11(7) – (1), D.2.1(7) – (1), D.3.2(7) – (2),

G.3.1(7) – (1), G.1.4(7) – (1), G.4.2(7) – (1), M.1.1(7) – (1), M.1.2(7) – (1), M.2.2(7) – (1), M.2.3(7) – (2), N.1.3(7) –

(3), N.2.1(7) – (8), N.2.3(7) – (2), N.2.7(7) – (1), N.2.8(7) – (2)

* (7) – Out of grade level standard to be used as baseline for 09-10 school year




5. Content


to know)






8.N.3.7: calculator, value, irrational number



8.A.2.2: two-step linear equations, two-step linear inequalities, rational solutions



8.A.2.7: symbols, variables, expressions, inequalities, equations, systems of equations










6. Skills


be able to do)






8.N.3.7: approximate



8.A.2.2: solve



8.A.2.5: graph


8.A.2.7: use symbols







8.A.4.7: recognize


8.M.2.7: solve




Coefficient, y-intercept, linear relationship, constant rate, equation of a line, linear function, steepness, coordinate pair, graph/coordinate graph, scale, table,

independent and dependent variables

8. Learning


Guided Practices)

Find solutions to a problem using a table or graph (CM2, Moving Straight Ahead, 2.1)

Understand the connections between linear equations and patterns in the tables and graphs of those relations, including rate of change, and x and y intercepts;

Translate information about linear relations given in a table, a graph or an equation to one of the other forms; Find solutions to a problem using a table or

graph; Connect solutions in graphs and tables to solutions of equations. (CM2, Moving Straight Ahead, 2.2, 2.3, 2.4)

Describe the information the variables and numbers in an equation represent, solve linear equations in one variable using tables, graphs and symbols, connect

solutions to equations to a table or graph (CM2, Moving Straight Ahead, 3.1)

Develop understanding of equality and use properties of equality to solve equations that are represented pictorially (CM2, Moving Straight Ahead, 3.2)

Use the properties of equality to solve equations and check solutions to equations (CM2, Moving Straight Ahead, 3.3)

Develop strategies for solving linear equations (CM2, Moving Straight Ahead, 3.4)

Interpret equations in an applied setting, find the point of intersection of two lines (CM2, Moving Straight Ahead, 3.5)

9. Assessments:

Formative Assessments

How will students and

teacher know what students

have learned so far?

Differentiated







Quiz: Determine scale of a graph and use the graph to write an equation, use an equation to solve problems (CM2, Moving Straight Ahead, Partner Quiz)

Essay: Explain how a table or graph for a linear relationship can be used to solve a problem. Explain how to use an equation to solve a problem. (CM2,

Moving Straight Ahead, Mathematical Reflections 2)

Quiz: Solve linear equations, use linear equations to solve problems (CM2, Moving Straight Ahead, Check-Up 2)

Essay: Describe a symbolic method for solving a linear equation compare this method to the method of using a table or graph. (CM2, Moving Straight Ahead,

Mathematical Reflections 3)

Summative Assessments will be done in October (CM2, Moving Straight Ahead)




ESSE�TIAL

COMPO�E�TS

Month: October MSA & Looking for Pythagoras

1. Big Ideas



The slope describes the steepness of a line. It is the ratio of vertical change to horizontal change. The slope can be

found in an equation if the equation is in the form y= mx + b, m is the slope. The slope can be found in a graph by

finding two points on the graph, find the difference between the vertical change and the difference between the

horizontal change, and then find the ration of vertical change to horizontal change. In a table, the slope can be found

by finding the change in 2 x values and the change in 2 corresponding y values. The slope is the ratio of change in the

y values to change in x values.



Big Ideas.

What is the slope of a line? How do you find the slope of a line?

How do square roots aid in the finding of side lengths of squares?



Problem Solving





Reasoning and Proof





Communication






Connections




Representation






(Continued)




5-8 Benchmark �.1 Understand numbers, ways of representing numbers, relationships among numbers, and number

systems.

�.1.1 Sort numbers by their properties (e.g., prime, composite, square, square root)

5-8 Benchmark �.2 Understand the meaning of operations and how they relate to one another.

�.2.2 Perform arithmetic operations and their inverses (e.g., addition/subtraction, multiplication/division, square roots

of perfect squares, and cube roots of perfect cubes) on real numbers.

�.2.3 Find roots of real numbers using calculators.




�.3.3 Differentiate between rational and irrational numbers.







situations.


5-8 Benchmark A.1 Understand patterns, relations and functions.




always the same.





A.2.3 Evaluate formulas using substitution.








(Continued)






expressions.






A.4.6 Generalize a pattern of change using algebra and show the relationship among the equation, graph, and table of

values.


Strand: GEOMETRY Students will understand geometric concepts and applications.

5-8 Benchmark G.1 Analyze characteristics and properties of two- and three-dimensional geometric shapes and

develop mathematics arguments about geometric relationships.

G.1.3 Use the Pythagorean theorem and its converse to find the missing side of a right triangle and the lengths of the

other line segments.



M.2.1 Use ratios and proportions to measure hard-to-measure objects.

M.2.3 Use proportional relationships in similar shapes to find missing measurements.



4. Assessments




5. Content


to know)

8.N.1.1: properties, prime, composite, square, square root

8.N.2.2: arithmetic operation, inverse, real number

8.N.2.3: root, real number, calculator











8.A.2.3: formula, substitution











8.M.2.1: ratio, proportion

8.M.2.3: proportional relationship, similar shape, missing measurement



8.G.1.3: Pythagorean theorem, converse, right triangle, length, line segment

6. Skills


be able to do)

8.N.1.1: sort numbers

8.N.2.2: perform operations

8.N.2.3: find roots









8.A.2.2: solve

8.A.2.3: evaluate

8.A.2.5: graph









8.A.4.7: recognize

8.M.2.1: use ratios and proportions

8.M.2.3: use proportional relationships


8.G.1.3: use Pythagorean theorem






Coefficient, y-intercept, linear relationship, constant rate, equation of a line, linear function, steepness, coordinate pair, graph/coordinate graph, scale, table,

independent and dependent variables, slope

Hypotenuse, legs, Pythagorean Theorem, real numbers, irrational numbers, rational numbers, right triangle, perimeter

8. Learning


Guided Practices)

Investigate the “steepness” of a set of stairs. This ratio of “rise” to “run” informally introduces the concept of slope (CM2, Moving Straight Ahead, 4.1)

Connect slope to patterns of change. Find the slope and y-intercept of a line from data in a table, graph or equation. Use the slope and y-intercept to write an

equation in the form of y=mx+b (CM2, Moving Straight Ahead, 4.2)

Explore patterns among lines with the same slope (parallel) and among lines whose slopes are negative reciprocals of each other (perpendicular) (CM2,

Moving Straight Ahead, 4.3)

Write an equation for an applied situation when the only information given is two data points (CM2, Moving Straight Ahead, 4,4)

Plot points on a grid and make connections between coordinates and distance (CM2, Looking for Pythagoras, 1.1)

Define shapes on a coordinate grid (CM2, Looking for Pythagoras, 1.2)

Find areas of irregular shapes draw on a dot grid(CM2, Looking for Pythagoras, 1.3)

Searching for all squares on a 5X5 dot grid (CM2, Looking for Pythagoras, 2.1)

Investigate square roots and make connections to side lengths (CM2, Looking for Pythagoras, 2.2)

Finding side lengths of squares (CM2, Looking for Pythagoras, 2.3)

9. Assessments:


How will students and

teacher know what students

have learned so far?

Differentiated







Essay: Explain what the slope of a line is. Explain how to find the slope of a line from an equation, a graph, a table of values and the coordinates of two points

on the line (CM2, Moving Straight Ahead, and Mathematical Reflections 4).

Quiz: Draw and identify areas and side lengths of polygons(CM2, Looking for Pythagoras, Check-up 1)

Investigation 4)

Unit Test: Solve problems involving linear relationships verbally, graphically, through an equation, and through a table (CM2, Moving Straight Ahead, Unit

Test)

Unit Project: Choose 1: Investigate the rate at which a leaking faucet loses water OR Investigate how the drop height of a ball is related to its bounce height

(CM2, Moving Straight Ahead, Unit Project)

Unit Review: Solve real-world problems involving linear relationships (CM2, Moving Straight Ahead, Looking Back and Looking Ahead).

Self-Assessment: Explain ideas that you have learned about linear relationships, cite evidence of your understanding. Explain ideas that you are still struggling

with, why you are struggling, and evidence that you are struggling (CM2, Moving Straight Ahead, Self Assessment).




ESSE�TIAL

COMPO�E�TS

Month: �ovember Looking for Pythagoras

1. Big Ideas



The Pythagorean Theorem can be used to solve problems.

Two-dimensional models (or nets), patterns, and formulas can be used to determine surface area of three-dimensional

objects.



Big Ideas.

How can the relationships between the sides of a right triangle be used to solve problems?

How is surface area of three-dimensional objects determined?



Problem Solving





Reasoning and Proof





Communication






Connections




Representation







(Continued)



5-8 Benchmark �.1 Understand numbers, ways of representing numbers relationships among numbers, and number

systems.

�.1.1 Sort numbers by their properties (e.g. prime, composite, square, square root)



of perfect squares, cube root of perfect cubes) on real numbers

�.2.3 Find roots of real numbers using calculators


�.3.2 Use a variety of computational methods to estimate quantities involving real numbers

�.3.3 Differentiate between rational and irrational numbers


�.3.7 Approximate mentally and with calculators the value of irrational numbers as they arise from problem situations

�.3.9 Estimate answers and use formulas to solve application problems involving surface area and volume



A.2.3 Evaluate formulas using substitution



develop mathematics arguments about geometric relationships/

G.1.3 Use the Pythagoras theorem and its converse to find the missing side of a right triangle and the lengths of the

other line segments

5-8 Benchmark G.4 Use visualization, spatial reasoning, and geometric modeling to solve problems.

G.4.4 Develop and use formulas for area, perimeter, circumference and volume

G.4.3 Represent and solve problems relating to size, shape, area, and volume using geometric models

G.4.5 Construct two-dimensional patterns for three-dimensional models (e.g. cylinders, prisms, cones)



M.2.1 Use ratio and proportions to measure hard-to-measure objects.

M.2.2 Use estimation to solve problems.

M.2.3 Use proportional relationships in similar shapes to find missing measurements.

M.2.4 Apply strategies to determine the surface area and volume of prisms, pyramids, and cylinders.



4. Assessments




5. Content


to know)

8.N.1.1: properties, prime, composite, square, square root

8.N.2.2: arithmetic operation, inverse, real number

8.N.2.3: root, real number, calculator


8.N.3.3: rational number, irrational number



8.N.3.9: answer, formula, application problem, surface area

8.A.2.3: formula, substitution

8.G.1.3: Pythagorean theorem, converse, right triangle, length, line segment

8.G.4.3: size, shape, area, volume, geometric models

8.G.4.4: formula, area, perimeter, circumference, volume

8.G.4.5: two-dimensional patterns, three-dimensional models

8.M.2.1: ratio, proportion

8.M.2.2: estimation

8.M.2.3: proportional relationship, similar shape, missing measurement

8.M.2.4: strategies, surface area, volume

6. Skills


be able to do)

8.N.1.1: sort numbers


8.N.2.3: find roots


8.N.3.3: differentiate



8.A.2.3: evaluate

8.G.1.3: use Pythagorean theorem

8.G.4.4: develop, use formulas

8.G.4.3: represent, solve

8.G.4.4: construct

8.M.2.1: use ratios and proportions

8.M.2.2: estimation, problems

8.M.2.3: use proportional relationships

8.M.2.4: apply strategies




net, prism, rectangular prism, surface area, right triangle, square root, square number, real numbers, calculators, rational, irrational, Pythagorean Theorem,

converse

8. Learning


Guided Practices)

8. Learning

Collection of right side areas leads to Pythagorean Theorem (CM2, Looking for Pythagoras,3.1)

Proof of the Pythagorean Theorem (CM2, Looking for Pythagoras, 3.2)

Use the Pythagorean Theorem to find distances (CM2, Looking for Pythagoras, 3.3)

Exploration of the converse Pythagorean Theorem (CM2, Looking for Pythagoras, 3.4)

Defining rational/irrational numbers as pertaining to the hypotenuse. (CM2, Looking for Pythagoras, 4.1)



Activities/Lesson Plans

(Continued)

Apply Pythagorean Theorem to find distances on a baseball diamond.(CM2, Looking for Pythagoras, 4.2)

Investigate properties of equilateral triangles. (CM2, Looking for Pythagoras, 4.3)

Apply strategies developed in unit using triangles. (CM2, Looking for Pythagoras, 4.4)

Making nets of cubes to determine surface area (CM2, Filling & Wrapping, 1.1)

Making nets of rectangular prisms to determine surface area (CM2, Filling & Wrapping, 1.2)

Use formulas to find area of polygons (Prentice Hall, Mathematics Course 3, 7-6)

Identify properties of circles and find circumference and area (Prentice Hall, Mathematics Course 3, 7-7 and Extension)

9. Assessments:











Quiz: Find side lengths and areas and perimeters (CM2, Looking for Pythagoras, Partner Quiz)

Essay: Prove that a triangle is a right triangle given two side lengths (CM2, Looking for Pythagoras, Mathematical Reflections 3)

Essay: In what ways is the Pythagorean Theorem useful? (CM2, Looking for Pythagoras, Mathematical Reflections 4)

Quiz: Find side lengths and areas and perimeters (CM2, Looking for Pythagoras, Partner Quiz)

Essay: Prove that a triangle is a right triangle given two side lengths (CM2, Looking for Pythagoras, Mathematical Reflections 3)

Essay: In what ways is the Pythagorean Theorem useful? (CM2, Looking for Pythagoras, Mathematical Reflections 4)




ESSE�TIAL

COMPO�E�TS

Month: December

1. Big Ideas



Two-dimensional models (or nets), patterns, and formulas can be used to determine surface area of three-dimensional

objects.

Patterns and formulas can be used to determine volume of three-dimensional objects.



Big Ideas

How are surface area and volume of three-dimensional objects determined?



Problem Solving





Reasoning and Proof





Communication






Connections




Representation









�.3.9 Estimate answers and use formulas to solve application problems involving surface area and volume



G.4.3 Represent and solve problems relating to size, shape, area, and volume using geometric models.

G.4.5 Construct two-dimensional patterns for three-dimensional models (e.g. cylinders, prisms, cones).


5-8 Benchmark M.1 Understand measurable attributes of objects and the units, systems, and processes of

measurement.

M.1.1 Understand the concept of volume and use the appropriate units in common measuring systems (e.g. cubic

centimeter, cubic inch, cubic yard) to compute the volume of rectangular solids.

M.1.2 Use changes in measurement units (e.g., square inches, cubic feet) to perform conversions from one-, two-, and

three- dimensional shapes.


M.2.2 Use estimation to solve problems.

M.2.4 Apply strategies to determine the surface area and volume of prisms, pyramids, and cylinders.

M.2.6 Estimate volume in cubic units.

4. Assessments




5. Content


to know)

8.N.3.9: answer, formula, application problem, surface area

8.G.4.3: size, shape, area, volume, geometric model

8.G4.4: formula, area, perimeter, circumference, volume

8.G.4.5: two-dimensional pattern, three-dimensional pattern

8.M.1.1: volume, common measuring system

8.M.1.2: change, measurement unit, conversion, two-dimensional shape, three-dimensional shape

8.M.2.2: estimation

8.M.2.4: strategies, surface area, volume

8.M.2.6: volume, cubic unit

8.N.3.8: scientific notation

6. Skills


be able to do)

8.N.3.8: express numbers

8.N.3.9: estimate, use formulas

8.G.4.3: represent, solve

8.G.4.4: develop, use formulas



8.G.4.5: construct

8.M.1.1: understand, use units, compute

8.M.1.2: use change, perform conversions

8.M.2.2: use estimation, solve

8.M.2.4: apply, determine

8.M.2.6: estimate volume




Base, cone, cylinder, dimensions, edge, face, net, prism, pyramid, rectangular prism, surface area, unit cube, volume

8. Learning


Guided Practices)

Use nets to develop a strategy for finding surface area and volume of a cube (CM2, Filling & Wrapping, 1.3)

Relate the dimensions of a rectangular prism to its surface area and calculate surface area using nets (CM2, Filling & Wrapping, 1.4)

Connect the dimension of a rectangular prism to its volume and surface area and understand the relationship between volume and surface area (CM2, Filling &

Wrapping, 2.1)

Predict the relationship between volume and surface area. Refine a strategy for surface area of a rectangular prism (CM2, Filling & Wrapping, 2.2)

Develop the formula for volume of a rectangular prism (CM2, Filling & Wrapping, 2.3)

Develop understanding of volume and surface area of prisms (CM2, Filling & Wrapping, 3.1)

Volume and surface area of cylinders (CM2, Filling & Wrapping, 3.2)

Develop strategy for finding surface area of a cylinder (CM2, Filling & Wrapping, 3.3)

Use volume to solve problems. Relate volume to surface areas (CM2, Filling & Wrapping, 3.4)

Find surface area of pyramids and Cones (Prentice Hall Mathematics Course 3, Lesson 8-5)

Find volume of a pyramid (Prentice Hall Mathematics Course 3, Lesson 8-7)

Use formulas to find area of polygons (Prentice Hall, Mathematics Course 3, 7-6)

Identify properties of circles and find circumferences and areas (Prentice Hall, Mathematics Course 3, 7-7 and Extension)

9. Assessments:











Quiz: find surface area of a rectangular prism, draw nets for boxes with given dimensions and find volume and surface area (CM2, Filling & Wrapping,

Check-up 1)

Quiz: find volume and surface area of cylinders and triangular prism (CM2, Filling & Wrapping, Partner Quiz)

Essay: For a given number of cubes, what arrangement will give the rectangular prism the least surface area? (CM2, Filling & Wrapping, Mathematical

Reflections 2)

Unit Test: Solving Problems involving surface area and volume of rectangular prisms and cylinders (CM2, Filling & Wrapping, Unit Test)

Performance Assessment: The Package Design Contest (CM2, Filling & Wrapping, Unit Project)




ESSE�TIAL

COMPO�E�TS

Month: January Kaleidoscopes, Hubcaps & Mirrors

1. Big Ideas



Symmetry, similarity, congruence are ways to describe and classify geometric shapes.



Big Ideas.

How can you use properties of geometric shapes to describe and classify them?



Problem Solving





Reasoning and Proof





Communication






Connections




Representation







(Continued)




develop mathematics arguments about geometric relationships.

G.1.1 Recognize, classify, and discuss properties of all geometric figures including point, line, and plane.

G.1.2 Identify arc, chord, and semicircle and explain their attributes.

5-8 Benchmark G.2 Specify locations and describe spatial relationships using coordinate geometry and other

representational systems.

G.2.1 Represent, formulate, and solve distance and geometry problems using the language and symbols of algebra and

the coordinate plane and space (e.g., ordered triplets).

5-8 Benchmark G.3 Apply transformations and use symmetry to analyze mathematical situations.

G.3.1 Describe the symmetry of three-dimensional figures.

G.3.2 Describe and perform single and multiple transformations that include rotation, reflection, translation, and

dilation (i.e., shrink or magnify) to two-dimensional figures.


G.4.1 Understand angle relationships formed by parallel lines cut by a transversal.

G.4.2 Recognize and apply properties of corresponding parts of similar and congruent triangles and quadrilaterals.

G.4.4 Develop and use formulas for area, perimeter, circumference, and volume.

4. Assessments Winter DBA standards & (items): N.2.8(7) – (2), A.1.1 – (2), A.1.2 – (2), A.2.3 – (3), A.3.1 – (1), A.4.1 – (1), A.4.2 –

(1), A.4.3 – (2), A.4.6 – (6), G.1.3 – (3), G.4.4 – (4), G.4.5 – (1), M.2.4 – (2), N.2.1 – (3), N.2.2 – (2), N.3.1 – (1),

N.3.2 – (1), N.3.4 – (1), N.3.8 – (1). Total items = 39.

* (7) – Out of grade level standard




5. Content


to know)

8.G.1.1: properties, geometric figures, point, line, plane

8.G.1.2: arc, chord, semicircle, attributes

8.G.2.1: distance problems, geometry problems, language of algebra, symbols of algebra, coordinate plane, space

8.G.3.1: symmetry, three-dimensional figures

8.G.3.2: single transformations, multiple transformations, rotation, reflection, translation, dilation, two-dimensional figures

8.G.4.1: angle relationship, parallel lines, transversal

8.G.4.2: properties, similar triangles and quadrilaterals, congruent triangles and quadrilaterals

6. Skills


be able to do)

8.G.1.1: recognize, classify, discuss

8.G.1.2: identify

8.G.2.1: represent, formulate, solve

8.G.3.1: describe

8.G.3.2: describe, perform transformations

8.G.4.1: understand

8.G.4.2: recognize, apply






Point, line, plane, arc, chord, semicircle, symmetry, reflection, line of symmetry, reflection symmetry, rotation, rotation symmetry, center of rotation, angle of

rotation, translation, translation symmetry, basic design element

8. Learning


Guided Practices)

Describe symmetries and use tools to analyze reflection (CM2, Kaleidoscopes, Hubcaps, and Mirrors, 1.1)

Describe rotation symmetry and use tools to analyze designs with rotation symmetry (CM2, Kaleidoscopes, Hubcaps, and Mirrors, 1.2)

Describe translation symmetry and use tools to analyze designs with translation symmetry (CM2, Kaleidoscopes, Hubcaps, and Mirrors, 1.4)

Use tools properties of reflections (line of reflection) to solve problems involving reflection (CM2, Kaleidoscopes, Hubcaps, and Mirrors, 2.1)

Use tools and properties of rotation (center of rotation, angle of rotation) to solve problems involving rotation (CM2, Kaleidoscopes, Hubcaps, and Mirrors,

2.2)

Use tools and properties of translations (magnitude and direction) to solve problems involving translation (CM2, Kaleidoscopes, Hubcaps, and Mirrors, 2.3)

Find lines of symmetry (for reflection symmetry) and center of rotation (for rotation symmetry) of three-dimensional shapes (John Van De Walle, Elementary

and Middle School Mathematics, Chapter 17, Activity 17.31 and 17.32)

Use coordinates to write directions for reflecting a figure; specify coordinate rules for reflections (CM2, Kaleidoscopes, Hubcaps, and Mirrors, 5.1)

Specify coordinates rules for translations (CM2, Kaleidoscopes, Hubcaps, and Mirrors, 5.2)

Specify coordinate rules for rotations of 90°, 180°, 270° and 360° (CM2, Kaleidoscopes, Hubcaps, and Mirrors, 5.3)

Specify coordinate rules for combinations of transformations and solve problems (CM2, Kaleidoscopes, Hubcaps, and Mirrors, 5.4)

Drawing dilations (Prentice Hall, Mathematics Course 3, 4-5a Activity Lab and 4-5)

Identify parallel lines and the angles formed by transversals (Prentice Hall, Mathematics Course 3, 7-2)

9. Assessments:











Quiz: solve problems involving reflection, rotation, and translation symmetry (CM2, Kaleidoscopes, Hubcaps, and Mirrors, Check-up 1)

Quiz: solve problems involving reflection, rotation, and translation symmetry (CM2, Kaleidoscopes, Hubcaps, and Multiple Choice, 2 and 5; Question Bank,

5, 8, 9)

Essay: How would you explain to someone what it means for a figure to have 1) reflection symmetry, 2) rotation symmetry, and 3) translation symmetry

(CM2, Kaleidoscopes, Hubcaps, and Mirrors, Mathematical Reflections 1)

Essay: In a line reflection, how are the points and their images related to the line of symmetry; in a rotation, how are the points, their images, and the center of

rotation related? (CM2, Kaleidoscopes, Hubcaps, and Mirrors, Mathematical Reflections 2)

Unit Test: reflection, rotation, translation informally and on the coordinate plane (CM2, Kaleidoscopes, Hubcaps, and Mirrors, Unit Test, 1, 2, 6; Prentice Hall,

Mathematics Course 3, Chapter 4 test, 33 and 35)

Performance Assessment: Making Tessellations (CM2, Kaleidoscopes, Hubcaps, and Mirrors, Unit Project)

Mini-Unit Test: identify angles formed by transversals, formulas for area and perimeter of polygons and circles, identify properties of circles (Prentice Hall,

Mathematics Course 3, Chapter 7 Test, 7, 26-28)




ESSE�TIAL

COMPO�E�TS

Month: February Samples and Populations

1. Big Ideas



Careful consideration of sampling techniques helps you to arrive at a good representative sample to draw conclusions

about the population.

Experimental probability is the number of times an event occurs/ over the number of trails.

Theoretical probability is the number of favorable outcomes/over the total of possible outcomes.

Odds in favor of an event is the ratio, (number of favorable outcomes: number of unfavorable outcomes).

Odds against an event is a ratio (number of unfavorable outcomes: number of favorable outcomes).

The probability of two unrelated events is the sum of the two individual possibilities.

The probability of one event following the other, in independent trails, is the product of the two probabilities.



Big Ideas.

How can you develop a statistical investigation to answer questions about a population?

How can analyzing theoretical and experimental probability help make predictions about real world events?

How does experimental and theoretical probability help predict and make inferences in a variety of situations?

What is the relationship between probability and odds in a simple experiment?

How does the outcome from one event affect the outcome of a second event?



Problem Solving





Reasoning and Proof





Communication






Connections






(Continued)


Representation





Strand: DATA A�ALYSIS A�D PROBABILITY Students will understand how to formulate questions, analyze

data, and determine probabilities.

5-8 Benchmark D.1 Formulate questions that can be addressed with data and collect, organize, and display relevant

data to answer them.

D.1.1 Represent two numerical variables on a plot, describe how the data points are distributed, and identify

relationships that exist between the two variables.

D.1.2 Generate, organize, and interpret real numbers in a variety of situations.

D.1.3 Organize, analyze, and display appropriate quantitative and qualitative data to address specific questions

including:

D.1.3.a frequency distributions

D.1.3.b plots

D.1.3.c histograms

D.1.3.d bar, line, and pie graphs

D.1.3.e diagram and pictorial displays

D.1.3.f charts and tables

D.1.4 Select the appropriate measure of central tendency to describe a set of data for a particular problem situation.

D.1.5 Simulate an event selecting and using different models.

D.1.6 Develop an appropriate strategy using a variety of data from surveys, samplings, estimations, and inferences to

address a specific problem.

5-8 Benchmark D.2 Select and use appropriate statistical methods to analyze data.

D.2.1 Use changes in scales, intervals, or categories to help support a particular interpretation of data.

D.2.2 Generate, organize, and interpret real number and other data in a variety of situations.

D.2.3 Analyze data to make decisions and to develop convincing arguments from data displayed in a variety of formats

including:

D.2.3.a plots

D.2.3.b distributions

D.2.3.c graphs

D.2.3.d scatter plots

D.2.3.e diagrams

D.2.3.f pictorial displays




(Continued)

D.2.3.g charts and tables

D.2.3.h Venn diagrams

D.2.4 Interpret and analyze data from graphical representations and draw simple conclusions (e.g., line of best fit).

D.2.5 Evaluate and defend the reasonableness of conclusions drawn from data analysis.

D.2.6 Use appropriate central tendency and spread as a means for effective decision-making in analyzing data and

outliers.

D.2.7 Identify simple graphic misrepresentations and distortions of sets of data (e.g., unequal interval sizes, omission

of parts of axis range, scaling).

D.2.8 Use appropriate technology to display data as lists, tables, matrices, graphs, and plots and to analyze the

relationships of variables in the data displayed.

5-8 Benchmark D.3 Develop and evaluate inferences and predictions that are based on data.

D.3.1 Describe how changes in scale, intervals, or categories influence arguments for a particular interpretation of the

data.

D.3.2 Describe how reader bias, measurement errors, and display distortion can affect the interpretation of data,

predictions, and inferences based on data.

D.3.3 Conduct simple experiments and/or simulations, record results in charts, tables, or graphs, and use the results to

draw conclusions and make predictions.

D.3.4 Compare expected results with experimental results and information used in predictions and inferences.

5-8 Benchmark D.4 Understand and apply basic concepts of probability.

D.4.1 Calculate the odds of a desired outcome in a simple experiment.

D.4.2 Design and use an appropriate simulation to estimate the probability of a real-world event (e.g., disk toss, cube

toss).

D.4.3 Explain the relationship between probability and odds and calculate the odds of a desired outcome in a simple

experiment.

D.4.4 Use theoretical or experimental probability to make predictions about real-world events.

D.4.5 Use probability to generate convincing arguments, draws conclusions, and makes decisions in a variety of

situations.

D.4.6 Understand that the probability of two unrelated events occurring is the sum of the two individual possibilities

and that the probability of one event following another, in independent trials, is the product of the two probabilities.

4. Assessments Winter DBA standards & (items): N.2.8(7) – (2), A.1.1 – (2), A.1.2 – (2), A.2.3 – (3), A.3.1 – (1), A.4.1 – (1), A.4.2 –

(1), A.4.3 – (2), A.4.6 – (6), G.1.3 – (3), G.4.4 – (4), G.4.5 – (1), M.2.4 – (2), N.2.1 – (3), N.2.2 – (2), N.3.1 – (1),

N.3.2 – (1), N.3.4 – (1), N.3.8 – (1). Total items = 39.

* (7) – Out of grade level standard






5. Content


to know)

8.A.2.4: relationships, ratios, proportions, percents, missing term

8.D.1.1: variable, plot, data points, relationship

8.D.1.2: real numbers

8.D.1.3: quantitative data, qualitative data, frequency distributions, histograms, diagram, pictorial display, plot, bar graph, line graph, pie graph, chart, table

8.D.1.4: measure of central tendency

8.D.1.5: event, model

8.D.1.6: strategy, survey, sampling, estimation, inference

8.D.2.1: change, scale, interval, category, interpretation

8.D.2.2: real number data

8.D.2.3: data, convincing argument, format, plot, graph, diagram, chart, table, distribution, scatter plot, pictorial display, Venn diagram

8.D.2.4: graphical representation, simple conclusion, line of best fit

8.D.2.5: reasonableness of conclusion

8.D.2.6: central tendency, spread, decision-making

8.D.2.7: graphic misrepresentation, distortion, unequal interval, omission, range, scaling

8.D.2.8: technology, list, table, matrix, graph, plot, relationship, variable

8.D.3.1: change, scale, interval, category, argument, interpretation

8.D.3.2: reader bias, measurement error, display distortion, interpretation, prediction, inference

8.D.3.3: simple experiment, simulation, result, chart, table, graph, conclusion, prediction

8.D.3.4: expected result, experimental result, prediction, inference

8.D.4.1: odds, desired outcome, simple experiment

8.D.4.2: simulation, probability, real-world event

8.D.4.3: probability, odds, desired outcome, simple experiment

8.D.4.4: theoretical probability, experimental probability, predication, real-world event

8.D.4.5: argument, conclusion, decision

8.D.4.6: probability, unrelated events, sum, individual possibilities, independent trial, product

6. Skills


be able to do)

8.A.2.4: demonstrate understanding and solve

8.D.1.1: represent, describe, identify

8.D.1.2; 2.2: generate, organize, interpret

8.D.1.3: organize, analyze, display

8.D.1.4: select measure of central tendency, describe data

8.D.1.5: simulate

8.D.1.6: develop strategy

8.D.2.1: use changes, support

8.D.2.3: analyze, make decision, develop arguments

8.D.2.4: interpret, analyze, draw conclusions

8.D.2.5: evaluate, defend

8.D.2.6: use central tendency

8.D.2.7: identify

8.D.2.8: use technology

8.D.3.1: describe change

8.D.3.2: describe reader bias

8.D.3.3: conduct experiment, record results, use results, draw conclusions, make predictions

8.D.3.4: compare

8.D.4.1: calculate odds

8.D.4.2: design, use simulation

8.D.4.3: explain, calculate odds

8.D.4.4: use probability, make predictions

8.D.4.5: use probability, draw conclusions, make decisions

8.D.4.6: understand probability of unrelated events






histograms, box-and-whisker plots, five-number summary, convenience sample, systematic sample, voluntary-response sample, random sample, measures of

central tendency (mean, median), distribution, sample, population, scatter plot, lines of best fit, quartile, Venn Diagram, simulations, expected results,

experimental probability, theoretical probability, odds, independent probability, dependent probability

8. Learning


Guided Practices)

Find experimental probability (Prentice Hall, Mathematics Course 3, 10-1)

Simulate a event to find outcomes (Prentice Hall, Mathematics Course 3, 10-2a)

Use probability to make convincing agreements (Prentice Hall, Mathematics Course 3, 10-3b)

Find probability of independent and dependent events (Prentice Hall, Mathematics Course 3, 10-4a, 10-4)

Compare sample distributions using measures of central tendency, measures of variability, and histograms (CM2, Samples & Populations, 1.1)

Compare samples using measure on central tendency, measures of variability, and histograms (CM2, Samples & Populations, 1.2)

Compare sample distributions using measures of central tendency, measures of variability, and box-and-whisker plots (CM2, Samples & Populations, 1.3)

Compare sample distributions using measures of central tendency, measures of variability, and histograms and box-and-whisker plots (CM2, Samples &

Populations, 1.4)

Distinguish between a sample and a population; use data from samples to make predictions about a populations (CM2, Samples & Populations, 2.1)

Sample plans (CM2, Samples & Populations, 2.2)

Random sampling (CM2, Samples & Populations, 2.3)

Sample size; use data from a sample to estimate a characteristic of a population (CM2, Samples & Populations, 2.4)

9. Assessments:











Quiz: Interpreting and making box-and-whisker plots (CM2, Samples & Populations, Check-up 1)

Quiz: Developing sampling methods and use sampling to make predictions about a population (CM2, Samples & Populations, Partner Quiz)

Essay: Describe several methods for selecting a sample from a population. Discuss the advantages and disadvantages of each method. (CM2 Mathematical

Reflection 2)

Quiz: Find probability of independent and dependent events. (Prentice Hall, Course 3, checkpoint quiz 2 pg. 490)

Quiz: Theoretical probability (Prentice Hall, Course 3, checkpoint quiz 1, pg. 479)

Summative will be done in March with end of unit test.




ESSE�TIAL

COMPO�E�TS

Month: March Samples and Populations

1. Big Ideas



Careful consideration of sampling techniques helps you to arrive at a good representative sample to draw conclusions

about the population.



Big Ideas.

How can you develop a statistical investigation to answer questions about a population?



Problem Solving





Reasoning and Proof





Communication






Connections




Representation







(Continued)


Strand: DATA A�ALYSIS A�D PROBABILITY Students will understand how to formulate questions, analyze

data, and determine probabilities.

5-8 Benchmark D.1 Formulate questions that can be addressed with data and collect, organize, and display relevant

data to answer them.

D.1.1 Represent two numerical variables on a plot, describe how the data points are distributed, and identify

relationships that exist between the two variables.

D.1.2 Generate, organize, and interpret real numbers in a variety of situations.

D.1.3 Organize, analyze, and display appropriate quantitative and qualitative data to address specific questions

including:

D.1.3.a frequency distributions

D.1.3.b plots

D.1.3.c histograms

D.1.3.d bar, line, and pie graphs

D.1.3.e diagram and pictorial displays

D.1.3.f charts and tables

D.1.4 Select the appropriate measure of central tendency to describe a set of data for a particular problem situation.

D.1.5 Simulate an event selecting and using different models.

D.1.6 Develop an appropriate strategy using a variety of data from surveys, samplings, estimations, and inferences to

address a specific problem.

5-8 Benchmark D.2 Select and use appropriate statistical methods to analyze data.

D.2.1 Use changes in scales, intervals, or categories to help support a particular interpretation of data.

D.2.2 Generate, organize, and interpret real number and other data in a variety of situations.

D.2.3 Analyze data to make decisions and to develop convincing arguments from data displayed in a variety of formats

including:

D.2.3.a plots

D.2.3.b distributions

D.2.3.c graphs

D.2.3.d scatter plots

D.2.3.e diagrams

D.2.3.f pictorial displays

D. 2.3.g charts and tables

D. 2.3.h Venn diagrams

D.2.4 Interpret and analyze data from graphical representations and draw simple conclusions (e.g., line of best fit).

D.2.5 Evaluate and defend the reasonableness of conclusions drawn from data analysis.

D.2.6 Use appropriate central tendency and spread as a means for effective decision-making in analyzing data and

outliers.

D.2.7 Identify simple graphic misrepresentations and distortions of sets of data (e.g., unequal interval sizes, omission




(Continued)

of parts of axis range, scaling).

D.2.8 Use appropriate technology to display data as lists, tables, matrices, graphs, and plots and to analyze the

relationships of variables in the data displayed.

5-8 Benchmark D.3 Develop and evaluate inferences and predictions that are based on data.

D.3.1 Describe how changes in scale, intervals, or categories influence arguments for a particular interpretation of the

data.

D.3.2 Describe how reader bias, measurement errors, and display distortion can affect the interpretation of data,

predictions, and inferences based on data.

D.3.3 Conduct simple experiments and/or simulations, record results in charts, tables, or graphs, and use the results to

draw conclusions and make predictions.

4. Assessments




5. Content


to know)

8.D.1.1: variable, plot, data points, relationship

8.D.1.2: real numbers

8.D.1.3: quantitative data, qualitative data, frequency distributions, histograms, diagram, pictorial display, plot, bar graph, line graph, pie graph, chart, table

8.D.1.4: measure of central tendency

8.D.1.5: event, model

8.D.1.6: strategy, survey, sampling, estimation, inference

8.D.2.1: change, scale, interval, category, interpretation

8.D.2.2: real number data

8.D.2.3: data, convincing argument, format, plot, graph, diagram, chart, table, distribution, scatter plot, pictorial display, Venn diagram

8.D.2.4: graphical representation, simple conclusion, line of best fit

8.D.2.5: reasonableness of conclusion

8.D.2.6: central tendency, spread, decision-making

8.D.2.7: graphic misrepresentation, distortion, unequal interval, omission, range, scaling

8.D.2.8: technology, list, table, matrix, graph, plot, relationship, variable

8.D.3.1: change, scale, interval, category, argument, interpretation

8.D.3.2: reader bias, measurement error, display distortion, interpretation, prediction, inference

8.D.3.3: simple experiment, simulation, result, chart, table, graph, conclusion, prediction

6. Skills


be able to do)

8.D.1.1: represent, describe, identify

8.D.1.2; 2.2: generate, organize, interpret

8.D.1.3: organize, analyze, display

8.D.1.4: select measure of central tendency, describe data

8.D.1.5: simulate

8.D.1.6: develop strategy

8.D.2.1: use changes, support

8.D.2.3: analyze, make decision, develop arguments

8.D.2.4: interpret, analyze, draw conclusions

8.D.2.5: evaluate, defend

8.D.2.6: use central tendency

8.D.2.7: identify



8.D.2.8: use technology

8.D.3.1: describe change

8.D.3.2: describe reader bias

8.D.3.3: conduct experiment, record results, use results, draw conclusions, make predictions




histograms, box-and-whisker plots, five-number summary, convenience sample, systematic sample, voluntary-response sample, random sample, measures of

central tendency (mean, median), distribution, sample, population, scatter plot, lines of best fit, quartile, Venn Diagram

8. Learning


Guided Practices)

Use information from sample to draw conclusions about populations and distinguish between samples and populations (CM2, Samples & Populations, 3.1)

Use probability (simulation) to select random samples from populations (CM2, Samples & Populations, 3.2)

Investigate a scatter plot in considering the relationships between two variables (CM2, Samples & Populations, 4.1)

Write an equation for a line of best fit to describe relationships between two variables (CM2, Samples & Populations, 4.2)

Explore relationship between two variables in a histogram, box-and-whisker plot, table, and line of best fit (CM2, Samples & Populations, 4.3)

9. Assessments:











Essay: Describe some situations you explored in which two variables are related in a predictable way (CM2, Samples & Populations, Mathematical

Reflections 4)

Unit Test: Interpreting data about a fish population based on data (CM2, Samples & Populations, Unit Test)

Unit Project: Estimating a Deer Population simulation (CM2, Samples & Populations, Unit Project)




ESSE�TIAL

COMPO�E�TS

Month: April Say It With Symbols

1. Big Ideas



If you know that two points lie on the graph of two linear equations, then the graphs of the equations are on the same

line, therefore the equations are equivalent. The distributive and commutative property can be used to show that two or

more expressions are equivalent.

Use symbols, variables and expressions to generate different representations to model a specific numerical relationship

given one representation of data (e.g., table, graph).



Big Ideas

How can you determine when different symbolic expressions are mathematically equivalent?

How can you represent patterns and relationships in symbolic forms?



Problem Solving





Reasoning and Proof





Communication






Connections




Representation






(Continued)




BE�CHMARK �.2 Understand the meaning of operations and how they relate to one another.

�.2.1 Use real number properties (e.g., commutative, associative, distributive) to perform various computational

procedures.


of perfect squares, cube roots of perfect cubes) on real numbers




A.2.2 Solve two-step linear equations and inequalities in one variable with rational solutions.

A.2.4 Demonstrate understanding of the relationships between ratios, proportions, and percents to solve for a missing

term in a proportion.

A.2.7 Use symbols, variables, expressions, inequalities, equations, and simple systems of equations to represent

problem situations that involve variables or unknown quantities.



(e.g., a table, a graph, an equation, a verbal description.)


A.4.4 Solve multi-step problems that involve changes in rate, average speed, distance, and time.

4. Assessments Spring DBA standards & (items): A.1.2 – (1), A.2.2 – (3), A.2.3 – (1), A.2.6 – (3), A.2.7 – (3), A.4.1 – (2)A.4.2 – (1),

A.4.6 – (1), D.1.3 – (1), D.1.4 – (1), D.2.1 – (1), D.2.3 – (1), D.2.4 – (1), D.4.4 – (1), G.1.3 – (1), G.2.1 – (1), G.3.2 –

(2), G.4.2 – (2), G.4.4. – (3), G.4.5 – (1), M.2.4 – (1), N.2.1 – (3), N.3.1 – (2), N.3.8 – (1). Total items = 38.




5. Content


to know)

8.N.2.1: real number properties, commutative, associative, distributive, procedures

8.N.2.2: arithmetic operations, inverses

8.A.2.1: equation, expression

8.A.2.2: two-step linear equations, two-step linear inequalities, rational solutions


8.A.3.1: representations, numerical relationship

8.A.4.4: multi-step problems, rate, average speed, distance, time

6. Skills


be able to do)

8.N.2.1: use properties, compute


8.A.2.1: demonstrate difference

8.A.2.2: solve





8.A.4.4: solve




Equivalent expressions, algebraic expression, commutative property, distributive property, linear relationship, patterns of change

8. Learning


Guided Practices)

Write equations to represent real world problems and justify the equivalence of two or more symbolic expressions for the same situation (CM2, Say it With

Symbols, 1.1 (OMIT question C)).

Interpret the information equivalent expressions represent in a given context and determine if two or more expressions are equivalent (CM2, Say it With

Symbols, 1.2 )

Interpret expressions in a given context (CM2, Say it With Symbols, 1.3 (OMIT problem D)).

Review distributive property, write equivalent expressions using the distributive property, use distributive property and other properties of real numbers to

determine if two or more expressions are equivalent (CM2, Say it With Symbols, 1.4)

Apply distributive and commutative property to write equivalent expressions (CM2, Say it With Symbols, 2.1 (OMIT C)).

Rewrite an equation that contains two variables by replacing one of the variables by an equivalent expression representing that variable (CM2, Say it With

Symbols, 2.2 (OMIT D)).

Model situations with symbolic statements and write a new algebraic expression by combining expressions (CM2, Say it With Symbols, 2.3)

9. Assessments:











Essay: What does it mean to say that two expressions are equivalent? How can the Distributive and Commutative properties can be used to write equivalent

expressions, and show that two or more expressions are equivalent (CM2, Say it With Symbols, Mathematical Reflections 1)?

Quiz : Decide if two expressions are equivalent and find equivalent expressions (CM2, Say it With Symbols, Check-UP 1, problems 1 and 2)

Essay: What are the advantages and disadvantages of working with one equation rather than two or more equations in a given situation (CM2, Say it With

Symbols, Mathematical Reflections, 2)

No unit summative assessment because the unit is not finished.




ESSE�TIAL

COMPO�E�TS

Month: May

1. Big Ideas



Use real number properties (commutative and distributive), perform arithmetic operations and their inverses, and use

symbolic and graphical methods to solve linear equations and inequalities.



Big Ideas.

How do you solve two-step linear equations and inequalities?



Problem Solving





Reasoning and Proof





Communication






Connections




Representation







(Continued)



5-8 Benchmark �.1 Understand numbers, ways of representing numbers, relationships among numbers, and number

systems.

�.1.2 Demonstrate the magnitude of rational numbers (e.g., trillions to millions).


�.2.1 Use real number properties (e.g., commutative, associative, distributive) to perform various computational

procedures.


of perfect squares, cube roots of perfect cubes) on real numbers.


�.3.8 Express numbers in scientific notation (including negative exponents) in appropriate problem situations using a

calculator.






A.4.4 Solve multi-step problems that involve changes in rate, average speed, distance, and time.

4. Assessments Spring DBA standards & (items): A.1.2 – (1), A.2.2 – (3), A.2.3 – (1), A.2.6 – (3), A.2.7 – (3), A.4.1 – (2)A.4.2 – (1),

A.4.6 – (1), D.1.3 – (1), D.1.4 – (1), D.2.1 – (1), D.2.3 – (1), D.2.4 – (1), D.4.4 – (1), G.1.3 – (1), G.2.1 – (1), G.3.2 –

(2), G.4.2 – (2), G.4.4. – (3), G.4.5 – (1), M.2.4 – (1), N.2.1 – (3), N.3.1 – (2), N.3.8 – (1). Total items = 38.




5. Content


to know)

8.N.2.1: real number properties, commutative, associative, distributive, procedures

8.N.2.2: arithmetic operations, inverses

8.A.2.2: twp-step linear equations, two-step linear inequalities, rational solutions

8.A.4.4: multi-step problems, rate, average speed, distance, time

6. Skills


be able to do)

8.N.2.1: use properties, compute


8.A.2.2: solve two-step equations

8.A.4.4: solve multi-step equations




Commutative property, distributive property, linear relationship, solving equations, patterns of change, inequality, system of linear equations, system of linear

inequalities.



8. Learning


Guided Practices)

Develop strategies for solving linear equations involving parentheses and negative signs (CM2, Say it With Symbols, 3.1)

Solve linear equations that have parentheses on both sides of the equation (CM2, Say it With Symbols, 3.2)

Identify situations calling for and write systems of linear equations and related inequalities, use graphs to estimate solutions to systems of linear inequalities

(CM2, Shapes of Algebra, 2.1)

Develop techniques for working with inequalities and finding their solutions (CM2, Shapes of Algebra, 2.2)

Use systematic methods for solving linear inequalities in one variable and make number line graphs of solutions to linear inequalities (CM2, Shapes of

Algebra, 2.3)

9. Assessments:











Essay: Describe some general strategies for solving linear equations, including those with parentheses. How are the solutions of linear equations related to the

graphs of equations (CM2, Say it With Symbols, Mathematical Reflections 3)

Essay: How can you use coordinate graphs to solve linear equations and linear inequalities? How can you use symbolic reasoning to solve inequalities (CM2,

Shapes of Algebra, Mathematical Reflections 2)?

No Summative Assessment for these units because only parts of the units were completed.


esse tial month: august moving straight ahead … · month: august moving straight ahead ... ouns...

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