pre-algebra - morris school district

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PRE-ALGEBRA/BIL

CURRICULUM MAP

M O R R I S S C H O O L D I S T R I C T

M O R R I S T O W N , N J

2 0 1 2 - 2 0 1 3

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Pre-Algebra Bil, focus on: grasping and applying the concepts of fractions, decimals, and percents, and the relationship that exists between them; (2) formulating and reasoning about expression and equations and the process in which to evaluate and solve; (3) grasping the concept of a function and using functions to describe quantitative relationships; (4) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

Pre-Algebra Bilingual Overview

The Number System

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Multiply and divide multi-digit numbers and find common factors and multiples.

Apply and extend previous understandings of numbers to the system of rational numbers.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Expressions and Equations

Use properties of operations to generate equivalent expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Work with radicals and integer exponents.

Understand the connections between proportional relationships, lines, and linear equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Reason about and solve one-variable equations and inequalities.

Represent and analyze quantitative relationships between dependent and independent variables.

Analyze and solve linear equations

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Functions

Define, evaluate, and compare functions.

Use functions to model relationships between quantities.

Geometry

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.

Ratios and Proportional Relationships

Analyze proportional relationships and use them to solve real-world and mathematical problems.

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Curriculum Map

Content/Objective Essential Questions/

Enduring Understandings

Suggested Activity/

Appropriate Materials-Equipment

Evaluation/Assessment

Unit 1- Adding, Subtracting,

Multiplying and Dividing

Fractions

Interpret and compute

quotients of fractions and

solve word problems

involving division of

fractions by fractions

(6.NS.1)

Fluently divide multi-

digit numbers using the

standard algorithm

(6.NS.2)

Essential Questions:

How can you use estimation to

check that your answer is

reasonable?

What does it mean when a whole

number is multiplied by a fraction?

Will the product be greater or less

than the whole number?

What does it mean to multiply

fractions?

How do you multiply a mixed

number by a fraction?

How do you divide by a fraction?

How can you use division by a

mixed number as part of a story?

When you write a terminating

decimal as a fraction, what type of

denominator do you get?

How can you tell the denominator

of a fraction if its decimal form is

terminating or repeating?

Enduring Understandings:

Computational fluency includes

understanding the meaning and the

appropriate use of numerical

operations.

The magnitude of numbers affects

Activities:

Using Models for Fractions

Estimating Sums and Differences of Fractions

Estimating Products of Fractions

Estimating Quotients of Fractions

Estimating Products and Quotients with Mixed Numbers

Using Overestimates

Using Compatible Numbers

Taking Math Deeper- Simplifying Questions using a

Racecar

Activities:

Multiplying a Fraction and a Whole Number

Multiplying a Whole Number and a Fraction

Standardized Test Practice

Real-Life Application- Weight of a Watermelon

Taking Math Deeper- Making Necklaces

Activities:

Multiplying Fractions

Multiplying Fractions with Common Factors


Real-Life Application- Bag of Flour

Activities:

Multiplying a Mixed Number and a Fraction

Buried Treasure Game

Using the Distributive Property

Multiplying Mixed Numbers

Real-Life Application- Resurfacing a Basketball Court

Taking Math Deeper- Changing Units

Activities:

Dividing by a Fraction

Writing Reciprocals

Dividing a Fraction by a Fraction

Pre-Assessments, DoNows,

oral questioning, closure,

self reflection journals,

projects, tests, technology

based assessments, reflect

and correct, year to date

cumulative assessments,

unit tests, standardized test

practice

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Suggested Activity/



the outcome of operations on them.

In many cases, there are multiple

algorithms for finding a

mathematical solution, and those

algorithms are frequently associated

with different cultures.

Dividing a Whole Number by a Fraction

Evaluating an Algebraic Expression

Using Order of Operations

Taking Math Deeper- Glazing Plates and Bowls

Activities:

Writing a Story

Dividing by a Mixed Number

Dividing a Mixed Number by a Fraction

Dividing Mixed Numbers

Using Order of Operations

Real-Life Application- Tortilla Soup

Taking Math Deeper- Trail Mix

Activities:

Writing Common Decimals as Fractions

4 in a Row Game

Vocabulary Patterns

Writing Decimals as Fractions

Writing Decimals as Mixed Numbers

Real-Life Application- Bird Species

Taking Math Deeper- Animal Exhibits

Activities:

Writing a Fraction as a Decimal

Real-Life Application- 40-yard Dash

Taking Math Deeper- Turtle Shell Length

Unit 2- Multiplying and

Dividing Decimals

The learner will:

Fluently add, subtract,

multiply and divide multi-

digit decimals using the

standard algorithm for

each operations. (6.NS.3)

Fluently divide multi-

digit numbers using the


How can you use estimation to

check that your answer is

reasonable?

What happens to the decimal point

when you multiply a whole number

by a decimal?

When multiplying decimals, how do

you know where to place the

Activities:

Newspaper ad activity decimal estimation

Estimating decimal products

Writing a estimation of decimal story

Estimate Decimal products and quotient


Real-Life Application: Beach Erosion

Taking it Deeper: Calories Burn

Activities:

Activity: Multiplying by the powers of 10

Activity: Multiplying a Decimal by a Whole Number-









practice

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Suggested Activity/



standard algorithm.

(6.NS.2)

decimal point in the product?

How is dividing a decimal by a

whole number similar to dividing a

whole number by a whole number?

How can you use the base ten

blocks to model decimal division


Numeric fluency includes both the

understanding of and the ability to

appropriately use numbers.

Computational fluency includes

understanding the meaning and the

appropriate use of numerical

operations.

The magnitude of numbers affects

the outcome of operations on them.

In many cases, there are multiple

algorithms for finding a

mathematical solution, and those

algorithms are frequently associated

with different cultures.

School Carnival

Activity: Back to School Shopping

Using estimation to find a product

Multiplying decimals and whole numbers

Inserting zeros in the product

Mental Math: product of base ten numbers

Taking it Deeper: Converting building heights from

meters to feet

Activities:

Activity: Multiplying decimal and converting fractions

to the product

Activity: Multiplying decimals using the circle maze

multiplying decimals

Evaluating Expressions using variables and substitution

Real-Life Application: Cost to pounds

Taking it Deeper: Area of a painting find the missing

dimensions

Activities:

Activity: Dividing a decimal using base ten blocks

Activity: Where does the decimal go using estimation

Activity: Using the perimeter formula

Dividing decimals by whole numbers

Dividing decimals by adding zeros to have the quotient

terminate

Real-Life Application: Sport Drink Comparative

Shopping

Taking it Deeper: Free Style Relay

Activities:

Activity: Dividing Decimals using Base Ten Blocks

Dividing Decimals

Dividing Decimals when there is a decimal in the

divisor

Real-Life Application: Cellular phone line graph

Taking it Deeper: Increasing the rectangular dimensions

will effect the area and perimeter

Unit 3-Fractions, Decimals,


Activities:

Writing Percents as Fractions



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Suggested Activity/



Percents

Find a percent of a

quantity as a rate per 100;

solve problems involving

finding the whole, given a

part and a percent

(6.RP.3c)

Understand the concept of

a ratio and use ratio

language to describe a

ratio relationship between

two quantities (6.RP.1)

Interpret statements as

statements about the

relative position of two

numbers on a number line

diagram (6.NS.7a)

Write, interpret and

explain statements of

order for rational numbers

in real-world contexts

(6.NS.7b)

How can you use a model to write a

percent as a fraction or write a

fraction as a percent?

How does the decimal point move

when you rewrite a percent as a

decimal and when you rewrite a

decimal as a percent?

How can you order numbers that are

written as fractions, decimals and

percents?

How can you use mental math to

find the percent of a number?

How can you use mental math and

estimation to help solve real-life

problems?

Enduring Understanding:

A quantity can be represented

numerically in various ways.

Problem solving depends upon

choosing wise ways.

Numeric fluency includes both

the understanding of and the

ability to appropriately use

numbers.

Context is critical when using

estimation.

Writing Fractions as Percents

Real-Life Application- Digital Cameras

Taking Math Deeper- Comparing Sizes of U.S. States

Activities:

Writing Percents as Decimals

Writing Decimals as Percents


Real-Life Application- Ultraviolet Rays

Taking Math Deeper- Circle Graph Tables

Activities:

Ordering Numbers

Using Fractions, Decimals and Percents

The Game of Math Card War

Comparing Fractions, Decimals and Percents

Real-Life Application- Soccer Goals

Taking Math Deeper- Ordering & Comparing Data

Activities:

Finding 10% of a Number

Finding 1% of a Number

Using Mental Math to find percents of numbers

Finding the Percent of a Number


Using Mental Math to Find Price of Concert Tickets

Real-Life Application- Area of a Room

Taking Math Deeper-Sale Prices

Activities:

Estimating a Percent

Using Mental Math to estimate percent of a Number

Estimating the Percent of a Number


Real-Life Application- Circle Graphs

Taking Math Deeper- Ratios







practice

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Suggested Activity/



Unit 4-Exponents

The learner will:

Know and apply the

properties of integer

exponents to generate

equivalent numerical

expressions (8.EE.1)

Use numbers expressed in the

form of a single digit times

and integer power of 10 to

estimate very large or very

small quantities, and to

express how many times as

much one is than the other

(8.EE.3)

Perform operations with

numbers expressed in

scientific notation, including

problems where both decimal

and scientific notation are

used. Use scientific notation

and choose units of

appropriate size for

measurements of very large or

very small quantities.

Interpret scientific notation

that has been generated by

technology (8.EE.4)


How can we model

situations using exponents?

How can you use exponents to

write numbers?

How can you multiply two

powers that have the same base?

How can you divide two powers

that have the same base?

How can you define zero and

negative exponents?

How can you read numbers that

are written in scientific notation?

How can you write a number in

scientific notation?


Real world situations

involving exponential

relationships can be solved using

multiple representations.

Activities:

Construct a table showing the power and value of a

series of exponents (-3) to the first, second, third,

power... How can you find the value of (-3) to the n

power.

Finding Products of Powers

Using a Calculator

Multiplying Powers with the Same Base

Raising a Product to a Power

Finding Quotients of Powers

Compare volumes of various cubes. Compare

larger to smaller cubes volumes. What patterns are

seen?

A drop of water leaks from a faucet every second.

How many liters of water leak from the faucet in 1

hour?

Use a calculator – experiment with multiplying

very large numbers until you get a number that is

not in standard form. What does the “e” mean on

the calculator? Can you explain it mathematically?

Try the same thing with very small numbers.

Use a table of distances and masses from the sun.

Match each planet to the distance. Then write in

scientific notation.

Multiplying Numbers in Scientific Notation

Adding Numbers Written in Scientific Notation

Subtracting Numbers Written in Scientific Notation

Dividing Numbers Written in Scientific Notation

Pre-Assessments, Do-

Nows, oral questioning,

closure, self-reflection

journals, projects, tests,

technology based

assessments, reflect and

correct, year to date



practice

Unit 5- Expressions and

Number Properties

The learner will:

Write and evaluate numerical

expressions involving whole

number exponents (6.EE.1)


How can you write and evaluate an

expression that represents a real-life

problem?

Which words correspond to the four

Activities:

Translate number stories into algebraic expressions.

Evaluating algebraic expressions using substitution

Evaluating an Expression substituting two variables

Evaluating Expressions with Two Operations

Real-Life Application (Saving for a skateboard)







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Suggested Activity/



Evaluate expressions at

specific values of their

variables. (6.EE.2c)

Write expressions that record

operations with numbers and

with letters standing for

numbers. (6.EE.2a)

Identify parts of an expression

using mathematical terms

(sum, term, product, factor,

quotient, coefficient); view

one or more parts of an

expression as a single entity.

(6.EE.2b)

Use variables to represent

numbers and write

expressions when solving a

real-world or mathematical

problem; understand that a

variable can represent an

unknown number, or,

depending on the purpose at

hand, any number in a

specified set. (6.EE.6)

Apply the properties of

operations to generate

equivalent expressions

(6.EE.3)

Identify when two

expressions are equivalent

(6.EE.4)

Find the greatest common

factor of two whole numbers

less than or equal to 100 and

the least common multiple of

two whole numbers less than

or equal to 12. Use the

distributive property to

operations of addition, subtraction,

multiplication and division?

Does the order in which you

perform an operation matter?

How do you multiply two 2-digit

numbers using mental math?

How can you use formulas to find

the area of an object with an

unusual shape?


Apply and extend previous

understandings of arithmetic to

algebraic expressions

Reason about and solve one-

variable equations and inequalities

Represent and analyze quantitative

relationships between dependant

and independent variables

Taking Math Deeper: Deck Activity

Activities:

Words that Imply Addition or Subtraction

Words that Imply Multiplication or Division

Find the Intruder Activity

Writing Numerical Expressions

Writing Algebraic Expressions


Real-Life Application – Cypress Tree

Taking Math Deeper- Using Tables to Organize

Information

Activities:

Does Order Matter?

Commutative Properties

Associative Properties

Using Properties to Simplify Expressions

Real Life Application (Basketball)

Taking Math Deeper (Drawing prisms & Project)

Activities:

Finding Products Involving Multiples of 10

Using Mental Math

Two Ways to Multiply

Simplifying Algebraic Expressions


Real Life Application (Mark’s age)

Taking Math Deeper (Marketing Poster)

Activities:

Using an Area Formula (Polygon Chart)

Finding an Area

Using a Simple Formula

Using an Area Formula

Taking Math Deeper (Translating words into Math)



practice

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Suggested Activity/



express a sum of two whole

numbers with no common

factor. (6.NS.4)

Unit 6- Equations

Identify parts of an

expression using

mathematical terms (sum,

term, product, factor,

coefficient); view one or

more parts of an

expression as a single

entity. (6.EE.2b)

Solve real-world and

mathematical problems

by writing and solving

equations of the form x +

p = q and px = q for cases

in which p, q, and x are

all nonnegative rational

numbers. (6.EE.7)

Understand solving an

equation or inequality as a

process of answering a

question; which values of

a specified set, if any,

make the equation or

inequality true? Use

substitution to determine

whether a given number

in a specified set makes

an equation or inequality

true. (6.EE.5)

Give examples of linear

equations in one variable,

and transform the

equation into simpler

forms (8.EE.7a)


How does rewriting a word problem

help you solve the word problem?

How can you use addition or

subtraction to solve an equation?

How can you use multiplication or

division to solve an equation?

What is a “two-step” equation?

How can you solve a two-step

equation?

How can you check the

reasonableness of your solution?

How can you use area and perimeter

formulas to find missing dimensions

of plane figures?

How can you use a volume formula

to find missing dimensions of

prisms?


Everyday objects have a variety of

attributes, each of which can be

measured in many ways.

What we measure affects how we

measure it.

Measurements can be used to

describe, compare, and make sense

of phenomena.

Activities:

Rewriting a Word Problem


Real-Life Application- Spelling Bee

Taking Math Deeper- Strawberries

Activities:

Solving an Equation using Subtraction

Solving Equations Using Mental Math

Solving Equations Using Addition or Subtraction

Checking Solutions

Real-Life Application – Rock Climbing

Taking Math Deeper- Amusement Park

Activities:

Writing and Solving Multiplication Equations

Using an Equation to Model a Story

Solving Equations Using Multiplication

Solving an Equation Using Division

Using the Formula for Distance

Taking Math Deeper- Frozen Juice Drinks

Activities:

Identifying Inverse Operations

Solving Two-Step Equations

Analyzing a Video Game


Real-Life Application- Tandem Bikes

Taking Math Deeper- Hardcover Book

Activities:

Finding Missing Dimensions

Finding Dimensions

Drawing a School Logo

Real-Life Application- Dance Studio

Taking Math Deeper- Door Dimensions









practice

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Suggested Activity/



Algebraic representation can be

used to generalize patterns and

relationships

The symbolic language of algebra is

used to communicate and generalize

the patterns in mathematics.

Activities:

Finding Missing Dimensions

Finding Dimensions

Counting Cubes

Finding the Volume of a Rectangular Prism

Finding a Missing Dimension of a Rectangular Prism

Finding the Surface Area of a Rectangular Prism

Finding the Surface Area of a Triangular Prism

Finding the Surface Area of a Square Pyramid

Chapter 7 – Proportions and

Variation The learner will:

Compute unit rates associated

with ratios of fractions,

including ratios of lengths,

areas and other quantities

measured in like or different

units (7.RP.1)

Identify the constant of

proportionality (unit rate) in

tables, graphs, equations,

diagrams, and verbal

descriptions of proportional

relationships (7.RP.2b)

Decide whether two quantities

are in a proportional

relationship (7.RP.2a)

Explain what a point (x,y) on

the graph of a proportional

relationship means in terms of

the situation, with special

attention to the points (0,0)

and (1,r) where r is the unit

rate (7.RP.2d)

Use proportional relationships

to solve multistep ratio and

percent problems (7.RP.3)


How do rates help you describe

real-life problems?

How can you compare two

rates graphically?

How can proportions help you

decide when things are ‘fair’?

How can you write a proportion

that solves a problem in real

life?

How can you use ratio tables

and cross products to solve

proportions in science?

How can you compare lengths

between the customary and

metric systems?

How can you use a graph to

show the relationship between

two variables that vary

directly? How can you use an

equation?

How can you recognize when

Define Ratio and Rate

Finding Ratios and Rates given data

Finding a Rate from a Table

Finding a Rate from a Line Graph

Define Slope

Finding Slopes given two points using formula Δy/Δx

Finding a slope in a given table using formula

Define Proportion and proportional

Determining Whether Ratios form a Proportion

Define Cross Products

Identify Proportional Relationships

Writing a Proportion given data in a table format or word

problem

Solving Proportions using Mental Math

Solve Proportions Using Multiplication

Solving Proportions Using the Cross Products Property

Real Life Application – Are costs of Pizza slices and Pizza

Pies cost proportional?

Define Customary and Metric System and rates of

conversion

Using proportions to convert units

Comparing Units of measure between the two systems

Converting Rates between systems









practice

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Suggested Activity/



Represent proportional

relationships by equations

(7.RP.2c)

two variables are inversely

proportional?

Enduring Understanding

Students graph proportional

relationships and understand the

unit rate informally as a measure of

the steepness of the related line,

called slope. They distinguish

proportional relationships from

other relationships.

Define direct variation

Identify Direct Variation in a table

Identify Direct Variation in an equation

Using a direct variation model to do calculations and graph

linear equations

Define indirect variation

Identifying Direct and Inverse Variation

Real Life Application

Unit 8 – Tables, Graphs and

Functions

Use variables to represent

two quantities in a real-

world problem that

change in relationship to

one another; write an

equation to express one

quantity, thought of as the

dependent variable, in

terms of the other

quantity, thought of as the

independent variable.

Analyze the relationship

between the dependent

and the independent

variable using graphs and

tables and relate these to

the equation. (6.EE.9)

Construct and analyze tables,

graphs, and models to

represent, analyze, and solve

problems related to linear


What is a mapping diagram? How

can it be used to represent a

function?

How can you describe a function

with words? How can you describe

a function with an equation?

How can you use a table to describe

a function?

How can you use a graph to

describe a function?

How can you analyze a function

from its graph?


Patterns and relationships can be

represented graphically,

numerically, symbolically, or

verbally

The symbolic language of algebra is

Activities:

Constructing Mapping Diagrams

Interpreting Mapping Diagrams

Listing Ordered Pairs

Drawing a Mapping Diagrams

Describing a Mapping Diagram

Real-Life Application- Songs Played

Taking Math Deeper- Scuba Diving

Activities:

Describing a Function

Writing an Equation in Two Variables

Evaluating a Function

Checking Solutions

Real-Life Application- “maXair Ride”

Taking Math Deeper-Bracelets

Activities:

Using a Function Table

Making a Function Table

Completing Input-Output Tables


Finding a Missing Input

Taking Math Deeper-Geography

Activities:









practice

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Suggested Activity/



equations including analysis

of domain, range, and

difference between discrete

and continuous data.(8.F.1)

Understand that a function is

a rule that assigns to each

input exactly one output.

The graph of a function is the

set of ordered pairs consisting

of an input and the

corresponding output (8.F.1)

Describe qualitatively the

functional relationship

between two quantities by

analyzing a graph. Sketch a

graph that exhibits the

qualitative features of a

function that has been

described verbally. (8.F.5)

used to communicate and generalize

the patterns in mathematics.

Algebraic representation can be

used to generalize patterns and

relationships

Interpreting a Graph

Conducting an Experiment

Graphing a Function

Taking Math Deeper- Furniture Sale

Activities:

Analyzing Graphs

Conducting an Experiment

Identifying Linear Functions

Comparing Linear Functions

Taking Math Deeper- Foot Race

Unit 9- Square Roots and

Pythagorean Theorem

The learner will:

Use square root, and cube

root symbols to represent

solutions to equations.

Evaluate square roots of small

perfect squares and cube roots

of small perfect cubes.

(8.EE.2)

Explain a proof of the

Pythagorean Theorem and its

converse (8.G.6)

Apply the Pythagorean

Theorem to determine


How can you find the side length

of a square when you are given

the area of a square?

How are the lengths of the sides

of a right triangle related?

How can you find decimal

approximations of square roots

that are irrational?

How can you use square roots to

describe the golden ratio?

Activities:

Finding Square Roots using square models and

area

Real-Life Application- Find the radius of a Crop

Circles given the area.

Discovering the Pythagorean Theorem using grid

paper, triangles, and quadrilaterals

Approximating Square Roots – try to approximate

the square root of radical 3 following in

Archimedes footsteps using calculators. How did

Archimedes do this without a calculator?

Approximating Square Roots Geometrically using

grid paper, a straight edge, and compass.

Constructing a Golden Ratio using grid paper,

compass, and Pythagorean theorem

Work with a partner to gather ratios of a the human









practice

14



Suggested Activity/



unknown side lengths in right

triangles – applying to real-

world problems (8.G.7)

Know that numbers that are

not rational are irrational.

Understand informally that

every number has a decimal

expansion, rational number

repeat eventually (8.NS.1)

Use rational approximations

of irrational numbers to

compare the size of irrational

numbers, locate the on a

number line and estimate the

value (8.NS.2)

Apply the Pythagorean

Theorem to find the distance

between two points in a

coordinate system (8.G.8)

How can you use the

Pythagorean Theorem to solve

real life problems?


The Pythagorean Theorem can

be derived / explained by

decomposing a square in two

different ways.

body like Leonardo da Vinci and approximate the

Golden Ratio

There is a fire in a building of a certain size, and

the recommended angle for the ladder is 75

degrees. Given specified height of the ladder, and

how far from the base the ladder should be placed,

how high will the ladder reach?

Finding a Volume

Taking Math Deeper- Ice Blocks

Unit 10- Data Analysis and

Displays

The learner will:

Construct and interpret scatter

plots for bivariate

measurement data to

investigate patterns of

association between two

quantities. Describe patterns

such as clustering, outliers,

positive/ negative association,

linear association, and non-

linear association. (8.SP.1)

Know that straight lines are

widely used to model

relationships between two

quantitative variables.

Informally fit a straight line.


How can you use measures of

central tendency to distribute an

amount evenly among a group of

people?

How can you use a box and

whisker plot to describe a

population?

How can you use data to predict

an event?

How can you display data in a

way that helps you make

decisions?


Activities

Exploring Mean, Median and Mode using coins.

Stack 45 coins into 9 stacks. Record the stack

number and number of coins in the stack. Find the

mean, median, and mode. Move coins from one

stack to the other. Will this change the mean?

Median? Mode?

Fair and Unfair Distributions – distribute 45 coins

to 9 people. How many different ways can you

distribute them to create a fair distribution? How is

each distribution related to the mean?

Look at a dataset of hourly wages. Increase each

hourly wage by 40 cents. How does this increase

affect the mean, median, and mode?

Create a Box-and-Whisker Plot based on the

number of cousins each student in class has.

Construct a plot to evaluate the data on a strip of

grid paper.

Taking math deeper – Evaluate box and whisker









practice

15



Suggested Activity/



(8.SP.2)

Variables are symbols that take

the place of numbers or ranges of

numbers; they have different

meanings depending on how

they are being used.

plots comparing battery life of two brands of cell

phones. Determine which battery has the longer

battery life and why.

Graph data points on the measures of a baby

alligator’s growth over time. Try to construct a

linear equation to predict the alligator’s growth in

two years.

Find the height and arm span of three people.

Make a scatter plot and draw a line of best fit. Is

there a relationship between height and arm span?

Unit 11- Circles and Area

The learner will:

Evaluate expressions at

specific values of their

variables. Include

expressions that arise

from formulas used in

real world applications.

Perform arithmetic

operations, including

those involving whole-

number exponents, the

conventional order when

there are no parentheses

to specify a particular

order. (Order of

Operations) (6.EE.2c)

Find the area if right

triangles, other triangles,

special quadrilaterals and

polygons by composing

into rectangles or

decomposing into

triangles and other

Essential Questions

How do you find the circumference

of a circle?

How can you find the perimeter of a

composite figure?

How can you find the area of a

circle?

How can you find the area of

composite figure?


Everyday objects have a variety

of attributes, each of which can

be measured in many ways.

What we measure affects how

we measure it.


describe, compare, and make

Activities:

Approximating pi to square

Approximating pi to hexagons

Find the radius and a diameter

Finding the circumference of circles

Standardized Test Practice: Decreasing the diameter will

effect the circumference

Finding the perimeter of a semicircular region

Taking It Deeper: Bicycle Wheel Rotational Turns

Activities:

Finding the pattern by finding the perimeter

Find the distance using scale factor

Submitting a bid –tiling a pool

Finding a perimeter using grid paper

Using tangrams, compare the perimeter of a square to

the perimeter of the house

Find the perimeter of irregular shapes

Taking it Deeper: Find compound area of an irregular

shaped garden

Activities:

Estimating the area of a circle

Approximating the area of a circle by cutting the circle

into circle

Find the area of circle using pi

Standardized Test Practice: Distance of wheel rotation









practice

16



Suggested Activity/



shapes; apply these

techniques in the context

of solving real-world

problems. (6.G1)

sense of phenomena.

Finding the area of a semicircle

Taking it Deeper: The dog path area

Real-life Application: Pool inscribe by a square

Activities:

Activity: Find the area of irregular shapes using grid

paper

Find the area of the basketball court

Find the compound area of irregular shapes

Taking It Deeper: Find the area of 2d nets of square

pyramid and rectangular prism

Volume of cylinders, cones, and

spheres

The learner will:

Solve real world and

mathematical problems

involving volume of

cylinders, cones, and spheres

(including knowing the

formulas) (8.G.9)


What is the relationship of the

volume of a sphere, cone, and

cylinder?

What is similar? What is

different?



describe, compare, and make

sense of phenomena.

Activities:

Construct cylinders – What shapes are needed to

construct a cylinder? How many blocks are

needed to fill the cylinder? How could find the

volume mathematically?

Construct a cone with the same height as the

cylinder. How many blocks are needed to fill this

shape?

Construct a sphere of similar height to the cone and

the cylinder. How many blocks are needed to fill

the sphere?

Rotations, reflections, and

Transformations

The learner will:

Understand congruence and

similarity using physical

models, transparencies or

geometry software.

Verify experimentally the

properties of rotations,

reflections, and translations

(8.G.1)


How are similarity, congruence,

and symmetry related?

What situations can be analyzed

using transformations and

symmetries?

How can transformations be

described mathematically?

Activities

Translating a Figure on the coordinate plane a

specified number of units to the left and down.

Record the new coordinates. Translate the figure

again. What do you notice about the coordinates

each time?

Reflecting a few figures on the coordinate plane,

recording the coordinates before and after. What

do you notice?

Rotate a few figures on the coordinate plane,

recording the coordinates before and after. What

do you notice?

17



Suggested Activity/



Understand that a two-

dimensional figure is

congruent to another if the

second can be obtained from

the first by a sequence of

rotations, reflections, and

translations (8.G.2)

Describe the effect of

dilations, translations,

rotations, and reflections on

two-dimensional figures using

coordinates (8.G.3)

Understand that a two-

dimensional figure is similar

to another if the second can

be obtained from the first by a

sequence of rotations,

reflections, and translations

(8.G.4)


Shape and area can be conserved

during mathematical

transformations.

pre-algebra - morris school district

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