Last updated: 6/25/2015 ## Math 7- Core Map Quarter 3

Ratio, Rates and Proportions

Converting Rates-Dimensional Analysis

Proportional vs. Non-proportional relationships

Graphing Proportional Relationships

Comparing / Analyzing Proportional Relationships

Solving Proportions

Scale Models/Drawings

Percents and Percent Equations

The percent proportion

The percent equation

Fluency - percents (Immediate Recall)

Percent of Change

Percent of error

Simple Interest

Expressions and Equations

Powers and exponents

Order of operations with sign rational numbers and powers

Square roots of perfect squares

Fluency (Perfect Squares 1-225)

Estimating Square roots

Determining two consecutive integers an irrational root is between

Placing square roots between consecutive integers

Geometry

Definition of circle

Determine parts of circle

Derivation of Pi

Using equations to find the area and circumference of circles

Using equations to find radius and circumference, given circumference or area

Using equations to find circumference, given area

Using equations to find area, given circumference

Statistics

Determining measures of central tendency-mean, median, mode

How do outliers affect the centers

Range

Quarter 3

Rate, Ratio and Proportion

Converting Rates -Dimensional Analysis

Identifying proportional relationships in list,chart or situation

Determining constant of proportionality

Coordinate plane characteristics

Identifying proportional relationships graphically

Solving Proportions

Equivalent Cross Products

Use the constant of proportionality (constant of variation) to write proportional linear equations

Direct Variation

Slope

Scale Drawing and models

Similar Figures

Similar Figures and Proportions

Using Similar Figures for indirect measurement

Percents

Percent of a value

Percent markers to know from sight

Percent and estimation

Percents greater than 100% and less than 1%

The percent equation

Connection to percent proportion

Percent of change

Sales, tax, tips and markups

Discount

Simple Interest

Compound Interest

Expressions and Equations

Evaluating powers

Evaluating roots of perfect squares

Fluency - Perfect squares 1-225

Estimating Square Roots

Determining the two consecutive integers an irrational root is between

Placing square roots on number line between integers within one tenth of accuracy

Evaluating expressions with powers and square roots

Geometry

Definition of a circle

Define parts of a circle

Derivation of Pi

Approximations of Pi

Using equations to find the area and circumference of circles

Using equations to find the radius and circumference, given circumference and area

Using equations to find circumference, given area

Using equations to find area, given circumference

Statistics

Determine measures of central tendency

Determine the best center

Determine the range

Describe how outliers affect centers

Determine the range of univariate data

Rates, Ratios and Proportions

How can we find rates when they form complex fractions?

What is a fraction? What operation does it signify?

How can we find unit rates - when we need to convert units?

How do forms of one allow us to use our identy property to convert units?

How can you identify and represent proportional relationships?

How can we demonstrate a comparison mathematically?

How can we determine a unit price from a ratio?

How can we determine a unit rate from a list or chart?

How can we determine a unit rate from a situation?

How do unit prices help us in the real world?

How do we determine which unit price is better?

How would you describe the coordinate plane?

What are the features of the coordinate plane?

How do you think the coordinate plane was developed?

How does graphing relationships coordinates help us determine if a line is proportional or not?

How does the constant of proportionality affect the graph?

How are proportional relationships graphed?

What are the two things to look for when you are determining if a line is proportional or not?

Can we use the constant of proportionality to find other points on a proportional line?

Can we build an equation that holds true for allo?

How does that equation help in real life situations?

If given one variable and you know the constant of proportionality, how can you determine the other variable?

Can we compare graphed proportional relationships with charted?  What should we look for?

Is there a connection between the constant of variatiion and the constant of proportionality?

Can we write the equation for direct variation if given a proportional pair of points?

How do scale factors and drawings help in real life?

How can we use similarity and proportions for indirect measure

Percents

How can you write and represent percents in multiple ways?

How can we represent percentages less than zero and greater than 100?

How can understanding percentages help understanding money and business?

How does estimation help us realize reasonability of answers?

How does knowing how to mentally compute 10 percent of a number help us in real life?

Can we use another method other than a proportion to determine missing parts, wholes or percent

What are the key words in a percent equation that help you determine the part and whole?

When there is an increase or decrease in numbers, how can we determine the percent of change?

Why do we find the "absolute" difference?  What does that mean?

What is tax, tip, gratuity and mark ups?  Where are these used in your life?

What is a disount? Does it get added to or taken from the original price?

How do you know how much money you will earn?

What is the difference between simple interest calculated over a period of months compared to years?

How does simple interest compare to compound interest?

Geometry

Can you define a circle?

Can we use parts of the circle to determine the length of the outside of the circle?

How could we determine the area of the inside of the circle?

Why do we measure circles in square units?

Can we use our knowledge of equations to find either the radius or diameter given either the area or circumference?

Statistics

How can we examine data?

Can we use centers to compare lists of univariate data?

How can we determine the central tendencies of univariate data?

How can we determine which is the best center to use for a list of data?

Can we compare centers of a list of data?

How does an outlier affect the centers?

Can we describe the range of data?

 (1) 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (1) 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour. (1) 7.RP.2 Recognize and represent proportional relationships between quantities. (1) 7.RP.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. (1) 7.RP.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. (1) 7.RP.2.c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. (1) 7.RP.2.d 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. (1) 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (1) 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. (1) 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Rate, Ratio and Proportions

Find unit rates with complex fractions

Comparing unit rates from complex fractions

Finding equivalent ratios using cross products

Solving proportions

Converting unit rates - with dimensional analysis

Identifying proportional and non-proportional relationships from situations, lists and charts

Define the difference between the independent and dependent variables of proportional and non proportional lines

Graphing proportional Relationship

Determine quadrants, axes, positions of coordinate pairs

Determine if a graph, table or situation is proportional

Determine the unit rate from a graph

Determine the constant of proportionality from a graph

Solving proportional relationships

Define a constant rate of change and how it affects graphs

Determine the slope of a line

Read and writing equations of direct variation

Recognize similar figures

Determine sides of similar figures using proportions

Percents

Writing percents as fractions, decimals (including fractional percents and greater than 100)

Estimate the percent of a number

Using the percent proportional to find either the percent, part or whole value of a number

Writing and using the percent equation to find either the part, whole or percent of a number

Determine the percent of change

Determine the percent of error

Using percents to solve problems with sales tax, tips, mark-ups and discounts

Solving simple interest problems

Rates, Rate and Proportion

Constant of Proportionality

Constant Rate of Change

Constant of Variation

Coordinate Plane

Cartesian Plane

Cross Products

Dimensional Analysis

Direct Variation

Equivalent Ratios

Non-proportional

Proportional

Ordered Pairs

Origin

Rate

Rate of Change

Slope

Unit Rate

X-axis

Y-axis

abscissa

ordinate

X-coordinate

Y-coordinate

discount

gratuity

markdown

markup

percent equation

percent of error

percent of change

percent of decrease

percent of increase

percent proportion

principal

sales tax

selling price

simple interest

tip

rational number

irrational numbers

perfect squares

between

powers

base

exponents

circle

diameter

circumference

Pi

Writing Assessment

Unit Assessment

Benchmark Assessment

IXL-technology informal assessment

Glencoe Course 2 Text

State Modules

IXL

Big Ideas Accelerated -Ron Larson 