7th Grade - Unit 1 – Accentuate The Negative (22 days) Things to Emphasize:

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7th Grade - Unit 1 – Accentuate The Negative (22 days)

Things to Emphasize:  Integers

 Number line

 Chip model

Standards:

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical line. 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Materials/Technology:

 Chips (two different colors)

 Large number line on wall is helpful

Additional Resources:

 DPI - Lessons for Learning – James Bond

 DPI - Lessons for Learning – Sign Your Name

Quick Glance:

Inv 1 (all): Extending the Number System

Inv 2 (all): Adding and Subtracting Rational Numbers

Inv 3 (all): Multiplying and Dividing Rational Numbers Inv 4 (all): Properties of Operations

Vocabulary:  Absolute value

 Additive inverse and identify

 Algorithm

 Commutative Property

 Distributive property

 Expanded form

 Factored form

 Integers

 Multiplicative inverse and identity

 Negative

 Order of Operations

 Positive

 Rational numbers

Evidence of Learning:

 Unit Readiness Assessment

 2 Check Ups

 1 Partner Quiz

 1 Unit Test

 1 Unit Project

 1 Self Assessment

 1 School Net Assessment - Named: 7th_{Grade –}

Accentuate the Negative

Important Notes:

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7th Grade - Unit 2 – Moving Straight Ahead (20 days)

Things to Emphasize:

 Expressions – writing, simplifying, and evaluating

 Equations – writing and solving

 Inequalities – writing and solving

Standards:

7.RP.2 – Recognize and represent proportional relationships between quantities. 7.EE.1 – Apply properties of operations as strategies to add, subtract, factor, and

expand linear expressions with rational coefficients.

7.EE.2 – Understand that rewriting an expression in different forms in a problem

context can shed light on the problem and how the quantities in it are related.

7.EE.3 – Solve multi-step real-life and mathematical problems posed with positive

and negative ration numbers in any form.

7.EE.4 – Use variables to represent quantities in a real-world or mathematical

problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

 Additional Resources: DPI - Lessons for Learning – Number Tricks

 DPI - Lessons for Learning - Sweet Algebra

Quick Glance:

Supplemental: Review of Expressions

Inv 3 (all but 3.5): Solving Equations

Supplemental: Solving Inequalities

Supplemental: Writing Equations and Inequalities

Vocabulary:  Coefficient

 Constant term

 Dependent variable

 Equation

 Equivalent

 Evaluate

 Expression

 Independent variable

 Inequality

 Like terms

 Linear relationship

 Proportional relationship

 Variable

 2 Check Ups

 1 Partner Quiz

 1 Unit Project

 1 Unit Test

 1 Unit Project

 1 School Net Assessment - Named: 7th_{Grade – Moving} Straight Ahead

 Make sure students get ample practice solving equations, they will have opportunites to practice throughout the school year, but this lays the foudnations

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Things to Emphasize:  Similarity

 Scale factor

 Proportional relationships

Standards:

7.RP.2 – Recognize and represent proportional relationships between quantities. 7.RP.3 – Use proportional relationships to solve multistep ratio and percent

problems.

7.NS.3 – Solve real-world mathematical problems involving the four operations with

rational numbers. (Extend to complex fractions)

7.EE.4 – Use variables to represent quantities in a real-world or mathematical

problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

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.

7.G.2 – Draw geometric shapes with given conditions, focus on constructing

triangles.

Materials/Technology:  Similar real life objects

 Rulers

 Shapes set

Additional Resources:

 DPI - Lessons for Learning – Murphy to Manteo

Quick Glance:

Inv 1 (all): Enlarging and Reducing Shapes

Inv 2 (all): Similar Figures Inv 3 (all): Scaling Perimeter and Area

Inv 4 (all): Similarity and Ratios

Vocabulary:

 Adjacent sides

 Corresponding sides and angles

 Equivalent ratios

 Midpoint

 Nested triangles

 Ordered pair

 Proportion

 Ratio

 Scale factor

 Similar

 2 Check Ups

 1 Partner Quiz

 1 Unit Project

 1 Unit Test

 1 Unit Project

Stretching and Shrinking

Important Notes: 

7th Grade - Unit 4 – Comparing and Scaling (18 days)

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 Proportionality in graph, table, and equation

 Scaling

 Equivalent ratios

 Unit rate

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.

7.RP.2 – Recognize and represent proportional relationships between quantities. 7.RP.3 – Use proportional relationships to solve multistep ratio and percent

problems.

7.NS.3 – Solve real-world mathematical problems involving the four operations with

rational numbers. (Extend to complex fractions)

Materials/Technology:  Grid Paper

 Calculators

Additional Resources: 

Quick Glance:

Inv 1 (all): Ways of Comparing: Ratios and Proportions

Inv 2 (all): Comparing and Scaling Rates

Inv 3 (3.1, 3.2): Using Ratios, Percents, and Proportions

Vocabulary:  Commission

 Complex fractions

 Constant of proportionality

 Discount

 Gratuity/tax

 Part-to-part ratio

 Part-to-whole ratio

 Percent of change

 Proportion

 Rate

 Ratio

 Simple interest

 Unit rate

 1 Check Up

 1 Partner Quiz

 1 Unit Project

 1 Unit Test

 1 Unit Project

Comparing and Scaling

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7th Grade - Unit 5 – Shapes and Design (20 days)

 Supplementary, complementary, vertical and adjacent angles

 Interior and exterior angles of polygons

Standards:

7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions.

7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem an dhow the quantities in it are related.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Materials/Technology:  Polystrips

 Protractors and rules

 Shapes set

Additional Resources: 

Quick Glance:

Inv 1 (all): The Family of Polygons

Inv 2 (all): Designing Polygons: The Angle Connection

Inv 3 (3.1, 3.2, 3.4): Designing Triangles and Quadrilaterals

Vocabulary:

 Adjacent angles

 Complementary angles

 Degree

 Exterior angles

 Interior angles

 Parallel

 Perpendicular

 Quadrilaterals

 Supplementary angles

 Symmetry

 Triangles (types)

 Vertical angles

 1 Check Up

 1 Partner Quiz

 1 Unit Test

 1 Unit Project

 1 School Net Assessment - Named: 7th_{Grade – Shapes} and Design

Important Notes: 

7th Grade - Unit 6 – Filling and Wrapping (25 days)

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 Volume

 Surface Area

 Circle – Circumference and Area

7.NS.3 – Solve real-world and mathematical problems involving the four operations

with rational numbers.

7.G.3 – Describe the two-dimensional figures that result from slicing

three-dimensional figures.

7.G.4 - Know the formulas for the area and circumference of a circle and use them to

solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

7.G.6 – Solve real-world and mathematical problems involving area, volume and

surface area of two-and three-dimensional objects composed of triangles, quadrilateral, polygons, cubes, and right prisms

 Additional Resources: DPI Lessons for Learning – Changing Surface Areas

 DPI - Lessons for Learning – Packing to Perfection

 DPI - Lessons for Learning – Slicing Pi

Quick Glance:

Inv 2 (2.2, 2.3) and Supplement: Polygonal Prisms: Volume and Surface Area

Inv 3 (all): Area and Circumference of Circles

Vocabulary:  Area

 Circumference

 Cross section

 Cube

 Diameter

 Dimensions

 Edge

 Face

 Horizontal

 Parallel cut

 Perpendicular cut

 Prism

 Pyramid

 Radius

 Surface area

 Vertical

 Volume

 2 Check Ups

 1 Partner Quiz

 1 Unit Project

 1 Unit Test

 1 Unit Project

 1 School Net Assessment - Named: 7th_{Grade – Filling} and Wrapping

 Students need to discover pi themselves

(circumference/diameter)!

 Only work with volume and surface area of prisms and pyramids (no cylinders, cones, or spheres in 7th_grade)

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 Probability models

 Sample space

 Compound events

7.SP.5 – Understand that the probability of a chance event is a number between 0

and 1 that expresses the likelihood of an even occurring.

7.SP.6 – Approximate the probability of a chance event by collecting data on the

chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

7.SP.7 – Develop a probability model and use it to find probabilities of events.

Compare probabilities from a model to observed frequencies.

7.SP.8 – Find probabilities of compound events using organized lists, tables, tree

diagrams, and simulation.

 Additional Resources:

Quick Glance:

Inv 1 (all): A First Look at Chance

Inv 2 (all): Experimental and Theoretical Probability Inv 3 (3.1, 3.2): Making Decisions With Probability

Inv 4 (all but 4.4): Analyzing Compound Events Using an Area Model

Vocabulary:  Area model

 Compound event

 Equally likely

 Expected value

 Experimental probability

 Fair game

 Favorable outcome

 Prediction

 Probability

 Relative frequency

 Sample space

 Simulation

 Theoretical probability

 Tree diagram

 Trial

 1 Check Up

 1 Partner Quiz

 1 Unit Project

 1 Unit Test

 1 Unit Project

 1 School Net Assessment - Named: 6th_{Grade – What Do} You Expect?

 There are so many real life examples with probability, think outside the box and do plenty of experiments

 Area models will be used throughout middle and high school math class, so make sure you expose students to them

7th Grade - Unit 8 – Statistics (14 days)

 Analyzing data more than creating data displays

 Comparing data and making predictions

 Measures of center

Standards:

7.SP.1 – Understand that statistics can be used to gain information about a

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7.SP.2 – Use data from a random sample to draw inferences about a population with

an unknown characteristic of interest. Generate multiple samples of the same size to gauge the variation of estimates or predictions.

7.SP.3 – Informally assess the degree of visual overlap of two numerical data

distributions with similar variability, measuring the difference between the centers by expression it as a multiple of the measure of variability.

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.

 Additional Resources: DPI - Lessons for Learning – X Marks the Spot

 Samples and Populations – CM Unit 8

 Georgia - Statistics

Quick Glance:

Samples and Populations

(validity and making predictions)

Box and Whisker Plots –

comparing IQRS and centers

Measures of Center –

median and mean

Comparing Data Sets

Vocabulary:  Box plot

 Distribution

 Frequency

 Histogram

 Inference

 MAD

 Mean

 Measures of center

 Median

 Mode Range

 Outliers

 Random sample

 Sample

 Skewed

 Variation

 Unit Readiness Assessment from Samples and Populations

 Quizzes and unit test from Samples and Populations

 1 School Net Assessment - Named: 7th_{Grade - Statistics}

 Try and allow students to gather as much real life data, make it applicable to their life (comparing twitter users, avg shoe sale)

 Can pick and choose which resources you would like to use, many options for this unit

 Grades is always a good topic to bring in here – can