Packet Support- Click on the (link) to see a PDF of the packet
7-1: Fractions & Decimals (link)
Key vocabulary:
• benchmark fraction • ordered pair • coordinate plane • repeating decimal • decimal • terminating decimal • division • unit fraction • fraction
• benchmark fraction • ordered pair • coordinate plane • repeating decimal • decimal • terminating decimal • division • unit fraction • fraction
1.1 Terminating DeimalsStudents learn strategies to convert between fractions and terminating decimals.
Standards 4.NF.A, 6.NS.B |
1.2 Repeating DecimalsStudents change thirds, sixths, and ninths to decimals and explore patterns in repeating decimals. Students continue to convert between fractions and decimals. Students continue to compare, order, and add simple fractions and decimals.
Standards 5.NF.A, 7.NS.A |
1.3 Graphing Fractions & DecimalsStudents order fractions and decimals. Students graph fractions and decimals on a number line. Students graph ordered pairs in the first quadrant of the coordinate plane.
Standards 4.NF.A, 4.NF.C |
7-2 Rational Numbers on the Number Line (link)
Key vocabulary:
• absolute value • opposite of a number • distance • origin • equation • quadrant • inequality • rational number • integer
• absolute value • opposite of a number • distance • origin • equation • quadrant • inequality • rational number • integer
2.1 Integers & the Number LineStudents extend the positive number line to represent all integers. Students extend the axes of the quarter plane (1st quadrant) to create a four-quadrant coordinate plane. Students use arrows to represent direction and distance. Students solve problems involving integers and temperature.
Standards 6.NS.C |
2.2 Opposites & Absolute ValueStudents learn to interpret and evaluate the opposite and absolute value of a number.
Standards 6.NS.C |
2.3 Rational Numbers & the Number LineStudents locate and order rational numbers on the number line. Students graph ordered pairs in the coordinate plane.
Standards 6.NS.C |
7-3 Integer Addition & Subtraction (link)
Key vocabulary:
• absolute value • integers • addend • minuend • additive identity property • opposite of a number • additive inverse property • subtrahend • difference • sum
• absolute value • integers • addend • minuend • additive identity property • opposite of a number • additive inverse property • subtrahend • difference • sum
3.1 Integer modelsStudents think about positive and negative numbers using “hot pieces” and “cold nuggets” in the context of a temperature change model. Students represent positive and negative integers with counters.
Standards 7.NS.A |
3.2 Addition: Counters & TempStudents use counter and temperature change models to generalize rules for integer addition. Standards 7.NS.A
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3.3 Subtraction: Counters & TempStudents use counter and temperature change models to generalize rules for integer subtraction. Standards 7.NS.A
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7-4 Addition on the Number Line (link)
Key vocabulary:
• absolute value • origin • addend • quadrant • difference • rational number • distance • subtrahend • minuend • sum
• absolute value • origin • addend • quadrant • difference • rational number • distance • subtrahend • minuend • sum
4.1 Addition on the Number LineStudents deepen their understanding of integer addition by exploring this operation on a number line.
Standards 6.NS.C, 7.NS.A |
4.2 Subtraction on the Number LineStudents use their knowledge of addition and subtraction as inverse operations to create adding up statements from subtraction statements. Students deepen their understanding of integer subtraction by exploring this operation on a number line.
Standards 6.NS.C, 7.NS.A |
4.3 Addition & Subtraction: Rational NumbersStudents extend their knowledge of integer addition and subtraction to adding and subtracting rational numbers.
Standards 7.NS.A |
7-5 Rational Numbers: Multiplication & Division 1 (link)
Key vocabulary:
• conjecture • product • deductive reasoning • quotient • inductive reasoning • rational number • inverse operation
• conjecture • product • deductive reasoning • quotient • inductive reasoning • rational number • inverse operation
5.1 Multiplication: ModelsStudents develop integer multiplication rules using the counter and temperature change models. Students verify the rules for multiplication using arrows on a number line.
Standards 6.NS.C, 7.NS.A |
5.2 Multiplication & Division: PatternsStudents use patterns and the inverse relationship between multiplication and division to establish sign rules for division. Students solve multiplication and division problems.
Standards 7.NS.A |
5.3 Reasoning about Products & QuotientsStudents use inductive reasoning to make conjectures and deductive reasoning to draw conclusions based on accepted facts and logic. Students write quotients of integers in different forms. Students explore why division by zero is not defined,
and prove that (-1)(-1) = 1. Standards 7.NS.A |
7-6 Rational Numbers: Multiplication & Division 2 (link)
Key vocabulary:
• complex fraction • ratio • exponential notation • rational number • order of operations • unit rate
• complex fraction • ratio • exponential notation • rational number • order of operations • unit rate
6.1 Order of OperationsStudents learn conventions for the order of operations and apply them to evaluate expressions.
Standards 7.EE.B |
6.2 Ratios of FractionsStudents compute the unit rate for various measurements. Students learn strategies for working with ratios of fractions.
Standards 6.RP.A, 7.RP.A, 7.EE.B |
6.3 Multiplication & Division: Rational NumbersStudents multiply and divide rational numbers. Standards 7.NS.A, 7.EE.B
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7-7 Probability (link)
Key vocabulary:
• event • probability experiment • experimental probability • sample • fair game • sample space • outcome • theoretical probability • probability • trial
• event • probability experiment • experimental probability • sample • fair game • sample space • outcome • theoretical probability • probability • trial
7.1 Introduction to ProbabilityStudents use vocabulary related to probability. Students write the probability of events using fractions, decimals and percents. Students perform a probability experiment.
Standards 7.NS.A, 7.SP.C |
7.2 SpinnersStudents use spinners and puzzles to explore probability concepts. Students compare experimental probability to theoretical probability. Students use logical reasoning to determine the probability of different events.
Standards 7.NS.A, 7.SP.C |
7.3 Flips, Rolls & Fair GamesStudents explore probability concepts as they flip a coin and roll a number cube. Students learn techniques for organizing data. Students analyze experiments by comparing experimental probabilities to the theoretical probability. Students use probability to determine if games are fair.
Standards 7.NS.A, 7.SP.C |
7-8 Exploring Expressions & Equations (link)
Key vocabulary:
• deductive reasoning • expression • distributive property • greatest common factor • equation • inductive reasoning • equivalent expressions • solve an equation • evaluate • variable
• deductive reasoning • expression • distributive property • greatest common factor • equation • inductive reasoning • equivalent expressions • solve an equation • evaluate • variable
8.1 Equivalent ExpressionsStudents write numerical expressions to represent geometric patterns, describe patterns in words, and generalize using variable expressions. Students apply properties to generate equivalent expressions that include integers.
Standards 6.NS.B, 7.EE.A, 7.EE.B |
8.2 Hundreds Chart PatternsStudents investigate patterns on the hundreds chart. Students write algebraic expressions and use them to prove conjectures based on the patterns. Students find equivalent expressions that involve variables and rational numbers.
Standards 6.NS.B, 7.EE.A, 7.EE.B |
8.3 Polygon Area PuzzlesStudents create expressions and equations based upon the areas of polygon puzzle pieces. Students evaluate expressions, solve equations, and solve problems.
Standards 6.NS.B, 6.EE.B, 7.NS.A, 7.EE.A, 7.EE.B |
7-9 Solving Equations (link)
Key vocabulary:
• addition property of equality • multiplication property of equality • consecutive integers • perimeter • equation • rational numbers • equivalent expressions • solve an equation • inequality
• addition property of equality • multiplication property of equality • consecutive integers • perimeter • equation • rational numbers • equivalent expressions • solve an equation • inequality
9.1 Solving Equations: Mental Math StrategiesStudents will solve equations using mental strategies. Students will solve problems involving the lengths of sides, the perimeter, and the area of triangles, rectangles and regular polygons.
Standards 6.EE.A, 6.EE.B, 7.NS.A, 7.EE.B |
9.2 Solving Equations: Balance StrategiesStudents explore the concept of balance and apply it to solving equations. Students solve problems using algebra.
Standards 6.EE.A, 6.EE.B, 7.NS.A, 7.EE.B |
9.3 Solving Equations with Rational CoefficientsStudents solve equations with coefficients that are rational numbers. Students solve problems using algebra.
Standards 6.EE.A, 6.EE.B, 7.NS.A, 7.EE.A, 7.EE.B |
7-10 Inequalities (link)
Key vocabulary:
• association • bivariate data • categ• boundary point of a solution set • inequality • equation
• association • bivariate data • categ• boundary point of a solution set • inequality • equation
10.1 Linear InequalitiesStudents write linear inequalities in one variable and graph their solutions.
Standards 6.NS.C, 6.EE.B, 7.EE.B |
10.2 Solving Linear InequalitiesStudents solve linear inequalities in one variable and graph their solutions.
Standards 6.NS.C, 6.EE.B, 7.EE.B |
10.3 Inequality ProblemsStudents solve problems that involve inequalities. Standards 6.NS.C, 6.EE.B, 7.EE.B
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7-11 Proportional Reasoning (link)
Key vocabulary:
• cross-multiplication property • ratio • proportion • unit price • proportional relationship • unit rate
• cross-multiplication property • ratio • proportion • unit price • proportional relationship • unit rate
11.1 Proportional ReasoningStudents use different strategies to solve proportional reasoning problems.
Standards 6.RP.A, 7.RP.A, 7.NS.A, 7.EE.B |
11.2 Rate ProblemsStudents solve a variety of rate problems. Standards 6.RP.A, 7.RP.A, 7.NS.A, 7.EE.B
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11.3 Best Buy ProblemsStudents use tables, graphs, and symbolic representations to determine whether a relationship is proportional.
Standards 6.RP.A, 7.RP.A, 7.NS.A, 7.EE.B |
7-12 Percent (link)
Key vocabulary:
• discount (markdown) • percent • interest • percent of a number • interest rate • principal • markup • simple interest
• discount (markdown) • percent • interest • percent of a number • interest rate • principal • markup • simple interest
12.1 Percent Increase & DecreaseStudents learn some common vocabulary related to percent. Students learn how to find percent increases and decreases.
Standards 6.RP.A*, 7.RP.A, 7.NS.A, 7.EE.A, 7.EE.B |
12.2 Simple InterestStudents learn what interest means, why it is important, and how it is used.
Standards 6.RP.A*, 7.RP.A, 7.NS.A, 7.EE.A, 7.EE.B |
12.3 Sales & ComissionsStudents solve problems involving sales, sales tax, markups, discounts, and commissions.
Standards 6.RP.A*, 7.RP.A, 7.NS.A, 7.EE.A, 7.EE.B |
7-13 Sampling (link)
Key vocabulary:
box plot • median • dot plot • mode • five number summary • population • interquartile range • range • mean • sample • mean absolute deviation • simulation
box plot • median • dot plot • mode • five number summary • population • interquartile range • range • mean • sample • mean absolute deviation • simulation
13.1 Introduction to SamplingStudents use measures of center and spread to describe data sets. Students make predictions about a population based on a sample of the population. Students display data sets using dot plots, box plots, and other visual representations.
Standards 6.SP.A, 6.SP.B |
13.2 Comparing SamplesStudents compare two data sets using visual displays and statistics. Students compute and interpret the mean absolute deviation for samples. Students explore the effect of potential outliers on a data set.
Standards 6.SP.A, 6.SP.B, 7.SP.A, 7.SP.B |
13.3 Fish in a LakeStudents do a sampling experiment to estimate the fish population in a lake. Students make inferences about populations using data displays and measures of center and spread.
Standards 7.RP.A, 7.SP.A, 7.SP.B |
7-14 Angles, Triangles & Quadrilaterals (link)
Key vocabulary:
• adjacent angles • supplementary angles • angle • triangle • complementary angles • vertical angles • quadrilateral
• adjacent angles • supplementary angles • angle • triangle • complementary angles • vertical angles • quadrilateral
14.1 Angle MeasurementsStudents explore angle measures by creating their own protractors. Students use a protractor to measure and draw angles. Students review facts about triangles and quadrilaterals.
Standards 7.EE.B, 7.G.A, 7.G.B |
14.2 Angle ExplorationsStudents use patterns to learn facts about angles. Students use these facts to write equations and solve for unknown angle measures in diagrams.
Standards 7.EE.B, 7.G.B |
14.3 Drawing Triangles & QuadrilateralsStudents classify triangles based on the measure of their sides and angles. They draw figures freehand, using rulers and protractors, and with technology. Students observe conditions that make a triangle unique.
Standards 7.G.A |
7-15 Scale Drawings & Circle Measurements (link)
Key vocabulary:
• center of a circle • pi • chord • radius • circle • scale • circumference • scale drawing • diameter • scale factor
• center of a circle • pi • chord • radius • circle • scale • circumference • scale drawing • diameter • scale factor
15.1 Scale DrawingsStudents make scale drawings by applying different scale factors. Students use ratio strips and rulers to construct and read drawings made to scale.
Standards 7.NS.A, 7.G.A |
15.2 Circumference of CirclesStudents explore the relationship between a circle's diameter and its circumference. Students learn about historical approximations for π . Students establish the formula for the circumference of a circle and use it to solve problems.
Standards 7.NS.A, 7.G.B |
15.3 Area of CirclesStudents use their knowledge of the area of rectangles and circumference of circles to give an informal derivation of the area formula for a circle. Students use the formula to solve problems. Standards 7.NS.A, 7.EE.A, 7.G.B
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7-16 Plane & Solid Figures (link)
Key vocabulary:
• apex • right prism • cross section • right rectangular pyramid • lateral face • solid figure • plane • vertex • plane figure
• apex • right prism • cross section • right rectangular pyramid • lateral face • solid figure • plane • vertex • plane figure
16.1 Problems Involving Plane FiguresStudents solve real world and mathematical problems involving area and scale drawings. Standards 7.NS.A, 7.EE.B, 7.G.A, 7.G.B
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16.2 Problems Involving Solid FiguresStudents solve real world and mathematical problems involving surface area and volume.
Standards 7.NS.A, 7.EE.B, 7.G.B |
16.3 Cross Sections of Solid FiguresStudents describe two-dimensional figures that result from slicing three-dimensional figures by planes.
Standards 7.G.A |