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Mathematics Grade 7
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Planning Grid (Gantt Chart)
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Links to MaterialsSequence instruction by academic year quarter.
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Click colored cells to download: Worksheet Series / Activities / Related Videos/ LinksIndicate when you are introducing a skill by flagging the appropriate quarter green.
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Worksheet #1πŸ“½ Related VideoWorksheet #2Related LinkWorksheet #3Worksheet #4Flag the skill red when students will practice the skill on independent assignments (homework).
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Same background color indicates that these resources are related.
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Blue flag: priority skill -to be assessed on Progress Monitoring TestsMCAS Grade 7 Math Reference SheetG7 Graphic Organizers for Grade 7Instructional level of skill: flag greenIndependent level of skill: flag red.
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CC #
Foundational Skills
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PrecursorKnow Core whole number multiplication and Γ· facts x 2,5,9,1,10 and associated divisibility rules Become functionally fluent using Multiplication and Division Facts for the Whole-to-Part Visual Learner.x/Γ· 2, 5,10x/Γ· 2, 5,10x/Γ· 2, 5,10,9,1
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Click for book link.Expand and Simplify Fractions While Practicing Fact Families and the Multiplication Table Area ModelLadder Chart BlanksπŸ“½ Woodin Ladder Chart Instructional VideoColor Coded Ladder Chart with Divisibility Rule Referencesx9, x1
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 %Benchmark Multiplication FactsBall Toss x ProcedureSemantic-based Distributive propertyx4 and x7 facts using Distributive property
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πŸ“½ Fraction VideoπŸ“½ Fraction Video #2πŸ“½ Regroup Mixed # Video
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Solve Various Word Problems Using Graphic Organizer Templatesβ€’ % Relative Products Drive x FactsShopping Computation Templates using Unit RatesHoliday Shopping Spend 1000 Game: Manual and Electronic Spreadsheet
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6.EE1
Write and evaluate numerical expressions involving whole-number exponents.
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Exponents Slides PresentationOrder of Ops. with exponents
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6.EE2
Write, read, and evaluate expressions in which letters stand for numbers.
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Commute Combine Evaluate Template
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πŸ“½ Commute Combine Evaluate
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6.EE2aWrite expressions that record operations with numbers and with letters standing for numbers. (e.g., express the calculation β€œSubtract y from 5” as 5 – y.)
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6.EE2bIdentify parts of an expression using terminology: (sum, term, product, factor, quotient, coefficient).
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Algebra vocabulary and key wordsIntro Algegra Vocab. Quiz
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CC #Expressions and EquationsSept-OctNov-JanFeb-MarApr -Jun
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7.EE1Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. For example, 4x + 2 = 2(2x + 1) and -3(x - 5/3) = -3x + 5.
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Precursor skill: Semantic-based Distributive propertyx4 and x7 facts using Distributive property
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7.EE2Understand 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. For example, a + 0.05a = 1.05a means that β€œincrease by 5%” is the same as β€œmultiply by 1.05.” A shirt at a clothing store is on sale for 20% off the regular price, β€œp”. The discount can be expressed as 0.2p. The new price for the shirt can be expressed as p – 0.2p or 0.8p.
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Precursor skill
Solve simple equations (one variable)
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Best Equation Starters3 Equations from Reach Diagram3 Equations from a linear diagram3 Equations from a matrix3 and 4 Term Related Equations Reach Diagram3 and 4 Term Related Equations with Reach Diagram+ Stool and Practice Evaluation
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πŸ“½ Equation VideoEquations and Related Diagrams3 Graduated Cyl. EquationsSolve ax=b EquationsSolve Equations involving Decimal Values with Box the Dollar StrategySolve all 4 basic equation types using inverse equations
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7.EE.4Use 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.
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Translate word problems into equationsWord Problems to x+q=r Linear Diagrams to Equations
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7.EE.4aSolve word problems leading to equations of the form px + q = r and p(x Γ· q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
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ax and ax+b Word ProblemsSolve for missing Dimensions within 2d and 3d figuresSolve Increasingly difficult Word Problems
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7.EE.4bSolve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
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7.EE.4cExtend analysis of patterns to include analyzing, extending, and determining an expression for simple arithmetic and geometric sequences (e.g., compounding, increasing area), using tables, graphs, words, and expressions.
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Ratios and Proportional RelationshipsSept-OctNov-JanFeb-MarApr -Jun
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7.RP.1Compute 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 Β½ mile in each ΒΌ hour, compute the unit rate as the complex fraction Β½/ΒΌ miles per hour, equivalently 2 miles per hour.
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Unit Rate introduction Worksheet seriesUnit Rates with Ratios of fractionsBubble Race Convert feet per second to miles per 1 hourHow fast is it going? Which is faster?Unit Rates with Slope
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7.RP.2aRecognize and represent proportional relationships between quantities. 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.
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Test for Proportionality
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7.RP.2bIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
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Proportion Problems Slides File with Video Links
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This row is SERIES!Reference Bank of Independent and Dependent Variables on x/y AxesFind, then extend Unit rate with Graph, X/Y Table and TableSolve a proportion problem with an equation, then validate the solution by extending the unit rate (no graph).Solve a proportion word problem, unit rate, and COP and graph Solve a proportion word problem then find and plot the COP and represent the equation as an equation: y=mx.
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Cop From TablesCOP from Graph Compare Prices at 2 Stores with Unit RatesProportion sets of 3 problems with the same theme, coefficient and Lined Paper LCCompare rates of speedWord Problem Proportion Templates with Diminishing Structure
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7.RP.2cGraph Unit Rates Level 1Graph Equivalent Rates and Ratios
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πŸ“½ Graph = Rates Precursor Activity videoπŸ“½ Companion Video of Graphing Rates
Ladder Fact Functions
Graph fractions to illustrate slope
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6.NS.6cPlot points on a number line and all 4 quadrants
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Plot Integers on Number LinesSwoosh Game Quadrant IBattleship Game
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7.RP.2dExplain 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.
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Ladder Fact FunctionsGraph fractions to illustrate slopeDefine the slope of a line using arbitrary objects.Graph Proportions from Descriptions
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7.G.1Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
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Indirect Measurement Shadowmaster ActivityπŸ“½ Video Indirect Measurement with the ShadowmasterProportions relating to finding corresponding sides of similar figuresFenway Park DistancesPicture Scale Proportion ProblemsMissing dimensions using a scale photo. Find a required diameter from a given circumference.
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PercentsSept-OctNov-JanFeb-MarApr -Jun
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Precursor (6.RP3.c)Understand benchmark percents as part of a 100% whole.
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β€’ % Relative Products Drive x Facts% Estimation TreesBenchmark % EstimatesFraction decimal % conversions
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7.RP.3Use proportional relationships to solve multi-step ratio, rate, and percent problems. Examples: simple interest, tax, price increases and discounts, gratuities and commissions, fees, percent increase and decrease, percent error.
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% of a whole: 15% 20% Tip Word ProblemsGarden % Composition by Quantity and AreaBaseball 2018 Texas Percents 3-types3 Types of Related % Problems
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1.2 Find the part % word problems Find the Part 2.5Turkey Part %% AreasMixed % Word Problems
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Integers and Number LinesSept-OctNov-JanFeb-MarApr -Jun
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Understand integers as nouns, defined by + hot or -cold adjectives. (-3 = 3 cold things.)
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7.NS.1Apply and extend previous understandings of addition and subtraction to add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
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Combine Integers
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πŸ“½ Combine Integers MovieCombine Integer PretestEncode or Diagram Single Integer TermsCombine Two Integers with Numbers and Red/Blue ModelsSimplify Complex Terms -(-3)=+3 Using Fading ModelsCombine Several Integers Using Color Cues
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Combine Several Integers Without Color Cues
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7.NS.1aDescribe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. A hydrogen atom has zero charge because its two constituents are oppositely charged; If you open a new bank account with a deposit of $30 and then withdraw $30, you are left with a $0 balance.
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7.NS.1bUnderstand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
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7.NS.1cUnderstand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
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7.NS.2aUnderstand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
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7.NS.2bUnderstand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.
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Computation With Rational NumbersSept-OctNov-JanFeb-MarApr -Jun
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5.NF.1Add and subtract fractions with unlike denominators (including mixed numbers).
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πŸ“½ Fraction VideoπŸ“½ Fraction Video #2πŸ“½ Regroup Mixed # VideoType 1 2 3 fraction addition flow chartπŸ“½ Type 1 2 3 Flow chart video