Consensus Map Grade Level



Grade Seven MathematicsIn seventh grade, students will focus on five main areas: The Number System, Ratios and Proportional Relationships, Expressions and Equations, Geometry, Statistics and Probability.We will extend the use of addition, subtraction, multiplication and division of rational numbers to solve real-world and mathematical problems.The concept of ratios and proportions will be used to solve various types of percent problems. Students will be asked to calculate discounts, interest, taxes, tips, and percent of increase and/ or decrease. Building on their prior knowledge of integers, students will solve multi-step problems involving whole numbers, decimals, and fractions. They will also use variables to represent quantities in real-world and mathematical problems.Geometric formulas will be used to solve problems involving: perimeter, area, surface area, and volume. They will also draw, construct, and describe geometric shapes with given conditions.The concept of random sampling will be studies as students will compare two population sets and describe the differences between them.Content: Rational numbers.Duration: August/Sept. (4 weeks) Essential Question:How is computation with rational numbers similar and different to whole number computation?Skills: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.Understand subtraction of rational numbers as adding the additive inversep-q = p + (-q)Represent addition and subtraction on a horizontal or vertical number line.Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.Convert a rational number to a decimal using long division.Demonstrate that the decimal form of a rational number terminates or eventually repeats.Solve real world and mathematical problems involving the four operations with rational numbers.Assessment:When two rational numbers are added is their sum rational?Is subtraction commutative for rational numbers?Use a number line to order rational numbers 2/5, -6, 5/3, and -1.6Resources:Mathematics Course 2 (pages 96-105)Standards:CC.2.1.7.E.1 Apply and extend previous understandings of operations with fractions to operations with rational numbers.Vocabulary:Rational number – any number that can be expressed as the quotient or fraction, p/q, of two integers, with the denominator q not equal to zero; Repeating decimal – a decimal fraction in which a figure or group of figures is repeated indefinitely, as in0.666…?or as in?1.851851851….; Terminating decimal – a decimal number that has digits that do not go on foreverComments:Content: Equivalent ExpressionsDuration: Sept/Oct (2 weeks) Essential Question:How can expressions, equations, and inequalities be used to quantify, solve, model and/or analyze mathematical situations?Skills: Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.Understand that rewriting an expression in different forms in a problem can shed light on the problem and how the quantities in it are related.Assessment:Is the expression 4w – 10 equivalent to 2(2w – 5)?Does a + 0.05a = 1.05a mean that increase by 5% is the same a multiply by 1.05a?Resources:Standards:CC.2.2.7.B.1 Apply properties of operations to generate equivalent expressions.Vocabulary:Coefficient – a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g.,?4?in?4x?y); Constant – is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9?...; Expression – a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add, subtract, multiply, and divide)Comments: Content: Numerical and Algebraic Expressions, Equations, and Inequalities.Duration: October (3 weeks) Essential Question:How can expressions, equations, and inequalities be used to quantify, solve, model and/or analyze mathematical situations?Skills: Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.Use variables to represent quantities in mathematical problemsConstruct simple equations and inequalities to solve problems by reasoning about the quantities. Solve multi-step problems with positive and negative rational numbers in any form.Assessment:If a woman is making $25 an hour gets a 10% raise, what will her new hourly rate be?Resources:Standards:CC.2.2.7.B.3 Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations.Vocabulary:Expression – a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add, subtract, multiply, and divide); Equation – a statement that the values of two mathematical expressions are equal (indicated by the sign =); Inequality – the relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”Comments: Content: Proportional RelationshipsDuration: November (3 weeks) Essential Question:How can probability and proportional reasoning be used to make reasonable predictions?Skills: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. Determine whether two quantities are proportionally related.Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.Represent proportional relationships by equations.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.Use proportional relationships to solve multi-step ratio and percent problems.Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease.Assessment:Write the ratio 10 s: 1 min. in simplest form.Determine if 15/45 and 3/15 forms a proportion.Resources:Standards:CC.2.1.7.D.1 Analyze proportional relationships and use them to model and solvereal‐world and mathematical problems.Vocabulary:Commission – is earnings based on a percentage of the total amount of sales; Proportion – two ratios (or fractions) are equal; Ratio – the quantitative relation between two amounts showing the number of times one value contains or is contained within the other ("the ratio of men's jobs to women's is 8 to 1"); Unit rate – is a comparison of two different quantities when they are combined ments: Content: Angle Measure, Area, Surface Area, Circumference, and VolumeDuration: Dec/Jan (4 weeks) Essential Question:How can the decomposition of 3-dimensional shapes aid in the understanding of surface areas and volumes?Skills: Identify and use properties of supplementary, complementary, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.Identify and use properties of angles formed when two parallel lines are cut by a transversal (e.g., angles may include alternate interior, alternate exterior, vertical, corresponding).Know the formulas for the area and circumference of a circle and use them to solve problems.Solve mathematical problems involving area, volume, and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.Assessment:The measure of ∠ Q is 49 degrees. What is measurement of its complement and supplement?How are vertical angles and adjacent angles different?Resources:Standards:CC.2.3.7.A.1 Solve real‐world and mathematical problems involving angle measure, area, surface area, circumference, and volume.Vocabulary:Adjacent – angles that have a common side and a common vertex; Area – the extent or measurement of a surface or piece of land; Circumference – the enclosing boundary of a curved geometric figure, especially a circle; Complementary – two angles that add to 90 degrees; Parallel –?lines?in a plane which do not meet; Polygon – a plane figure with at least three straight sides and angles, and typically five or more; Supplementary – two angles that add to 180 degrees; Surface area – the total area that can be measured on the entire surface. This can only be measured if the object is a three-dimensional object; Volume – the amount of space that a substance or object occupies, or that is enclosed within a containerComments: Content: Properties of Geometric Figures.Duration: January (2 weeks)Essential Question:How can we use the relationship between surface area and volume to help us draw, construct, model, and represent real situations and/or solve problems of surface area and volume?Skills: Solve problems involving scale drawings of geometric figures, including finding length and area from a scale drawing and reproducing a scale drawing at a different scale.Draw (freehand, ruler and protractor, or with technology) geometric shapes with given conditions.Identify or describe the properties of all types of triangles based on angle and side measures.Use and apply the triangle inequality theorem.Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and pyramids.Assessment:Describe plane sections of right rectangular prisms and right rectangular pyramids.Resources:Standards:CC.2.3.7.A.2 Visualize and represent geometric figures and describe the relationships between them.Vocabulary:Polyhedron – a solid figure with many plane faces, typically more than six; Prism – a solid geometric figure whose two end faces are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms; Pyramid – a polyhedron that has a base and triangular faces meeting at a point; Scale – the ratio of the length in a drawing (or model) to the length of the real thing; Triangle inequality theorem – any side of a triangle must be shorter than the other two sides added together. If it was longer, the other two sides could not meet!Comments: Content: Statistical MeasuresDuration: February (2 weeks) Essential Question:How can we use the mean, median, mode, and range to describe a set of data? Why do we need three different measures of central tendency?Skills: Compare two numerical data distributions using measures of center and variability.Describe data using mean, median, mode and range.Represent and interpret data using box and whisker plots.Represent and interpret data using stem and leaf plots.Use line plots, frequency tables, and histograms to represent data.Assessment: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.The mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team. This difference is equal to approximately twice the variability (mean absolute deviation) on either team. On a line plot, note the difference between the two distributions of heights.Resources:Mathematics Course Three (chapter 9)Standards:CC.2.4.7.B.2 Draw informal comparative inferences about two populations.Vocabulary:Box and whisker plot – are uniform in their use of the?box: the bottom and top of the?box?are always the first and third quartiles, and the band inside the?box?is always the second quartile (the median); Central tendency – the mean, median, and mode;?Measures of center – these statistics are commonly referred to as?measures?of central tendency; Measures of variability – a mathematical determination of how much the performance of the group as a whole deviates from the mean or median (box and whisker)Comments: Content: ProbabilityDuration: February /March (3 weeks) Essential Question:How do we make predictions based on the outcomes of a probability experiment?How does the collection, analysis, organization, and interpretation of data help us to answer real world questionsSkills: Predict or determine whether some outcomes are certain, more likely, less likely, equally likely, or impossible.Find the experimental probability.Find the probabilities of compound events using organized lists, tables, tree diagrams, and simulation.Assessment:Find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open end up. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?Resources:Mathematics Course 2 (pages 580 – 605)Standards:CC.2.4.7.B.3 Investigate chance processes and develop, use, and evaluate probability models.Vocabulary:Compound events –two or more events; Probability – is the chance that something will happen; Sample space – the collection of all possible outcomes in an experimentComments: Content: Random SamplesDuration: March/April (2 weeks) Essential Question:How can we use proportionality represented through models of and models for ratio tables, factor-of-change (scale factor), a unit rate, and cross-multiplication to solve real world problems?Skills: Understand that statistics can be used to gain information about a population by examining a sample of the population.Determine whether a sample is a random sample given a real-world situation.Identify a random sample and to write a survey question.Use data from a random sample to draw inferences about a population with an unknown characteristic of interestEstimate population size using proportionsAssessment:Predict the winner of a school election based on a randomly sampled survey data.Resources:Standards:CC.2.4.7.B.1 Draw inferences about populations based on random sampling concepts.Vocabulary:Biased question – a question that makes an unjustified assumption or makes some answers appear better than others; Sample – part of a population; Random sample – when each member of a population has the same chance of being selectedComments: Content: Rational and Irrational NumbersDuration: April/ May 2 weeks Essential Question:How are irrational numbers communicated?Skills: Determine whether a number is rational or irrational.Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144).Use rational approximations of irrational numbers to compare and order irrational numbers.Locate/identify rational and irrational numbers at their approximate locations on a number line.Assessment:Roof A has a rise of 5 and a run of 3. Roof B has a rise of 3 and a run of 5. Explain which roof is steeper?Explain why it is more difficult to run up a hill with a slope of ? than a hill with a slope of 1/6?The area of a square garden is 170 sq. ft. Estimate the perimeter of the garden.Resources:Mathematics Course 2 (pages 486-508), (400-408)Standards:CC.2.1.8.E.1?Distinguish?between?rational?and?irrational?numbers?using?their?properties.??CC.2.1.8.E.4?Estimate?irrational?numbers?by?comparing?them?to?rational?numbers.Vocabulary:Irrational number – a number that cannot be written as a ratio of two integers. As decimals, irrational numbers neither terminate nor repeat; Rational number –?is any?number?that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero; Repeating decimal – a decimal fraction in which a figure or group of figures is repeated indefinitely, as in0.666…?or as in?1.851851851…;Terminating decimal – a decimal number that has digits that?do not?go on foreverComments: This is an 8th grade standard to help students entering Algebra next year.Content: Linear Equations and SlopeDuration: May (2 weeks) Essential Question:How does the representation support the linear relationship? Where in each representation can you find the rate of change, the y-intercept, etc.?)Skills: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different waysUse similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.Assessment:Find three solutions of y = x + 5Is the slope of the line positive or negative?Draw a line with the given slope through the given point.Resources:Standards:CC.2.2.8.B.2?Understand?the?connections?between?proportional?relationships,?lines,?and?linear?equations.Vocabulary:Linear equation – the graph of its solutions lies on a line; Rise – the vertical change; Run – the horizontal change; Slope – ratio that describes the steepness of a lineComments: This is an 8th grade standard to help students entering Algebra next year. Content: Duration: Essential Question:Skills: Assessment:Recommended Activity:Standards:Vocabulary:Comments: ................
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