AZ 7th Grade Math Curriculum

AZ 7th Grade Math Curriculum

• 7.RP.A.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
  • Rates with fractions
  • Rates
  • Proportions
• 7.RP.A.2Recognize and represent proportional relationships between quantities.
  • Applications of ratios
  • Ratios
  • Understanding graphs of linear relationships
  • Understanding tables of values of linear relationships
  • Applications of linear relationships
• 7.RP.A.3Use proportional relationships to solve multistep ratio and percent problems.
  • Identifying proportional relationships
  • Representing percents
  • Percents, fractions, and decimals
  • Percent of a number
  • Adding and multiplying percents
  • Taxes, discounts, tips and more
  • Simple interest
• 7.NS.A.1Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
  • Introduction to integer addition
  • Adding integers
  • Introduction to integer subtraction
  • Subtracting integers
  • Application of integer operations
• 7.NS.A.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
  • Multiplying and dividing monomials
  • Understanding integer multiplication
  • Multiplying integers
  • Understanding integer division
  • Dividing integers
• 7.NS.A.3Solve real-world and mathematical problems involving the four operations with rational numbers.
  • Applications of integer operations
  • Applications of fraction operations
• 7.EE.A.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
  • Common factors of polynomials
  • Evaluating algebraic expressions
• 7.EE.A.2Understand 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.
  • Factoring polynomials by grouping
• 7.EE.B.3Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
  • Word problems of polynomials
  • Order of operations (PEMDAS)
• 7.EE.B.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.
  • Solving two-step linear equations using addition and subtraction: ax + b = c
  • Model and solve one-step linear equations: ax = b, x/a = b
  • Solving two-step linear equations using multiplication and division: x/a + b = c
  • Solving two-step linear equations using distributive property: a(x + b) = c
  • Solving one - step equations: x + a = b
• 7.G.A.1Solve 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.
  • Enlargements and reductions with scale factors
  • Draw on coordinate planes
  • Horizontal and vertical distances
• 7.G.A.2Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
  • Parallel and perpendicular line segments
  • Classifying triangles
  • Perpendicular bisectors
• 7.G.A.3Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
  • Nets of 3-dimensional shapes
• 7.G.B.4Know 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.
  • Circles and circumference
  • Arcs of a circle
  • Areas and sectors of circles
• 7.G.B.5Use 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.
  • Angle bisectors
• 7.G.B.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
  • Volume of prisms
  • Introduction to surface area of 3-dimensional shapes
  • Surface area of prisms
  • Introduction to volume
  • Volume of cylinders
  • Word problems relating volume of prisms and cylinders
  • Surface area of cylinders
• 7.SP.A.1Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.
  • Influencing factors in data collection
  • Data collection
• 7.SP.A.2Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.
  • Reading and drawing bar graphs
• 7.SP.B.3Informally 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.
  • Box-and-whisker plots and scatter plots
• 7.SP.B.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
  • Application of averages
  • Median and mode
  • Mean
  • Range and outliers
• 7.SP.C.5Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
  • Introduction to probability
• 7.SP.C.6Approximate 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.
  • Organizing outcomes
• 7.SP.C.7Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
  • Probability of independent events
• 7.SP.C.8Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
  • Comparing experimental and theoretical probability
  • Determining probabilities using tree diagrams and tables
  • Probability of independent events
  • Probability with Venn diagrams