Scope and Sequence Number and Fractions Comparing and ordering fractions with fractions Connecting fractions to percents Connecting fractions to decimals Connecting fractions to ratios Finding common denominators Simplifying fractions Benchmark fractions/estimation Percents Comparing and ordering percents with percents 96 Teacher Implementation Guide Scope and Sequence
Number and Percents Connecting percents to fractions Connecting percents to decimals Connecting percents to ratios It's All the Same Benchmark percent/ estimation Finding the percent of a number, or finding a number that is a percent Percents greater than 100 Decimals Comparing and ordering decimals with decimals Connecting decimals to fractions Connecting decimals to percents Connecting decimals to ratios Scope and Sequence Teacher Implementation Guide 97
Decimals Number and Benchmark decimals/estimation Rounding decimals Ratios and Proportions Rates and ratios It's All the Same Speed Equivalent ratios Scale factor/scale ratio/multiplication factor/growth factor It's All the Same Connecting ratios to fractions Connecting ratios to percents It's All the Same Connecting ratios to decimals Comparing ratios Estimating Irrational Numbers Pi (π) Square roots 98 Teacher Implementation Guide Scope and Sequence
Number and Real Numbers Exponential notation Scientific notation Calculator notation Finding real numbers on a number line Understanding subsets Place value Prime numbers Composite numbers Factors, divisors Divisibility rules Prime factorization Squares Even, odd numbers Properties and Associative property Commutative property Distributive property Order of operations with powers (laws of exponents) Scope and Sequence Teacher Implementation Guide 99
Properties and Number and Inverse operations Integers with integers Integers on a number line Comparing and ordering integers Models/Representations Ratio tables It's All the Same Bar models Double number lines Number lines Circle graphs/pie charts Area models Multiple representations and models 100 Teacher Implementation Guide Scope and Sequence
Algebra Patterns/Relationships Linear relationships Geometric relationships Quadratics Exponential relationships Periodic relationships Identifying linear or nonlinear patterns Inequalities Symbols/Variables/Expressions Equivalent expressions/equations/ formulas Solving equations using addition/subtraction inverse relationship Solving equations using multiplication/division inverse relationship Solving equations using square/square root inverse relationship Equivalent expressions/equations/ formulas Grouping Scope and Sequence Teacher Implementation Guide 101
Symbols/Variables/Expressions Algebra Substitution principle Systems of equations Representations/Models Graphs Tables Words Symbolic rules Direct formulas Recursive formulas Number strips Arrow strings Arithmetic trees Combination charts Choosing appropriate tools Multiplication trees 102 Teacher Implementation Guide Scope and Sequence
Algebra Representations/Models Relating and comparing representations Choosing appropriate representation 1st and 2nd differences Graphing Polar coordinate system Cartesian coordinate system Origin x-axis Ordered pairs Graphs related to formulas and tables Recognizing graph types Graphing calculator Slope/rate of change y-intercept x-intercept Systems of equations Scope and Sequence Teacher Implementation Guide 103
Lines Geometry and Measurement Parallel lines Transversal Symmetry Slopes of lines Perpendicular lines Length/Distance/Perimeter Distance (direct/indirect) Estimating length Solving problems with lengths Finding area using multiplication factors Finding length using trigonometric ratios Relating perimeters of similar figures Circumference of a circle Relate perimeter to area Estimating and calculating perimeter and area Angles Estimating angle measure Measuring angles Drawing angles 104 Teacher Implementation Guide Scope and Sequence
Geometry and Measurement Angles Classifying angles Notation and terminology for angles Angles of a polygon Angle sum of an n-gon Angles on a circular or polar grid Angles as turns Corresponding angles Alternate interior angles Trigonometric ratios Two-Dimensional Shapes Corresponding parts of polygons Differentiating between three-dimensional shapes Identifying polygons Polygons Regular polygons Nets Triangles, recognizing and classifying Quadrilaterals, recognizing and classifying It's All the Same Scope and Sequence Teacher Implementation Guide 105
Two-Dimensional Shapes Geometry and Measurement Circles Congruent figures Similar figures Tessellations Area It's All the Same Irregular shapes Rectangles Regular polygons Polygons Triangles Parallelograms Circles Formal vocabulary and methods Using formulas Estimating area Areas related to perimeter/side lengths Three-Dimensional Shapes Differentiating between two-dimensional shapes Prisms Cones 106 Teacher Implementation Guide Scope and Sequence
Three-Dimensional Shapes Geometry and Measurement Spheres Cubes Cylinders Pyramids Identify edges, vertices, and faces Euler's Formula Rigidity Nets Regular polyhedra, Platonic solids Spatial sense Theorems Pythagorean theorem Triangle Inequality theorem Opposite Parts or Hinge theorem Triangle Angle Sum theorem Surface Area Irregular shapes Using and critiquing models Surface area related to volume Scope and Sequence Teacher Implementation Guide 107
Surface Area Geometry and Measurement Prisms Pyramids Cylinders Volume Using formulas Estimating volume Irregular shapes Using and critiquing models Cylinders Pyramids Prisms Cones Volume related to surface area Transformations Informal Translations Rotations 108 Teacher Implementation Guide Scope and Sequence
Geometry and Measurement Transformations Reflections On a coordinate plane Units of Measure Converting within the same measurement system Converting between customary and metric system Customary system Metric system It's All the Same Using appropriate tools and units Using appropriate tools and units Historic units Tools Compass cards Protractors Rulers, measuring tape Scope and Sequence Teacher Implementation Guide 109
Data Investigation Data Analysis and Probability Collecting data Comparing data Conducting surveys Building arguments Describing patterns Population Sample Randomness Bias Describing Data Mean Median Mode Range Maximum, minimum Quartile Selecting summary statistic Describing correlation Drawing trend lines 110 Teacher Implementation Guide Scope and Sequence
Data Analysis and Probability Probability Estimating and calculating probability Comparing and ordering the likeliness of an event Experimental probability Theoretical probability Comparing theoretical and experimental probability Expressing probability using percents Expressing probability using fractions Expressing probability using ratios/proportions Expressing probability using decimals Counting techniques Simulations and experiments Dependent and independent events Expected value Multiplication rule for probabilities Addition rule for probabilities Models/Representations Chance ladders Tree diagrams Scope and Sequence Teacher Implementation Guide 111
Models/Representations Data Analysis and Probability Area models Chance scale Chance trees Charts Picture graphs/ pictographs Stacked bar graphs Number line plots Circle graphs/pie charts Line graphs Scatter plots Box plots Stem-and-leaf plots Histograms Relative frequency graph Comparing representations Creating models Interpreting graphs Choosing representation/model Identifying misrepresentation 112 Teacher Implementation Guide Scope and Sequence