1	Topic 1 Using ratios
Scaling images		Ratios and proportions 1. Understanding ratios 2. Write an equivalent ratio 3. Ratio tables 4. Do the ratios form a proportion? 5. Do the ratios form a proportion: word problems Scale drawings 6. Scale drawings: word problems 7. Scale drawings: scale factor word problems 8. Perimeter and area: changes in scale Also consider: • Scale drawings of polygons
Scaling images
Ratios and proportions 1. Understanding ratios 2. Write an equivalent ratio 3. Ratio tables 4. Do the ratios form a proportion? 5. Do the ratios form a proportion: word problems Scale drawings 6. Scale drawings: word problems 7. Scale drawings: scale factor word problems 8. Perimeter and area: changes in scale Also consider: • Scale drawings of polygons
Applying proportional reasoning		1. Use tape diagrams to solve ratio word problems 2. Solve proportions 3. Find an equivalent ratio: word problems 4. Estimate population size using proportions
Applying proportional reasoning
1. Use tape diagrams to solve ratio word problems 2. Solve proportions 3. Find an equivalent ratio: word problems 4. Estimate population size using proportions

2	Topic 2 Ratios and rates
Unit rates		1. Unit rates 2. Unit rates: word problems 3. Calculate unit rates with fractions 4. Unit prices 5. Compare rates: word problems
Unit rates
1. Unit rates 2. Unit rates: word problems 3. Calculate unit rates with fractions 4. Unit prices 5. Compare rates: word problems
Solving problems with unit rates		1. Graph a proportional relationship: word problems
Solving problems with unit rates
1. Graph a proportional relationship: word problems

3	Topic 3 Patterns in proportional relationships
Proportional and non-proportional relationships		Interpret graph of proportional relationships 1. Interpret graphs of proportional relationships Find the constant of proportionality 2. Find the constant of proportionality from a graph 3. Find the constant of proportionality from a table Write equations for proportional relationships 4. Write equations for proportional relationships from tables 5. Write equations for proportional relationships from graphs 6. Write and solve equations for proportional relationships
Proportional and non-proportional relationships
Interpret graph of proportional relationships 1. Interpret graphs of proportional relationships Find the constant of proportionality 2. Find the constant of proportionality from a graph 3. Find the constant of proportionality from a table Write equations for proportional relationships 4. Write equations for proportional relationships from tables 5. Write equations for proportional relationships from graphs 6. Write and solve equations for proportional relationships
Identifying proportional relationships		1. Identify proportional relationships by graphing 2. Identify proportional relationships
Identifying proportional relationships
1. Identify proportional relationships by graphing 2. Identify proportional relationships

4	Topic 4 Applications of percents
Percent increase and percent decrease		Percent of a number 1. Solve percent problems using strip models 2. Percents of numbers and money amounts 3. Percents of numbers: word problems 4. Solve percent equations 5. Solve percent equations: word problems Percent increase and percent decrease 6. Percent of change 7. Percent of change: word problems 8. Percent of change: find the original amount word problems Also consider: • What percentage is illustrated? • Convert between percents, fractions, and decimals
Percent increase and percent decrease
Percent of a number 1. Solve percent problems using strip models 2. Percents of numbers and money amounts 3. Percents of numbers: word problems 4. Solve percent equations 5. Solve percent equations: word problems Percent increase and percent decrease 6. Percent of change 7. Percent of change: word problems 8. Percent of change: find the original amount word problems Also consider: • What percentage is illustrated? • Convert between percents, fractions, and decimals
Applying percents to business situations		1. Percent error: word problems 2. Tips and commission Also consider: • Estimate tips
Applying percents to business situations
1. Percent error: word problems 2. Tips and commission Also consider: • Estimate tips
Applying percents to consumer situations		1. Markups and sales 2. Find the percent: markups and sales 3. Multi-step problems with percents 4. Sale prices: find the original price Also consider: • Which is the better coupon? • Simple interest
Applying percents to consumer situations
1. Markups and sales 2. Find the percent: markups and sales 3. Multi-step problems with percents 4. Sale prices: find the original price Also consider: • Which is the better coupon? • Simple interest

5	Topic 5 Adding and subtracting integers
Modeling with algebra tiles		Add integers 1. Understanding integers 2. Add integers using counters 3. Integer addition rules 4. Quantities that combine to zero: word problems Subtract integers 5. Subtract integers using counters 6. Integer subtraction rules Add and subtract integers 7. Add and subtract integers using counters 8. Integer addition and subtraction rules
Modeling with algebra tiles
Add integers 1. Understanding integers 2. Add integers using counters 3. Integer addition rules 4. Quantities that combine to zero: word problems Subtract integers 5. Subtract integers using counters 6. Integer subtraction rules Add and subtract integers 7. Add and subtract integers using counters 8. Integer addition and subtraction rules
Using the number line		Add and subtract integers using number lines 1. Add integers using number lines 2. Subtract integers using number lines Absolute value 3. Understanding absolute value 4. Absolute value and opposite integers
Using the number line
Add and subtract integers using number lines 1. Add integers using number lines 2. Subtract integers using number lines Absolute value 3. Understanding absolute value 4. Absolute value and opposite integers
Using the vertical number line		1. Add integers 2. Subtract integers 3. Complete addition and subtraction equations with integers Also consider: • Add and subtract integers
Using the vertical number line
1. Add integers 2. Subtract integers 3. Complete addition and subtraction equations with integers Also consider: • Add and subtract integers

6	Topic 6 Multiplying and dividing integers
Visualizing multiplication and division of integers Patterns of multiplying and dividing integers		Multiply integers 1. Integer multiplication rules 2. Multiply integers Divide integers 3. Integer division rules 4. Divide integers Multiply and divide integers 5. Integer multiplication and division rules 6. Apply multiplication and division rules 7. Multiply and divide integers 8. Complete multiplication and division equations with integers Also consider: • Understand multiplying by a negative integer using a number line • Properties of addition and multiplication • Equal quotients of integers • Add, subtract, multiply, and divide integers
Visualizing multiplication and division of integers Patterns of multiplying and dividing integers
Multiply integers 1. Integer multiplication rules 2. Multiply integers Divide integers 3. Integer division rules 4. Divide integers Multiply and divide integers 5. Integer multiplication and division rules 6. Apply multiplication and division rules 7. Multiply and divide integers 8. Complete multiplication and division equations with integers Also consider: • Understand multiplying by a negative integer using a number line • Properties of addition and multiplication • Equal quotients of integers • Add, subtract, multiply, and divide integers
Patterns in operations with exponents		1. Powers with negative bases 2. Evaluate numerical expressions involving exponents Also consider: • Understanding exponents • Evaluate powers
Patterns in operations with exponents
1. Powers with negative bases 2. Evaluate numerical expressions involving exponents Also consider: • Understanding exponents • Evaluate powers

7	Topic 7 Rational Numbers
Operations with positive rational numbers		Rational numbers 1. Classify rational numbers 2. Classify rational numbers using a diagram 3. Convert fractions or mixed numbers to decimals Multiply and divide with positive rational numbers 4. Multiply and divide fractions 5. Multiply fractions and mixed numbers: word problems 6. Divide fractions and mixed numbers: word problems Also consider: • Convert between mixed numbers and improper fractions • Identify quotients of rational numbers: word problems
Operations with positive rational numbers
Rational numbers 1. Classify rational numbers 2. Classify rational numbers using a diagram 3. Convert fractions or mixed numbers to decimals Multiply and divide with positive rational numbers 4. Multiply and divide fractions 5. Multiply fractions and mixed numbers: word problems 6. Divide fractions and mixed numbers: word problems Also consider: • Convert between mixed numbers and improper fractions • Identify quotients of rational numbers: word problems
Understanding rational number operations		1. Add and subtract integers: word problems 2. Add and subtract rational numbers 3. Multiply and divide rational numbers 4. Convert between customary and metric systems 5. Celsius and Fahrenheit temperatures Also consider: • Solve one-step addition and subtraction equations with rational numbers • Solve one-step multiplication and division equations with rational numbers
Understanding rational number operations
1. Add and subtract integers: word problems 2. Add and subtract rational numbers 3. Multiply and divide rational numbers 4. Convert between customary and metric systems 5. Celsius and Fahrenheit temperatures Also consider: • Solve one-step addition and subtraction equations with rational numbers • Solve one-step multiplication and division equations with rational numbers
Applying rational number operations		1. Simplify complex fractions 2. Multi-step word problems with positive rational numbers 3. Multi-step word problems: identify reasonable answers Also consider: • Add, subtract, multiply, and divide decimals: word problems • Add, subtract, multiply, and divide fractions and mixed numbers: word problems
Applying rational number operations
1. Simplify complex fractions 2. Multi-step word problems with positive rational numbers 3. Multi-step word problems: identify reasonable answers Also consider: • Add, subtract, multiply, and divide decimals: word problems • Add, subtract, multiply, and divide fractions and mixed numbers: word problems
Consolidating your skills with rational number operations		Operations with rational numbers 1. Add and subtract positive and negative decimals 2. Add and subtract positive and negative mixed numbers 3. Multiply and divide positive and negative decimals 4. Multiply and divide positive and negative fractions and mixed numbers 5. Add, subtract, multiply, and divide rational numbers Evaluate expressions with rational numbers 6. Evaluate numerical expressions involving decimals 7. Evaluate numerical expressions involving fractions
Consolidating your skills with rational number operations
Operations with rational numbers 1. Add and subtract positive and negative decimals 2. Add and subtract positive and negative mixed numbers 3. Multiply and divide positive and negative decimals 4. Multiply and divide positive and negative fractions and mixed numbers 5. Add, subtract, multiply, and divide rational numbers Evaluate expressions with rational numbers 6. Evaluate numerical expressions involving decimals 7. Evaluate numerical expressions involving fractions

8	Topic 8 Equations and inequalities
Modeling and solving linear equations		1. Model and solve equations using algebra tiles 2. Solve two-step equations without parentheses 3. Solve equations of the form px + q = r with fractions Also consider: • Solve one-step equations
Modeling and solving linear equations
1. Model and solve equations using algebra tiles 2. Solve two-step equations without parentheses 3. Solve equations of the form px + q = r with fractions Also consider: • Solve one-step equations
Linear expressions and equations		Identify equivalent linear expressions 1. Identify equivalent linear expressions I 2. Identify equivalent linear expressions II 3. Identify equivalent linear expressions: word problems Write equivalent linear expressions 4. Simplify expressions by combining like terms 5. Add and subtract linear expressions 6. Multiply using the distributive property 7. Factors of linear expressions 8. Write equivalent expressions using properties Solve two-step equations 9. Solve two-step equations with parentheses 10. Solve equations of the form p(x + q) = r with fractions 11. Solve two-step equations 12. Solve two-step equations: word problems 13. Solve equations: complete the solution Also consider: • Solve equations involving like terms • Choose two-step equations: word problems
Linear expressions and equations
Identify equivalent linear expressions 1. Identify equivalent linear expressions I 2. Identify equivalent linear expressions II 3. Identify equivalent linear expressions: word problems Write equivalent linear expressions 4. Simplify expressions by combining like terms 5. Add and subtract linear expressions 6. Multiply using the distributive property 7. Factors of linear expressions 8. Write equivalent expressions using properties Solve two-step equations 9. Solve two-step equations with parentheses 10. Solve equations of the form p(x + q) = r with fractions 11. Solve two-step equations 12. Solve two-step equations: word problems 13. Solve equations: complete the solution Also consider: • Solve equations involving like terms • Choose two-step equations: word problems
Solving and graphing inequalities		Understand inequalities 1. Solutions to inequalities 2. Graph inequalities on number lines 3. Write inequalities from number lines One-step inequalities 4. Solve one-step inequalities 5. Graph solutions to one-step inequalities 6. One-step inequalities: word problems Two-step inequalities 7. Solve two-step inequalities 8. Graph solutions to two-step inequalities
Solving and graphing inequalities
Understand inequalities 1. Solutions to inequalities 2. Graph inequalities on number lines 3. Write inequalities from number lines One-step inequalities 4. Solve one-step inequalities 5. Graph solutions to one-step inequalities 6. One-step inequalities: word problems Two-step inequalities 7. Solve two-step inequalities 8. Graph solutions to two-step inequalities

9	Topic 9 Probability
Defining probability		Experimental probability 1. Experimental probability 2. Make predictions using experimental probability 3. Use collected data to find probabilities and make predictions Theoretical probability 4. Sample spaces of simple events 5. Probability of simple events 6. Probability of simple events and opposite events 7. Make predictions using theoretical probability
Defining probability
Experimental probability 1. Experimental probability 2. Make predictions using experimental probability 3. Use collected data to find probabilities and make predictions Theoretical probability 4. Sample spaces of simple events 5. Probability of simple events 6. Probability of simple events and opposite events 7. Make predictions using theoretical probability
Probability of compound events		1. Sample spaces for compound events 2. Probability of compound events Also consider: • Compound events: find the number of outcomes • Compound events: find the number of sums • Find the number of outcomes: word problems
Probability of compound events
1. Sample spaces for compound events 2. Probability of compound events Also consider: • Compound events: find the number of outcomes • Compound events: find the number of sums • Find the number of outcomes: word problems
Probability of dependent events		1. Probability of dependent events
Probability of dependent events
1. Probability of dependent events

10	Topic 10 Representing and interpreting data
Sampling and variability		Populations and samples 1. Populations and samples 2. Identify representative, random, and biased samples Data displays 3. Interpret line plots 4. Create line plots 5. Describe distributions in line plots 6. Box plots 7. Interpret histograms 8. Create histograms Measures of center and spread 9. Calculate mean, median, mode, and range 10. Interpret charts and graphs to find mean, median, mode, and range 11. Calculate quartiles and interquartile range 12. Calculate mean absolute deviation
Sampling and variability
Populations and samples 1. Populations and samples 2. Identify representative, random, and biased samples Data displays 3. Interpret line plots 4. Create line plots 5. Describe distributions in line plots 6. Box plots 7. Interpret histograms 8. Create histograms Measures of center and spread 9. Calculate mean, median, mode, and range 10. Interpret charts and graphs to find mean, median, mode, and range 11. Calculate quartiles and interquartile range 12. Calculate mean absolute deviation
Interpreting graphs		1. Compare populations using measures of center and spread
Interpreting graphs
1. Compare populations using measures of center and spread
Outliers and misleading graphs		1. Identify an outlier
Outliers and misleading graphs
1. Identify an outlier

11	Topic 11 Designing simulations
Will it rain?
Will it rain?
Cereal box prize
Cereal box prize
Simulating baseball seasons		1. Which simulation represents the situation?
Simulating baseball seasons
1. Which simulation represents the situation?

12	Topic 12 Angles and triangles
Angle relationships		1. Name, measure, and classify angles 2. Identify complementary, supplementary, vertical, and adjacent angles 3. Find measures of complementary, supplementary, vertical, and adjacent angles
Angle relationships
1. Name, measure, and classify angles 2. Identify complementary, supplementary, vertical, and adjacent angles 3. Find measures of complementary, supplementary, vertical, and adjacent angles
Consolidating your skills with equation solving		1. Write and solve equations using angle relationships
Consolidating your skills with equation solving
1. Write and solve equations using angle relationships
Angle relationships in triangles		1. Find missing angles in triangles 2. Triangle Angle-Sum Theorem
Angle relationships in triangles
1. Find missing angles in triangles 2. Triangle Angle-Sum Theorem
Drawing and constructing triangles		1. Triangle inequality 2. Congruence statements and corresponding parts 3. Congruent triangles: SSS, SAS, and ASA
Drawing and constructing triangles
1. Triangle inequality 2. Congruence statements and corresponding parts 3. Congruent triangles: SSS, SAS, and ASA

13	Topic 13 Solving Problems with 2-D shapes
From polygons to circles		1. Lines of symmetry: regular polygons 2. Parts of a circle 3. Circumference of circles Also consider: • Identify and classify polygons • Perimeter
From polygons to circles
1. Lines of symmetry: regular polygons 2. Parts of a circle 3. Circumference of circles Also consider: • Identify and classify polygons • Perimeter
Estimating areas
Estimating areas
Area of triangles and quadrilaterals		1. Area of rectangles and parallelograms 2. Area of triangles and trapezoids 3. Area of rhombuses
Area of triangles and quadrilaterals
1. Area of rectangles and parallelograms 2. Area of triangles and trapezoids 3. Area of rhombuses
Areas of polygons and circles		1. Area of compound figures with triangles 2. Area of circles Also consider: • Circles: word problems
Areas of polygons and circles
1. Area of compound figures with triangles 2. Area of circles Also consider: • Circles: word problems

14	Topic 14 Prisms, pyramids, and plane sections
Surface area		1. Nets of prisms and pyramids 2. Lateral area of prisms and pyramids 3. Surface area of cubes and prisms 4. Surface area of pyramids
Surface area
1. Nets of prisms and pyramids 2. Lateral area of prisms and pyramids 3. Surface area of cubes and prisms 4. Surface area of pyramids
Volume		1. Volume of cubes and prisms 2. Volume of cubes and rectangular prisms: word problems 3. Volume of pyramids Also consider: • Volume of prisms: advanced
Volume
1. Volume of cubes and prisms 2. Volume of cubes and rectangular prisms: word problems 3. Volume of pyramids Also consider: • Volume of prisms: advanced
Plane sections		1. Cross sections of three-dimensional figures
Plane sections
1. Cross sections of three-dimensional figures

15	Topic 15 Effects of change
Changes in 1-dimensional measurements Changes in 2-dimensional measurements		1. Scale drawings: word problems 2. Scale drawings: scale factor word problems 3. Perimeter and area: changes in scale
Changes in 1-dimensional measurements Changes in 2-dimensional measurements
1. Scale drawings: word problems 2. Scale drawings: scale factor word problems 3. Perimeter and area: changes in scale

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