Instructional Strategies/Resources Textbook. Clarifications and Examples. Course: 7 th Bundle 1: Rational Numbers Compare & Order, 9 days

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1 Course: 7 th Bundle 1: Rational Numbers Compare & Order, grade Math Integer Computations Fluently, add, subtract, multiply, and divide rational numbers. 9 days How do you choose the best operations(s) to use in given situations with positive and negative rational numbers? Divisor, dividend, quotient, factor, product, sum, difference, numerator, denominator, subsets, sets, rational numbers 7.2A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers 7.3A add, subtract, multiply, and divide rational numbers fluently 7.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems 7.1D communicate ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate Teksing Toward STAAR Focus: 2A Use Venn diagrams along with other visual representations Focus: 3A (emphasize integers, fractions and decimals in Bundle 2) Review integer rules Real-life situations: o Temperatures o Game points o Altitude o Mountains and oceans Review order of operations 7.1G display, explain, and justify ideas and arguments using precise language in written or oral communication

2 Course: 7 th Bundle 2: Rational Numbers Computations grade Math with Decimals & Fractions Fluently, add, subtract, multiply, and divide rational numbers. 18 days How do you choose the best operations(s) to use in given situations with positive and negative rational numbers? Divisor, dividend, quotient, factor, product, sum, difference, numerator, denominator, subsets, sets, rational numbers 7.3A add, subtract, multiply, and divide rational numbers fluently 7.3B apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers 7.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution 7.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems Teksing Toward STAAR Focus: 3A, 3B (emphasize fractions and decimals) Real-life situations: o Temperatures o Game points o Altitude o Mountains and oceans o Money Review order of operations Include positive and negative fractions and decimals 7.1F analyze relationships to connect and communicate ideas 7.1G display, explain, and justify ideas and arguments using precise language in written or oral communication

3 Course: 7 th grade Math Bundle 3: Ratios and Proportions 18 days Ratios and rates can be used to express the relationship between two different quantities. Why are unit rates needed to make effective comparisons? How do unit rates help to determine which deal is best? Ratio, rates, constant rate, unit rate 7.4A represent constant rates of change in and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt 7.4B calculate unit rates from rates in and real-world problems 7.4C determine the constant of proportionality (k = y/x) within and real-world problems 7.4D solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems 7.1A apply mathematics to problems arising in everyday life, society, and the workplace 7.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution 7.1G display, explain, and justify ideas and arguments using precise language in written or oral communication TEKSing Toward STAAR Manipulatives for modeling Focus: 4A, 4B, 4C Represent constant rates of change given: o o Pictorial Table (sequence, use vertical and horizontal tables) o Verbal o Numeric o Graphical o Algebraically Use real-world problems: o Unit costs o Speed o Distance Focus: 4D (Percents in Bundle 4) Solve multi-step problems involving ratios and rates 7.4E convert between measurement systems, including the use of proportions and the use of unit rates

4 Course: 7 th grade Math Bundle 4: Percents 18 days Percents are used in the real-world to describe part of a whole. Why are percents used in store sales signs rather than fractions or decimals? What methods can you use to estimate a 20% tip using mental math? Percent, percent increase, percent decrease, mark-up, discount, sales tax, tip, simple interest 7.4D solve problems involving rations, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems 7.1A apply mathematics to problems arising in everyday life, society, and the workplace 7.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution 7.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems TEKSing Toward STAAR Focus: 4D (Emphasize Percents) Solve multi-step problems Review finding: percent of a whole, percent given the part, and percent given the whole Percent increase and percent decrease Financial literacy problems, include but not limited to: o Simple interest o Sales tax o Tip o Mark-up o Discount

5 Course: 7 th grade Math Bundle 5: Measurement Application with Ratios 7 days Similar figures are the same shape, but can be different sizes. The scale factor between similar figures is the factor by which the image/object is reduced or enlarged. What happens to a shape given a scale factor larger than 1? What can a ratio tell you about two similar shapes? Similar, ratio, scale, scale drawings, scale factor 7.5A generalize the critical attributes of similarity, including ratios within and between similar shapes 7.5C solve and real-world problems involving similar shape and scale drawings 7.1A apply mathematics to problems arising in everyday life, society, and the workplace 7.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution Teksing Toward STAAR Focus: 5A, 5C Two types of ratios in similar figures (within and between) Use real-world problems involving similar shapes and scale drawings 7.1D communicate ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate 7.1F analyze relationships to connect and communicate ideas

6 Course: 7 th grade Math Bundle 6: Linear Relationship 8 days Real life situations can be represented in multiple ways (verbal, algebraic, tables, and graphs). How can representing data in multiple ways be useful? How can we determine different representations given one representation? Linear, linear relationship, slope, slope-intercept 7.7A represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx+b 7.1D communicate ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate 7.1E create and use representations to organize, record, and communicate ideas Teksing Toward STAAR Focus: 7A Represent linear relationships using: o Tables o Graphs o Equations ( y = mx +b) Introduce slope in relation to m Introduce slope-intercept in relation to b 7.1F analyze relationships to connect and communicate ideas

7 Course: 7 th grade Math Bundle 7: Equations & Inequalities 11 days Solving an equation means finding the value of the variable that makes the number sentence ly true. Solving an equality means finding the value (s) that make the number sentence ly true. What is a process you could use to determine the value of the variable in the model of an equation? What is a process you could use to determine the value(s) of the variable in the model of an inequality? Equation, inequality, variable, one-variable, two-step, one-step, greater than (>), less than (<), equal to (=) 7.10A write one-variable, two-step equations and inequalities to represent constraints or conditions within problems 7.10B represent solutions for onevariable, two-step equations and inequalities on number lines 7.10C write a corresponding real-world problem given a one-variable, two-step equation or inequality 7.11A model and solve one-variable, two-step equations and inequalities 7.11B determine if the given value(s) make(s) one-variable, two-step equations and inequalities true 7.1A apply mathematics to problems arising in everyday life, society, and the workplace 7.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution 7.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems Teksing Toward STAAR Manipulatives for modeling Focus: 10A, 10B, 10C Translate sentences to equations or inequalities Write a real-world situation given an equation or inequality Choose correct equation or inequality for a problem situation Focus: 11A, 11B Model and solve equations with one-variable Model and solve inequalities with one-variable Prove a given value is true for an equation or inequality Use number lines to represent solutions 7.1D communicate ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs,

8 and language as appropriate 7.1E create and use representations to organize, record, and communicate ideas 7.1G display, explain, and justify ideas and arguments using precise language in written or oral communication

9 Course: 7 th Bundle 8: Geometry Angles, Circumference, grade Math 13 days Area Perimeter is a linear measurement, and area is not. Develop understanding of circumference and area of a circle. Formulas can be used to calculate circumference, and area of two-dimensional shapes. Pi represents the constant relationship between the circumference and the diameter of all circles. When would you have to calculate an area in the real-world? Why do circles not have a perimeter? What is a set of possible angle measures for a parallelogram that is not a rectangle? If you know the distance a tire travels in one revolution, how can you find the radius of the tire? Circle, Pi, diameter, radius, circumference, area, rectangle, square, parallelogram, trapezoid, triangle, semicircle, quarter circles, composite figure, triangle, angle 7.5B describe π as the ratio of the circumference of a circle to its diameter 7.8C use models to determine the approximate formulas for the circumference and area of a circle and connect the models to the actual formulas 7.9B determine the circumference and area of circles 7.9C determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles 7.11C write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle 7.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems 7.1D communicate ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate 7.1E create and use representations to organize, record, and communicate ideas 7.1F analyze TEKSing Toward STAAR Manipulatives for modeling Focus: 5B, 8C, 9B Describe π as a ratio and decimal Model circumference and area of a circle Connect circumference and area formula of a circle to a model Determine the circumference and area of a circle Use π as 3.14 and 22/7 to solve problems Focus: 9C Determine area of the following shapes: o Composite figures o Rectangles o Squares o Parallelograms o Trapezoids o Triangles o Semicircles

10 relationships relationships to connect and communicate ideas 7.1G display, explain, and justify ideas and arguments using precise language in written or oral communication o Quarter circles Find the area of the shaded or unshaded region Focus: 11C Write and solve equations

11 Course: 7 th grade Math Bundle 9: Geometry Volume & Surface Area 11 days 3D figures can be viewed from the unfolded perspective of its 2D faces (net). Volume is seen in real world situations such as filling containers with liquids, laying cement, filling holes, etc Surface area of a 3D figure is calculated by find the area of the 2D faces. How can you draw a net for a triangular prism? What are different ways to determine the volume of a prism or pyramid? Is it your opinion that finding the surface area using the formula or the net is better? Please explain your choice. Volume, rectangular prism, prism, rectangular pyramid, pyramid, base, height, formula, triangular prism, triangular pyramid, lateral surface area, lateral, surface area, net 7.8A model the relationship between the volume of a rectangular prism and a rectangular pyramid having both congruent bases and heights and connect that relationship to the formulas 7.8B explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to formulas 7.9A solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids 7.9D solve problems involving the lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid by determining the area of the shape s 7.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems 7.1E create and use representations to organize, record, and communicate ideas 7.1G display, explain, and justify ideas and arguments using precise language in written or oral communication TEKSing Toward STAAR Manipulatives for modeling Focus shapes: Rectangular Prism Triangular Prism Rectangular Pyramid Triangular Pyramid Focus: 8A, 8B, 9A (Volume) Model volume relationship for focus shapes Connect models to volume formulas Explain symbolically and verbally volume relationships for focus shapes Solve volume for focus shapes with formulas Differentiate between height of 2D shape in a 3D shape and the height of the 3D shape Focus: 9D

12 net Discuss and model nets for the focus shapes Match nets and models to appropriate formulas to problem solve Lateral surface area using formula and net Total surface area using formula and net Identify perimeter of the base as P

13 Course: 7 th grade Math Bundle 10: Probability & Data Analysis 17 days Theoretical probability is found by analyzing a situation and predicting outcomes and experimental probability is found as the result of an experiment. Theoretical probabilities can be analyzed by constructing sample spaces and experimental probabilities can be analyzed by collecting experimental data. Data can be represented in many forms, some of which can be misleading. Consumers must critically view the graph or chart in order to evaluate its validity. All events are not equally likely to happen. Are experimental and theoretical probabilities always equivalent? How are theoretical and experimental probabilities alike and different? How can you determine all possible outcomes of an event? How do you determine the probability of an event and its complement? How does displaying data in tables or graphs help you identify patterns or properties of a distribution? What strategies can be used to identify possible outcomes and analyze probabilities? Probability, sample space, simple events, compound events, prediction, theoretical probability, experimental probability, complement, qualitative, quantitative, data, bar graphs, dot plots, circle graphs, box plots, spread, population, tree diagram 7.6A represent sample spaces for simple and compound events using lists and tree diagrams 7.6B select and use different simulations to represent simple and compound events with and without technology 7.6C make predictions and determine solution using experimental data for simple and compound events 7.6D make predictions and determine solutions using theoretical probability for simple and compound events 7.6E find the probabilities of a simple 7.1A apply mathematics to problems arising in everyday life, society, and the workplace 7.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems 7.1D communicate ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, Teksing Toward STAAR Manipulatives for modeling Focus: 6A, 6B, 6C, 6D, 6E, 6F, 6H, 6I Identify all possible outcomes Display possible outcomes as lists, tables, and tree diagrams Determine the results of simple events and its complement Collect data using frequency tables Determine the results of compound events Interpret the results of a given experiment Find probabilities of a simple event and its complement. Display results as a fraction, decimal or percent Use proportions to make

14 event and its complement and describe the relationship between the two 7.6F use data from a random sample to make inferences about a population 7.6H solve problems using qualitative and quantitative predictions and comparisons from simple experiments 7.6 I determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces 7.6G solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents 7.12A compare two groups of numeric data using comparative dot plots or box plots by comparing their shapes, centers, and spreads 7.12B use data from a random sample to make inferences about a population and language as appropriate 7.1E create and use representations to organize, record, and communicate ideas 7.1F analyze relationships to connect and communicate ideas 7.1G display, explain, and justify ideas and arguments using precise language in written or oral communication predictions 7.12C compare two populations based on data in random samples from these populations, including informal comparative inferences about differences between the two populations

15 Course: 7 th grade Math Bundle 11: Personal Financial Literacy 5 days Understand the components of a personal budget. Build a personal budget. Understand the difference between sales tax and income tax and be able to calculate each. Establish the difference between simple interest and compound interest earnings. What is the difference between a sales tax and an income tax? What information do you need to establish a budget? What is the difference between simple interest and compound interest earnings? Sales tax, income tax, earned wages, budget, income, savings, retirement, variable expenses, financial assets, assets, liabilities, net worth, net worth statement, hourly wage, simple interest earning, compound interest earning, sales, rebates, coupons, fixed expenses, expenses 7.13A calculate the sales tax for a given purchase and calculate income tax for earned wages 7.13B identify the components of a personal budget, including income; planned savings for college, retirement, and emergencies; taxes; and fixed and variable expenses, and calculate what percentage each category comprises of the total budget 7.13C create and organize a financial assets and liabilities record and construct a net worth statement 7.13D use a family budget estimator to determine the minimum household budget and average hourly wage 7.13E calculate and compare simple 7.1A apply mathematics to problems arising in everyday life, society, and the workplace 7.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution 7.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems Focus: Calculate sales tax Calculate income tax for earned wages Components of a personal budget, include but not limited to: o Income o Savings o Retirement o Emergencies o o Taxes Fixed and variable expenses Construct a net worth statement Create and organize a financial assets and liabilities record Calculate and compare simple interest and compound interest earnings.

16 interest and compound interest earnings 7.13F analyze and compare monetary incentives, including sales, rebates, and coupons 7.1E create and use representations to organize, record, and communicate ideas 7.1G display, explain, and justify ideas and arguments using precise language in written or oral communication

17 7 th Grade Mathematics Year at a Glance First Semester Second Semester 1 st Six Weeks 4 th Six Weeks Unit 1: Converting and Comparing Positive Rational Numbers Unit 7: Measurement and Application (15 days) (17 days) Unit 8: Measurement and Application 3D (6 days) Unit 2: Adding, Subtracting, Multiplying and Dividing Fractions and Decimals (26 days) 2 nd Six Weeks 5 th Six Weeks Unit 3: All Operations with Integers (10 days) Unit 9: Transformations (6 days) Unit 4: Proportionally including Percent Application (19 days) Unit 10: Representing Data and Probability (4 days) Unit 11: Measures of Central Tendency/Range (8 days) Review for STAAR testing 3 rd Six Weeks 6 th Six Weeks Unit 5: Equations/Sequences (16 weeks) Unit 6: Classifying Shapes and Solids (9 days)

18 7.1A Apply mathematics to problems arising in everyday life, society, and the workplace. Current Standard: 6.11A/7.13A /8.14A identify the mathematics in everyday situations Cognitive Change: changed identifying to applying mathematics in everyday situations Content Change: added the identification of mathematics in the workplace and society Mathematical Process Standards *Process Standards MUST be integrated within EACH Bundle to ensure the success of students. 7.1B Use a problem- solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem- solving process and the reasonableness of the solution. Current Standard: 6.11B/7.13B/8.14B use a problem- solving strategy that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution of reasonableness Cognitive Change: added evaluating the problem- solving process added analyzing information added justifying solution Content Change: N/A 7.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems. Current Standard: 6.11D/7.13D/8.14D select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems Cognitive Change: N/A Content Change: changed such as to including 7.1D Communicate ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. Current Standard: 6.12A/7.14A/8.15A communicate ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic models Cognitive Change: added create and use representations to organize [and] record ideas Content Change: added emphasis to the implications of ideas changed graphical, numerical, physical, or algebraic models to multiple representation, including symbols, diagrams, graphs 7.1E Create and use representations to organize, record, and communicate ideas. Current Standard: 6.12A/7.14A/8.15A communicate ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic models Cognitive Change: added create and use representations to organize [and] record ideas Content Change: added emphasis to the implications of ideas changed graphical, numerical, physical, or algebraic models to multiple representation, including symbols, diagrams, graphs 7.1F Analyze relationships to connect and communicate ideas. Current Standard:. 6.13B/7.15B/8.16B validate his/her conclusions using properties and relationships Cognitive Change: changed validate conclusions to justify ideas and arguments Content Change: added analyze relationships added connections between various ideas added an emphasis to both written and oral communications changed using properties to using precise language 7.1G Display, explain, and justify ideas and arguments using precise language in written or oral communication. Current Standard:. 6.13B/7.15B/8.16B validate his/her conclusions using properties and relationships Cognitive Change: changed validate conclusions to justify ideas and arguments Content Change: added analyze relationships added connections between various ideas added an emphasis to both written and oral communications changed using properties to using precise language