Unit Overview. Concepts & Understandings. Learning Targets

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1 Content Area: Math Garfield Middle School Unit Title: Algebraic Reasoning, Integers and Rational Numbers Target Course/Grade Level Duration: 30 blocks 7 th Description Students will simplify numerical expressions involving order of operations and exponents, compare and order integers and rational numbers, convert between fractions and decimals mentally, on paper, and with a calculator and use models to add, subtract, multiply, and divide integers. Order of operations. Properties of numbers. Variables and algebraic expressions. Translating words into math Simplifying algebraic expressions. Integers. Adding integers. Subtracting integers. Multiplying and dividing integers. Solving equations containing integers. Equivalent fractions and decimals. Comparing and ordering rational numbers. Simplify numerical expressions involving order of operations and exponents. Using variables and symbols to translate words into math. Simplifying algebraic expressions using properties of addition and multiplication. Comparing and ordering integers and rational numbers. Converting between fractions and decimals mentally, on paper, and with a calculator. Using models to add, subtract, multiply and divide integers. MA.CC - EE.7.01, MA.CC - EE.7.02, MA.CC - EE.7.03,MA.CC -EE.7.04, MA.CC - G.7.03, MA.CC - NS.7.01, MA.CC - NS.7.02, MA.CC-NS. 7.03, MA.CC - RP.7.02 What is the order of operations? What are the properties of rational numbers? How do you simplify numerical expressions? How do you evaluate algebraic expressions? How do you translate words into numbers, variable and operations? Explain how to combine like terms? What is the difference between whole numbers and integers? Explain absolute value? What are the rules for adding integers? Explain how to subtract integers?

2 What are the rules for multiplying and dividing integers? Explain which operation are the inverse of each other? Why is it necessary to perform the same operation on both sides of the equation? How do you write fraction as a decimal? Explain how to use place value to convert a decimal into a fraction? What needs to be the same before you can add or subtract fractions? How do you compare fractions with different denominators? The student will use the order of operations to simplify numerical expressions. The student will identify properties of rational numbers and use them to simplify numerical expressions. The students will evaluate algebraic expressions. The students will translate words into numbers, variables, and operations. The students will simplify algebraic expressions. The student will compare and order integers and determine absolute value. The student will add and subtract integers. The student will multiply and divide integers. The student will solve one step equations with integers. The student will write fractions as decimals, and vice versa, and determine whether a decimal is terminating or repeating. The student will compare and order fractions and decimals. Practice-worksheet Chapter project- Step-By-Step Algebra. Hands on Lab: Modeling integer addition/subtraction Extension: Additive Inverse and absolute value Hands on Lab: Modeling integer multiplication/division Hands on Lab: Modeling integer equations Real World Connections Lab Technology: Explore the order of operations. Game Time: Jumping Beans, Magic Squares

3 Content Area: Math Unit Title : Applying Rational Numbers Target Course/Grade Level 7 th Duration: 15 blocks Description Students will learn how use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals. Students will solve equations with rational numbers. Adding and subtracting decimals. Multiplying decimals. Dividing decimals. Solving equations containing decimals. Adding subtracting fractions. Multiplying fractions and mixed numbers. Dividing fractions and mixed numbers. Solving equations containing fractions. MA.CC - EE.7.04, MA.CC - NS.7.03, MA.CC - NS.7.02 MA.CC - NS.7.01 Use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals. Solve equations with rational numbers. See Addendum Describe the steps necessary to add and subtract decimals? How can you check an answer when adding or subtracting decimals? Compare multiplication of decimals with multiplication of integers. How do you determine the decimal placement in a product when multiplying decimals? What are the rules when dividing an integer by a decimal? Explain how to solve each type of decimal equation; addition, subtraction, multiplication, and division. How do you obtain a common denominator? Describe the process for subtracting/adding fractions with different denominators. Describe how to multiply and divide mixed number and a fraction. How do you determine the steps of a product? Compare the steps used in multiplying mixed numbers with those used in dividing mixed numbers? What is the process of solving an equation that involves mixed numbers? Add and subtract decimals. Multiply decimals. Divide decimals and integers by decimals.

4 Solve one step equations that contain decimals. Add and subtract fractions. Multiply fractions and mixed numbers. Divide fractions and mixed numbers. Solve one step equations that contain fraction. Practice-worksheet Chapter project- Flipping Over Integers and Rational Numbers Real World Connections Game Time-number patterns Content Area: Math Unit Title: Proportional relationships Target Course/Grade Level 7 th Duration: 20 blocks Description Students will use division to find unit rates and ratios in proportional relationships. Estimate and find solutions to application problems involving proportional relationships. Use critical attributes to define similarity. Use ratios and proportions in scale drawings and scale models. Rates Identifying and writing proportions Solving Proportions Similar figures and proportions Using similar figures Scale drawings and scale models Use division to find unit rates and ratios in proportional relationships Estimate and find solutions to application problems involving proportional relationships. Use critical attributes to define similarity. Use ratios and proportions in scale drawings and

5 Garfield Middle School MA.CC - RP.7.01, MA.CC - RP.7.02, MA.CC - G.7.01 scale models. See addendum Explain how you can tell whether a rate represents a unit rate? What does it mean for ratios to be proportional? Explain how the term cross product can help you remember how to solve a proportion. What are the characteristics of corresponding angles and corresponding sides in similar figures? How do you know if two shapes are proportional? How do you find a missing side length for one or two similar figures? How do find the actual height of an object whose scale drawing is smaller than the object? Find and compare unit rates, such as average speed and unit price. Find equivalent ratios and identify proportions. Solve proportions by using cross products. Use ratios to determine if two figures are similar. Use similar figures to find unknown measures. Understand ratios and proportions in scale drawings and use ratios and proportions with scale. The following activities can be incorporated into the daily lessons Practice-worksheet Chapter project- Paper Plate Proportions Hands-on lab-make scale drawings and models Hands-on lab- Use scale drawings Real World Connections Game Time-Water works

6 Content Area: Math Unit Title: Graphs Garfield Middle School Target Course/Grade Level: 7 th Grade Duration: 10 blocks Description : Plot and identify ordered pairs of integers on a coordinate plane and graph in order to demonstrate relationships between data sets. The Coordinate Plane Interpreting graphs Slope and rates of change Direct Variation MA.CC - RP.7.02, MA.CC - RP.7.01 Student understandings from the concepts include Plotting and identifying ordered pairs of integers on a coordinate plane. Graphing to demonstrate relationships between data sets. Using rates of change to solve problems. Writing and graphing linear equations to solve problems. See addendum Explain the meaning of a horizontal segment on a graph that compares distance to time? Describe a real world situation that could be represented by a graph that has connected lines or curves? Compare constant and variable rates of change? Describe a line with a negative slope? Explain how to use the table of data to check whether the relationship between two variables is a direct variation. Describe how to recognize a direct variation from an equation, from a table, and from a graph? Plot and identify ordered pairs on a coordinate plane. Relate graphs to situations. Determine the slope of a line and recognize constant and variable rates of change? Identify, write, and graph an equation of direct variation.

7 . Practice-worksheet. Chapter project- Graphs Fold-A- Book Hands On lab- graph proportional relationships. Real World Connections. Game Time- Clothes Encounters. Content Area: Math Unit Title : Percents Target Course/Grade Level: 7th Duration: 15 blocks Description : Modeling and estimating percents, writing equivalent fractions, decimals, and percents including percents less than 1 and greater than 100. Solving percents problems involving discounts, sales tax, tips, profit, and simple interest. Comparing fractions, decimals, and percents. Fractions, decimals, and percents Estimating with percents Using properties with rational numbers Percent of change Applications of percents Simple interest MA.CC,EE.7.03 MA.CC,EE.7.02, MA.CC - NS.7.01, MA.CC - NS.7.02 MA.CC - RP.7.03, Understanding Modeling and estimating percents Writing equivalent fractions, decimals and percents, including percents less than 1 and greater than 100 Solving percent problems involving discounts, sales tax, tips, profit, and percent of change, commission, and simple interest. Comparing fractions, decimals, and percents. See addendum

8 Explain two methods for writing a decimal as a percents and for writing a fraction as a percent? Describe two ways to estimate with percents and tell when each is more appropriate to use? Explain how the multiplication property of equality is used to write an equivalent equation without fractions or decimals? Explain what is meant by 100 percent decrease? Explain how to find a price of an item if you know the total cost after 5 percent sales tax? How is finding commission similar to finding sales tax? Explain the meaning of each variable in the interest formula? Name the variables in the simple interest formula that represent dollar amounts. Write decimals and fraction as fractions and percents. Estimate percents. Use properties of rational numbers to write equivalent expressions and equations. Solve problems involving percent of change. Find commission, sales tax, and percent of earnings. Compute simple interest. Practice-worksheet Chapter project-percent Strips Technology lab- Explore Compound Interest Real World Connections Game Time- Lighten Up. Content Area: Math Unit Title: Collecting, Displaying, and Analyzing Data. Target Course/Grade Level: 7 th

9 Duration: 5 blocks Garfield Middle School Description : Students will choose among mean, median, mode, or range to describe a set of data. Make inferences and convincing arguments based on analysis of data. Mean median, mode, and range. Box-and-whisker plots. Populations and samples. MA.CC. SP 7.01, MA.CC. SP 7.02, MA.CC. SP 7.03, MA.CC. SP 7.04 Using an appropriate representation for displaying relationships among data. Choosing among mean, median, mode, or range to describe a set of data. Making inferences and convincing arguments based on analysis of data. See addendum Explain how the outlier affects the mean, median, and mode of a data set? Describe what you can tell about a data set from a box-and-whisker plot? Explain why it might be difficult to obtain a truly random sample of a very large population? Find the mean, median, mode, and range of a data set. Display and analyze data in box-and whisker plots. Compare and analyze sampling methods. Practice-worksheet Chapter project-graph match Technology Lab- Explore Box and Whisker Plots. Hands On Lab- Explore samples Hands-on Use Random sample

10 Real Word Connections Game Time- Code Breaker Content Area: Math Unit Title: Geometric Figures Target Course/Grade Level: 7 th grade Duration: 10 blocks Description : Classifying pairs of angles as complementary or supplementary. Graphing translations and reflections on a coordinate plane. Using congruence and similarity to solve problems. G.7.02 G.7.05 Building blocks of geometry Classifying angles Line and angle relationships Angles in polygons Congruent figures Classifying pairs of angles as complementary or supplementary. Identifying parallel and perpendicular lines. Using congruence to solve problems. See addendum How many ways can a line segment be named? What are three different ways to classify an angle? How do you find a complementary angle when one angle is given? Explain why perpendicular lines can also be called intersecting lines? Explain how to find the measure of an angle in a triangle when the measure of the two other angles are known? Why are congruent figures always similar figures? What does it mean when two polygons are congruent? Identify and describe geometric figures Identify angles and angle pairs

11 Identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Find the measures of angles in a polygon. Identify congruent figures and use congruence to solve problem. Practice-worksheet Chapter project- Brochure Book of Geometric Figures. Hands On Lab- Explore Complementary And Supplementary Angles. Hands On Lab- Explore Parallel Lines and Transversals. Hands On Lab- Construct Bisectors and Congruent Angles. Technology lab- Construct Triangles with Given Side Lengths. Technology Lab- Explore Transformations. Technology Lab- Construct Triangles with given Angle Measures. Game Time- Networks Content Area: Math Unit Title : Measurement and geometry Target Course/Grade Level: Duration: 15 blocks Description : Comparing perimeter and circumference with the area of geometric figures. Finding the area of a circle and irregular figures. Finding the volume of prism and cylinders. Using nets and formulas to find the surface area of prisms and cylinders. Perimeter and circumference. Area of circles. Area of irregular figures. Three-dimensional figures. Volume of prism and cylinders. Finding the circumference and area of circles. Finding the area of irregular figures. Finding the volume and surface area of threedimensional figures.

12 Surface area of prisms and cylinders. MA.CC,G.7.03, MA.CC,G.7.04, MA.CC,G.7.06 See addendum Describe two ways to find a perimeter of a volleyball court? How are the circumference of a circle and a perimeter of a polygon alike? Compare finding the area of a circle when given a radius with finding an area when given a diameter? Describe two different ways to find the area of irregular figures? Compare and contrast cylinders and prisms. What is a cubic unit? Compare and contrast the formulas for volume of a prism and volume of a cylinder. Explain how to use a net to find the surface area of a rectangular prism and a cylinder? Find the perimeter of a polygon and the circumference of a circle. Find the area of circles. Find the area of irregular figures. Identify various three-dimensional figures. Find the volume of prisms and cylinders. Find the surface area of prisms and cylinders. Practice-worksheet Chapter project- CD-3D Hands on Lab- Explore Perimeter and Circumference. Hands on Lab- Explore the Volume of Prisms and Cylinders. Hands On lab- Use Nets to build Prisms and Cylinders. Real World connections Game Time- Blooming Minds

13 Content Area: Math Unit Title: Probability Garfield Middle School Target Course/Grade Level: 7th Duration: 20 blocks Description : Finding experimental and theoretical probabilities, including those of dependent and independent events. Using lists and tree diagrams to find combinations and all possible outcomes of an experiment. Using the fundamental counting principle and factorials to find permutations. Probability Experimental probability Sample spaces Theoretical probability Making predictions. Probability of independent and dependent events. Combinations Permutations Probability of compound events MA.CC,SP.7.05, MA.CC,SP.7.06, MA.CC,SP.7.07, MA.CC,SP.7.08, Finding experimental and theoretical probabilities, including those of dependent and independent events. Using lists and tree diagrams to find combinations and all possible outcomes of an experiment. Using the fundamental counting principle and factorials to find permutations. See addendum Describe an event that has a probability of zero percent and an event that has a probability of 100 percent. Explain how experimental probability can be used to make predictions? Compare using a tree diagram and using the fundamental counting principle to find a sample space? Give an example of an experiment in which all of the outcomes are not equally likely? Explain a difference between a prediction based on experimental probability and one based on theoretical probability? Compare probabilities of independent and dependent events. Describe how combinations could help you find the probability of an event? What are the possible ways to find the number of permutations of a group of objects? Explain how organized list, tree diagram, and tables help find the sample space in an experiment? Use informal measures of probability Find experimental probability Use counting methods to determine all possible outcomes

14 Find the theoretical probability of an event Use probability to predict events Find the probability of an independent and dependent events Find the numbers of possible combinations Find the number of possible permutations Find probability of compound events Practice-worksheet Chapter project- The Business of Probability Hands-On Lab- Develop a Probability Model Technology Lab- Simulations Hands On Lab- Experimental and Theoretical Probability Real world Connections Game Time- Buffon s Needle Content Area: Math Unit Title Target Course/Grade Level: 7 th Duration: : Multi-Step equations and Inequalities 15 blocks Description : Solving two-step and multi-step equations and equations with variables on both sides. Reading, writing, and graphing inequalities on a number line. Solving one-step and two-step inequalities. Solving two-step equations. Solving multi-step equations. Solving equations with variables on both sides. Inequalities Solving inequalities by adding or subtracting.. Solving two-step and multi-step equations and equations with variables on both sides. Reading, writing, and graphing inequalities on a number line.

15 Solving inequalities by multiplying or dividing. Solving multi-step inequalities Solving one-step and two-step inequalities Solving equations for a variable M.A.CC. EE 7.01, M.A.CC. EE 7.04 See addendum. Explain how you decide which inverse operations to use first when solving two-step equation? Select a multi-step equation and challenge students to list the required steps. Select an equation with variables on both sides and challenge students to decide which variable term to add or subtract. Explain how to graph each type of compound inequalities. Compare solving addition and subtraction equations with solving addition and subtraction inequalities. Compare solving multiplication and division equations with solving multiplication and division inequalities. Explain how to solve a simple two step inequality. Solve two- step equations Solve multistep equations Solve equations that have variables on both sides Read and write inequalities and graph them on a number line Solve one-step inequalities by adding or subtracting Solve one-step inequalities by multiplying and dividing Solve simple two- step inequalities Practice-worksheet Chapter project Wired for Multi-Step Equations Hands on lab- Model two-step equations. Game Time-Flapjacks

Montana City School GRADE 5

Montana City School GRADE 5 Montana Standard 1: Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and applications, and using appropriate