# Bracken County Schools Curriculum Guide Math. Grade 7 Math Unit 1: Decimal, Algebra, and Statistics Suggested Length: 5 weeks

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1 Grade 7 Math Unit 1: Decimal, Algebra, and Statistics Suggested Length: 5 weeks Program of Studies 1. How do you evaluate and simplify algebraic expressions? 2. How can you use variables to represent everyday situations as algebraic expressions? 3. How do you find mean, median, mode, and range given a set of data? When should each be used? 4. How do you decide which graph to use to display your data? NC-1 extend number sense for percents and integers. NC-2 extend understanding of operations (=, -, x, ) to include integers. NC-5 use whole number exponents. NC-12 explain and apply properties (e.g., commutative, associative, distributive, inverse, identity). PS-1 collect, organize, analyze, and interpret data in a variety of graphical methods, including circle graphs, multiple line graphs, double bar graphs, and double stem and leaf plots. PS-2 make predictions, draw conclusions, and verify results from statistical data and probability experiments. PS-3 select an appropriate graph to represent given data and justify its use. PS-4 compare data from various types of graphs. PS-7 determine and apply the most appropriate measures of central tendency (e.g., mean, median, mode) and/or dispersion (e.g., range). A-1 recognize, create, and continue patterns and generalize the pattern by giving the rule for any term. A-4 simplify numeric and algebraic expressions. A-7 organize data into tables and plot points onto all four quadrants of a coordinate (Cartesian) system/grid and interpret resulting patterns or trends. Core Content Integers Fractions Decimals Percents Pi Order of operations Exponents Commutative property Associative property Identity property Distributive property Line plot Line graph Bar graph Histogram Venn diagram Stem-and-leaf plot Scatter plot Box-and-whisker plot Mean Median Mode Range Clusters Gaps Outliers Equations Variables Algebraic expressions Two-step equation Inequalities Students are given algebraic expressions to solve one at a time with their team. They are given 3 that involve different combinations of operations and are all of different difficulty. They may not move onto the second without approval from the teacher. The first group finished is the winner Play Remember that Expression. Students have to play a memory game to match the algebraic expression with its meaning in words Research baseball salaries, compute their averages, compare each salary to the average, rank 10 players by salary and then by average on a graph. Describe your results on a poster and in writing. Construct a frequency table showing the most popular music among seventh graders Construct frequency table, line graph and a histogram using M&M s (individual and class results) comparing color. Determine the mode, and mean in each pack DOK 3 Design a week-long program of fitness, determine what activities burn the least calories per hour, calculate the number of calories consumed on a weekly average, (construct a spreadsheet of food and drinks consumed), formulate equations to find how many hours you would have to do certain activities to burn 2400 calories, write expressions showing total calories burned for activities Resource Web Quest, Projects & Interdisciplinary investigations McGraw Hill msmath2.net. Complete Tower of Hanoi activity. Students make predictions on how to move 1,2,3,4, and 5 disks from one spike to another according to a few rules. Then they must find the algebraic expression for n number of disks Play Sequence Scramble. Students are spit into groups of 4 and are to be dealt 6 cards each. They then must figure out which cards form a sequence. The group that Pathway to Proficiency 1of 12

2 Grade 7 Math Unit 1: Decimal, Algebra, and Statistics Suggested Length: 5 weeks MA Students will provide examples of and identify integers, fractions, decimals, percents, and π. DOK 1 MA Students will describe and provide examples of representations of numbers (whole numbers, fractions, decimals, percents, integers, square roots, and π) and operations in a variety of equivalent forms using models, diagrams and symbols (e.g., number lines, 10 by 10 grids, rectangular arrays, number sentences) based on realworld and mathematical problems. MA Students will estimate to solve real-world and mathematical problems with fractions, decimals and percents, checking for reasonable and appropriate computational results. MA Students will add, subtract, multiply and divide whole numbers, fractions and decimals to solve real-world problems and apply order of operations (including positive whole number exponents) to simplify numerical expressions. MA Students will identify the use of properties (commutative properties of addition and multiplication, the associative properties of addition and multiplication, and the identity properties for addition and multiplication) to justify a given step in solving problems. DOK 1 MA Students will convert units within the same measurement system and use these units to solve real-world problems. MA Students will analyze and make inferences from data displays (drawings, tables/charts, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs, stem-and-leaf plots, puts all 24 cards in their sequences first is the winner Test: Decimal Patterns and Algebra Open Response: Movie Tickets Measure size of students feet, collect and analyze data, design a method to display the results, calculate the mean, median, mode and range of foot length for boys, for girls, and for boys and girls together. Display results graphically and write a concluding statement that describes the data Extension Research the contribution Jan Earnst Matzeliger made to the industry. Include statistics that tell the economic effect of his invention Measure student s height with a partner and then line up from shortest to tallest. As the class discusses what is typical, review each of the central tendency measures. Create a box-and-whisker plot from this, and also a stem-and-leaf plot DOK 3 Play Median Spin in teams of 4. A spinner is spun to determine how many cards a student draws. The student then finds the median of the numbers on the cards. Points are given for the correct answer Extension Students may also be given points for finding the median and mode in the given time period Skittle Investigation. Using a large bag of skittles and a smaller bag, predict (after counting the smaller bag) how many of each color are in the larger bag. Develop a plan for determining this without dumping out the bag, show data, and justify how you cam up with the data Construct a histogram of the class quiz scores. Use the histogram to answer questions about the scores DOK 3 Analyze some Kentucky Quick Facts comparing neighboring counties and create graphs to show interpretation of them Test: Statistics: Analyzing Data Open Response: Allowances Pathway to Proficiency 2of 12

3 Grade 7 Math Unit 1: Decimal, Algebra, and Statistics Suggested Length: 5 weeks scatter plots). DOK 3 MA Students will explain how different representations of data (e.g., tables, graphs, diagrams, plots) are related. MA Students will read/interpret, analyze and make inferences from box and whisker of data and make predictions and draw conclusions from the data. MA Students will determine and construct appropriate data displays (bar graphs, line plots, Venn diagrams, tables, line graphs, stem-and-leaf plots) and will explain why the type of display is appropriate for the data. MA Students will make decisions about how misleading representations affect interpretations and conclusions about data (e.g. changing the scale on a graph). MA Students will determine the mean, median, mode and range of a set of data and will identify clusters, gaps and outliers within the data. MA Students will apply counting techniques to determine the size of a sample space for a real-world or mathematical situation. MA Students will: determine theoretical probabilities of simple events; determine probabilities based on the results of an experiment and make inferences from probability data. DOK 3 MA Students will extend, describe rules for patterns and find a missing term in a pattern from real-world and mathematical problems. DOK 3 MA Students will explain how tables, graphs, patterns, verbal rules and Pathway to Proficiency 3of 12

4 Grade 7 Math Unit 1: Decimal, Algebra, and Statistics Suggested Length: 5 weeks equations relate to each other. MA Students will explain how the change in one quantity affects the change in another quantity (e.g., in tables or graphs). MA Students will substitute values for variables (up to three different variables) and evaluate algebraic expressions. MA Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical problems. MA Students will model and solve real-world and mathematical problems with one- or two-step single variables, first degree equations or inequalities (e.g., 2x+1=9, 3x+3<9). (Statements and solutions use only non-negative numbers.) Grade 7 Math Unit 2: Integers and Algebra Suggested Length: 5 weeks Program of Studies 1. How do you relate integers to whole numbers, rational Ordered pair Coordinate plane Origin Axes numbers, and irrational numbers? 2. How do you display solutions to NC-1 extend number sense for percents and integers. NC-2 extend understanding of operations (=, -, x, ) to include integers. A-2 represent, interpret, and describe functional relationships through tables, graphs, and verbal rules (input/output). A-3 understand the concept of equations and inequalities using variables as they relate to everyday situations. A-4 simplify numeric and algebraic Play Walking the Plank, which compares walking the plank to walking the number line DOK 1 Read, write, and compare integers using the number line DOK 1 Play Integer War with a deck of cards. The red cards are negative numbers and the student with the highest cards gets to add those cards to his pile. The player to loose all their cards or the person with the most cards when time is called is the winner DOK 1 Write integers for real life situations. For example, the average rainfall in Virginia for November was 5 inches Pathway to Proficiency 4of 12

6 Grade 7 Math Unit 2: Integers and Algebra Suggested Length: 5 weeks analyze and generalize first degree relationship using tables, graphs and words and will apply the relationship to solve real-world and mathematical problems. MA Students will substitute values for variables (up to three different variables) and evaluate algebraic expressions. MA Students will describe, define and provide examples of variables and expressions with a missing value based on real-world and mathematical situations. MA Students will model and solve scales Test: Algebra Integers Open Response: Integers Solve equations using cups and colored counters Write a word problem consisting of an equation for a class member to solve Create a short infomercial about how to solve a two step-equation Play Find that Rule in groups Open Response: Popcorn Open Response: Jeans Open Response: Baseball Cards Test: Algebra: Linear Equations and Functions real-world problems with one- or two-step single variable, first degree equations or inequalities (e.g., 2x+1=9, 3x+3<9). (Statements and solutions use only nonnegative numbers.) Grade 7 Math Unit 3: Fractions Suggested Length: 4 weeks Program of Studies 1. How do you add, subtract, multiply, and divide fractions? 2. What is the difference between a ratio and a fraction? 3. How do you NC-6 extend and apply addition, subtraction, multiplication, and division of integers both concretely and symbolically (mental, pencil and paper, calculators). NC-7 extend concepts and application of operations with fractions and decimals to include percents. GM-1 find circle measurements (radius, diameter, circumference, area) and the relationships among them. GM-3 investigate fixed area with changing perimeter and fixed perimeter with changing Prime numbers Composite numbers Prime factorization Factors Multiples Divisibility rules Lcm Gcf Irregular polygons Regular polygons Area Perimeter Play Prime Time. Students are asked to find all the prime numbers from 1 to 100 in groups Play Factor Mania to review factors along with prime and composite numbers. Students are split into two groups or partners and compete against one another Team 1 picks a number and gets those points. Team 2 has to find the factors of that number and gains all those points. The object is to pick a number that is prime so the other teams points are limited. (Each number can only be covered once therefore counting towards the points once Play Fractions Decimal Percent Bingo. Students Pathway to Proficiency 6of 12

7 Grade 7 Math Unit 3: Fractions Suggested Length: 4 weeks convert between different customary units? area. Core Content MA Students will provide examples of and identify integers, fractions, decimals, percents, and π. DOK 1 MA Students will convert among whole numbers, fractions, decimals, percents and π and will compare these numbers. MA Students will identify and apply prime numbers, composite numbers, prime factorization, factors, multiples and divisibility to solve real-world and mathematical problems (e.g., prime factorization to determine a least common multiple [LCM] or greatest common factor [GCF]). DOK -2 MA Students will measures lengths (to the nearest eighth of an inch or nearest centimeter) and will determine and use in real-world and mathematical problems: area and perimeter of triangles; area and perimeter of quadrilaterals (rectangles, squares, trapezoids) (using the Pythagorean theorem will not be required as a strategy.); area and circumference of circles and area and perimeter of compound figures composed of triangles, quadrilaterals and circles. MA Students will explain how measurements and measurement formulas are related or different (e.g., perimeter and area of rectangles). Circumference Ratios are to cover equivalent values on the game board with the number called Order ratios. They are split into groups and given cards with three different ratios on them. They are to order those ratios and with the teacher s approval, they can move on to the next card. When they have successfully completed all 5 cards they are the winners DOK 2 Match seashells with different fractions, decimals, mixed numbers and improper fractions written on them. Students are split in to small groups and are asked to gather as many seashells as they can that are equivalent Review adding, subtracting, multiplying, and dividing fractions by completing a fraction maze in small groups. The group who is finished first and has the right answer is the winner DOK 3 Create their own fraction maze DOK 3 Play Fraction Speed to help reinforce their skills with fractions. They are given a fraction with 10 different fractions on it. In the center they write another fraction and an operation that is chosen by the teacher. They then complete the wheel. The first one correctly finished with their wheel chooses the next fraction and operation for the remaining wheels DOK 3 Calculate the perimeter and area of a door and a window from their house Explore the room to find circular objects from which they can measure and calculate the circumference of Test: Applying Fractions Open Response: Pool Open Response: Height Pathway to Proficiency 7of 12

8 Grade 7 Math Unit 4: Proportional Reasoning Suggested Length: 7 weeks Program of Studies 1. How are using percent proportion and percent equation alike? 2. How is probability used in everyday situations? 3. How do you design and conduct probability experiments? 4. How are dependent and independent events different? NC-1 extend number sense for percents and integers. NC-4 apply meaning of ratio and proportion to problems. NC-8 compute percentages of numbers and use percentages in proportional reasoning. NC-9 estimate and mentally compute using integers and percents. NC-10 solve proportions. NC-11 compare, order, and determine equivalent relationships among fractions, decimals, and percents. NC-13 develop proportional thinking, rates, scaling, and similarity. PS-5 determine appropriate techniques to use when investigating solutions to probability problems (using counting techniques; tree diagrams; area models; and exhaustive, organized lists, charts, and tables). PS-6 investigate and explain the role of probability in decision making. PS-8 design and conduct probability experiments. PS-9 determine theoretical (mathematical) probabilities, compare to experimental results, and explain reasons why there might be differences, (e.g., express probability as a ratio, decimal, or a percent as appropriate for a given situation). PS-10 explore concepts of randomness and independent events. A-5 use a variety of methods and representations to create and solve singlevariable equations that may be applied to everyday situations Proportion Experimental probability Theoretical probability Simple event Sample space Congruent figures Similar figures Sales tax Discounts Rates Simple interest Calculate and compare unit costs from local newspapers Create a booklet of unit prices Investigate rate of change using square tiles and grid paper Play Racing with Proportions. Students spin a spinner and substitute in x for a proportion and then move their marker x spaces until one of the partners reaches the End square Create a scale drawing of the classroom Explore real-life examples of numbers greater than 100% and less than 1% DOK 1 Write his or her own real-life problem using a given percent DOK 1 Work with a partner to find a part using the percent model on grid paper DOK 1 Use the percent proportion to complete Venn Diagrams DOK 3 Test: Ratios and Proportions Open Response: Mr. Thompson s Living Room Compare the percent proportion and the percent equation DOK 3 Formulate a hypothesis of the study habits of their middle school students; construct a survey, analyze results, and lastly, evaluate their hypothesis Use a graphic from USA Today to predict how many students in our school do not have restrictions on their television viewing DOK 3 Play The Accounting Game where they roll dice to determine the amount of money they earn before they reduce the tax amount that they have to pay. The winner is the person with the most money when time is called Choose from a list of items that they can buy from local Pathway to Proficiency 8of 12

9 Grade 7 Math Unit 4: Proportional Reasoning Suggested Length: 7 weeks Core Content MA Students will provide examples of and identify integers, fractions, decimals, percents, and π. DOK 1 MA Students will convert among whole numbers, fractions, decimals, percents, and π, and will compare these numbers. DOK 3 MA Students will estimate to solve real-world and mathematical problems with fractions, decimals and percents, checking for reasonable and appropriate computational results. MA Students will apply ratios and proportional reasoning to solve real-world problems (e.g., percents, sales tax, discounts, rate). DOK 3 MA Students will describe and provide examples of congruent and similar figures and will apply congruent and similar figures to solve real-world and mathematical problems. MA Students will apply counting techniques to determine the size of a sample space for a real-world or mathematical situation. MA Students will: determine theoretical probabilities of simple events; determine probabilities based on the results of an experiment and make inferences from probability data. DOK 3 MA Students will tabulate experimental results from simulations and explain how theoretical and experimental newspaper sales without going over a given budget DOK 3 Compare and contrast different banking options for simple interest earned and paid DOK 3 Choose from a list of items to purchase with a credit card and they must determine the amount they will pay back within a given period of time DOK 1 Test: Applying Percent Open Response: Simple Interest Determine the different probabilities using dice, a deck of cards, and a spinner Analyze different games, like Monopoly, Life, and Uno to determine if they are fair. Students should create a write up of the object of the game, the number of possible players, and a brief description of the rules. Lastly, they should determine the way in which probability is used Create tree diagrams that correspond to real-life situations (food choices, outfits, coin flipping, etc.) Create a tree diagram that represents the many different orders the class could stand in. This will be done in groups. This diagram will take awhile so after 15 minutes or so they will be introduced to a quicker method of calculating all the possible outcomes, the Fundamental Counting Principle Explore permutations by choosing 4 classes that they want to take their first semester in high school. They will then determine the many different orders that these classes could be taken (disregarding the fact that they are offered at specific times.) Students must be told that they are using the Fundamental Counting Principle when finding the permutations DOK 3 Identify some events when order does not matter to begin discussion of combinations. Some examples include pizza toppings, sundae toppings, and choosing to do 6 questions out of 12 on a quiz. (Order does not matter.) Discuss ways to distinguish between permutations and Pathway to Proficiency 9of 12

10 Grade 7 Math Unit 4: Proportional Reasoning Suggested Length: 7 weeks probabilities are related. MA Students will model and solve real-world and mathematical problems with one- or two-step single variable, first degree equations or inequalities (e.g., 2x+1=9, 3x+3<9). (Statements and solutions use only non-negative numbers.) combinations Explore independent and dependent events by placing their names in a hat and predicting the probabilities that a boy or girl is chosen. Students should notice how the probabilities change as names are removed from the hat. The second name removed is dependent on the first name removed Test: Probability Open Response: Birthday Party Open Response: Tara s Hobbies Grade 7 Math Unit 5: Geometry and Measurement Suggested Length: 5 weeks Program of Studies 1. What is the relationship of angles to lines that form them? 2. How can you compare area to perimeter and vice versa of any twodimensional shapes? 3. What are the results of moving a shape in a plane? NC-3 develop number sense for pi as one example of an irrational number. GM-1 find circle measurements (radius, diameter, circumference, area) and the relationships among them. GM-2 develop and use the formulas for area of triangles, parallelograms, and trapezoid; relate to the formula for area of rectangles (1 x w). GM-4 investigate area of polygons and other two-dimensional shapes. GM-5 identify and classify characteristics of two-dimensional shapes, such as regular and irregular quadrilaterals, special triangles, and regular polygons. GM-6 identify characteristics of angles (e.g., adjacent, vertical, corresponding, interior, exterior). GM-7 represent three-dimensional geometric figures with special attention to developing spatial sense (e.g., top view, side view, three- Metric units Points Rays Lines Angles Planes Sides Vertices Congruent parts Acute Right Obtuse Scalene Isosceles Equilateral Square rectangle Rhombus Parallelogram Trapezoid Regular polygons Faces Edges Use an analog clock to classify the different types of angles. (acute, obtuse, right and straight) Identify other objects in the classroom that portray the different types of angles. Use protractors to measure angels. Use a compass to construct and bisect angles. Create a multiple choice survey question and pass it out to the class. They will then create a circle graph of their results by hand and then with the computer. Students will then report their findings to the class so that other students can interpret their information. Construct parallel lines and discover angle relationships using a compass, protractor, and coloring pencils. Construct a triangle of their own by placing three dots anywhere on their paper. They will then connect the dots with a ruler and determine the angle measures. They must understand that any three points on a page can be connected to make a triangle and that the sum of all the angles is always 180º. Create a Venn diagram that shows how the different types of triangles relate to one another. Identify and classify quadrilaterals by using shapes. Pathway to Proficiency 10of 12

11 Grade 7 Math Unit 5: Geometry and Measurement Suggested Length: 5 weeks dimensional shapes drawn on isometric dot paper). Spheres Cones They are to match the quadrilateral shape with the name GM-8 move shapes in a plane: (e.g., translate (slide), rotate (turn), reflect (flip)). Cylinders Prisms Students create a short commercial on how to decipher between the quadrilaterals A-6 solve problems involving formulas. Pyramids Play Pentominoes. Students are split into groups and Similar figures are asked to arrange the pentominoes into different size Translate rectangles Core Content Reflect Identify everyday situations when a smaller or larger Rotate model of an object is useful. For example, an atom or a MA Students will provide model of a house. examples of and identify integers, fractions, decimals, percents, and π. DOK 1 Construct similar figures using geoboards and rubber bands MA Students will measure lengths (to the nearest eighth of an inch or the nearest centimeter) and will determine and use in real-world and mathematical Experiment with different polygons to determine whether they tessellate or not. If so, students create their own tessellation using coloring pencils problems; area and perimeter of triangles; area and perimeter of and quadrilaterals (rectangles, squares, trapezoids) (using the Pythagorean theorem will not be required as a strategy.); area and circumference of circles and area and perimeter of compound figures composed of triangles, quadrilaterals and circles. MA Students will estimate measurements of regular and irregular polygons and circles in standard units. MA Students will find the measures of angles by estimation and measurement with a protractor or angle ruler. MA Students will convert units within the same measurement system and use these units to solve real-world problems. MA Students will describe, provide examples of and identify (using correct notation, label and name) the basic geometric Work in groups of three with specific roles assigned to each. One person will describe a translation while the other two draw it on graph paper. The students then switch role and someone else describes a new translation. (Students should know that the order of translating a figure does not matter; 6 units up and 3 units left is the same as 3 units left and 6 units up Use a mirror or geomirror to determine if a shape has reflectional symmetry Use the folding method to determine if a shape has reflectional symmetry Identify the letters of the alphabet that have reflectional symmetry Graph rotations of Morris the Cat on a coordinate plane. Test: Geometry Open Response: Polygon MATH Use square tiles to create different rectangles. Using these shapes, students will find squares of numbers and square roots of their perfect squares Draw a number from a bag and explain how to estimate its square root. Play Tic-Tac-Root. Distinguish between right triangles and other triangles Pathway to Proficiency 11of 12

12 Grade 7 Math Unit 5: Geometry and Measurement Suggested Length: 5 weeks elements (e.g., points, segments, rays, lines, angles, and planes) in real-world and mathematical problems. by the lengths of their sides. Use grid paper to help them determine the area of parallelograms MA Students will describe and provide examples of the elements (e.g., sides, vertices, angles, congruent parts) of two-dimensional figures (circles, triangles [acute, right, obtuse, scalene, isosceles, equilateral], quadrilaterals [square, rectangle, rhombus, parallelogram, trapezoid], regular polygons) and will Use colored grid paper to make a mosaic of triangles and trapezoids. They must find the area of each shape Find the area of cardboard shapes by discovering how the complex figures can be divided into a combination of rectangles, semicircles, triangles, and trapezoids. Test: Geometry: Measuring Two-Dimensional Figures Open Response: apply these elements and figures to solve real-world and mathematical problems. Construct three-dimensional figures with centimeter cubes discussing the different views they have. MA Students will describe, provide examples of and identify elements (e.g., vertices, angles, faces, edges, congruent parts) of common three-dimensional figures (spheres, cones, cylinders, prisms, and pyramids). MA Students will describe and provide examples of congruent and similar figures and will apply congruent and similar figures to solve real-world and mathematical problems. MA Students will translate (slide) and reflect (flip) figures in a coordinate plane. Use isometric dot paper to draw different threedimensional figures given the top, side and front views. Use centimeter cubes to determine the volume of rectangular prisms. Identify everyday items that are cylinders and calculate the volume of a few of them. (soup can, mug, and a cake pan, etc.) Complete the Geometry Scavenger Hunt. Students are split into teams and are asked to locate items within the school, their home and in their community that has specific criteria. This project will take more than one day. Use centimeter cubes to find the surface area of rectangular prisms. Find the surface are of cylinders using grid paper. Test: Geometry: Measuring Three-Dimensional Figures Open Response: Pathway to Proficiency 12of 12

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