1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity B-3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, Applying Figuring the amount of 6-pack sodas to buy for the family reunion, the pounds of lunch meat to buy, the number pizzas to order, based on the number of people being served. How many people can you serve if a serving amount is given along with the total amount of food being bought, etc.? Also, buying multiples of grocery items (multiplying) or figuring how many can be bought within a certain amount of money (dividing) http://www.youtube.com/watch?v=AJL1lobzHQU B-3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = 􀃍 ÷ 3, 6 × 6 = ? Determine the unknown whole number in a multiplication or division equation relating three whole numbers Analyzing Set up equations given the three unknowns in reference to planning a party: how many tables seating 4 each will it take to accommodate 64 guests?; how many seats will 4 tables each need to seat all 64 guests?; how many people will fit in a space that has 16 tables that seat 4 people?
sunscreen costs $12 and another brand costs $16 for an 8 ounce bottle, which is the better deal? Why? 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Multiply and divide within 100. B-3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Multiply and Divide Know from Memory within 100 products using strategies such as the relationship between multiplication and division or properties of operations two one-digit numbers Apply Understand (See 3.OA 1-6) serving sizes, number of tables at a party, number of soft drinks for a party, etc.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Levels of Thinking 6 Sample Activity B-3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Explain Compare Understand Recognize/ generate Explain Express Recognize Compare Recognize Record Justify equivalence of fractions fractions two fractions as equivalent (equal) Simple equivalent fractions Why the fractions are equivalent whole numbers as fractions fractions that are equivalent to whole numbers two fractions with the same numerator or the same denominator Recognize that comparisons are valid only when the two fractions refer to the same whole the results of comparisons with the symbols >,=, or < the conclusions In special cases by reasoning about their size if they are the same size, or the same point on a number line A visual fraction model Number line diagram Visual fraction model Evaluate Use rulers from 3.NF.2. Have students explore the sizes of the fractional inches with relation to each other. Which is larger, 1/12 or 1/16? Is 4/16 equal to ¼? etc. The relational size of fractions can also be relayed through discussion of food serving sizes. If two equal -sized pizzas, cakes, etc. are divided into different numbers of servings, which servings are larger? Grade 3- Measurement and Data
B-3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Tell Write Measure Solve time time time intervals time word problems to the nearest minute to the nearest minute in minutes addition and subtraction Apply Have students use manipulative analog clock, moving the hands to illustrate given times, then show students various times on the clock, having them write the times. Give starting times for class transitions and ask students how much time has elapsed in minutes. B-3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.7 Measure Estimate liquid volumes using standard (metric) units Understand Have various objects for students to estimate their mass and volume and have students measure and make a chart of estimations and actual measurements. Based on measurements of small portable items (a jar of pickles), have students estimate the mass and volume of a barrel of pickles. This can be useful in a discussion of buying items at warehouse type stores, Costco, Sam’s Club, etc. An extension topic can be determining which is cheaper to buy per volume unit, a small jar of pickles or a giant one? 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity
Standards Skills Included in Standard Concepts Included in Standard Through a Particular Context Cognitive Demand/ Levels of Thinking Sample Activity Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. B-3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Solve Exhibit problems involving perimeter finding an unknown side length and exhibiting rectangles rectangles with the same perimeter and different areas or with the same area and different perimeters Given the side lengths Same perimeter and different area or same area and different perimeters Real world and mathematical Apply Using the previous activities’ rectangles, and using rulers, students will measure side lengths to calculate perimeter. Then, create “mystery” rectangles with the perimeter and 2 sides given and have students find the unknown side length. Examples can be used of the perimeter and areas of parks and gardens, fence lines enclosing areas, room dimensions and carpeting or flooring, wall dimensions and paint or wall covering. Finally, have students discuss the following statements: 1. two rectangles with the same area always have the same perimeter. 2. two rectangles with the same perimeter always have the same area
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity C-04.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Solve Represent Assess Multistep Word Problems Multistep Word Problems The of Answers With Whole Numbers and Having Whole Number Answers, Using the Four Operations Using Equations with a Letter Standing for the Unknown Quantity (Variable) Using Mental Computation and Estimation Strategies (Including Rounding) Apply Apply Evaluate Discuss real-life situations where math problems could occur and have students create problems for situations and create situations for equations. For example: Mr. Smith baked 3 trays of 36 cookies for an adult education fundraiser. After they cooled, he divided the cookies evenly into 4 bags. How many cookies did Mr. Smith place in each bag? 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Gain familiarity with factors and multiples. C-4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Find Recognize Determine Determine Factor Pairs Whole Number is a Multiple of Factors Whether a Given Number is a Multiple of a Given Number If a Number is Prime or Composite For Whole Number in Range of For Whole Number in Range of For Whole Number in the Range of 1-100 For Whole Number in the Range of 1-100 Understand Understand Understand Understand Provide a calendar for a specific month. Prime Computer Co. gives bonuses in the month of _________ to celebrate the founding of the company Employees work M-F. On work days that are not a multiple of 2, 3, 5 or 7 each employee receives an extra $100. How much would an employee receive for the month?
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Generate and analyze patterns. C-4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Generate Identify A Number or Shape Pattern Apparent Features of the Pattern that Follows a Given Rule Not Explicit in the Given Rule Create Understand The city of Mason is creating a community garden. Each plot is square and the entire community garden will be square. Each plot costs $8. The plots sold in the first 3 weeks are shown below. If the pattern continues, how many plots will be sold by the 6th week? How many by the 9th? The city is hoping to raise $1000 through sales of the plots. How many weeks will this take if the pattern continues? (Have students note any patterns they see, for example, the number of plots in odd weeks is odd and in even weeks is even.) Level C- Grade 4- Number and Operations in Base Ten
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity C-4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Understand Have learners create blueprints with a room that has dimensions one-digit by up to four digits. Have an elbow partner determine how much floor covering is needed for their buddy’s room. C-4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Remember Use the blueprints (4.NBT.5)to divide the rooms into sections for decorations (screens, carpet stripes) or warring siblings Grade 4- Number Operations- Fractions
C-4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ;3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Decompose Justify a fraction decompositions, into a sum of fractions with the same denominator in more than one way By using a visual fraction model. Create Evaluate (from 4.NF.3a)The running back and the quarterback each ate 5 slices of pizza. The tight end, offensive lineman and kicker ate 3, 4 and 7 slices respectively. What fractional part of a pizza did each group eat? How many pizzas did these five players consume? C-4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Add and subtract subtract mixed numbers with like denominators By replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction Understand Recipes are an area where mixed numbers come in to play. Calculate the amount of flour needed in all if someone wants to make two separate cookie recipes.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. C-4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Use Represent the four operations measurement quantities to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. using diagrams such as number line diagrams that feature a measurement scale. Apply Discuss, create and solve math problems that arise on holidays and special occasions: distance and time to a relative’s home, budgeting for a party or buying gifts, measurements for cooking traditional dishes C-4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Apply Jaime installs carpet and trim for a living. On his last job he laid 120 square feet of carpet. He remembers that the room was rectangular and was 10 ft. wide, but didn’t write down the length of the room. Tomorrow, he will install baseboard trim in the same room. How
Level C- Grade 4- Geometry 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. C-4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Draw Identify Points, Lines, Line Segments, Rays, Angles (Right, Acute, Obtuse), Perpendicular and Parallel Lines (Listed Above) (Singly and) In Figures In Figures Apply Understand In planning a walking tour through an historical district of town, there are 7 (or any number) points of interest the chamber of commerce would like to highlight. They would like to have two straight walks that would pass through all of the points. (Have a graphic with the points mapped on a grid or dot paper) How many different ways can these walks be made? Use mathematical vocabulary to label and describe your line segments.
Level C- Grade 5- Operations and Algebraic Thinking Grade 5- Number and Operations in Base Ten 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Number and Operations in Base Ten Understand the place value system. C-5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Recognize In a multi-digit number, a in one place represents 10 times as much as it represents in the place to its right and 1/10 For ones, tens and tenths places a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 Understand (See 4.NBT.1) Add dimes and pennies.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity C-5.NBT.4 Use place value understanding to round decimals to any place. Use Place value understanding To round decimals Apply Purchasing list of items at grocery to nearest dime, dollar, ten dollars or hundreds dollar. Which type of rounding (to what place) is most useful when buying groceries, running a race?, pumping gas? Perform operations with multi-digit whole numbers and with decimals to hundredths. C-5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply Muti-digit whole numbers Using the standard algorithm Apply Rounding grocery ads to whole number amounts, calculate numbers of bags or boxes of snacks and packages of drinks needed for a class party. What is the cost for these items?
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity C-5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find Illustrate Explain Quotients Calculations Calculations Whole numbers 4 digit dividends 2 digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division By using equations, rectangular arrays And/or area models Apply Analyze Analyze Clark County Extension Service has 1560 seedling trees to distribute for Arbor day. The trees will be divided between 15 sites. How many seedlings will each site have to distribute? Have students create situations and problems where division comes into play. Dividing snacks among backpacks, dividing a tax return among family members, etc. Solve student-created problems in small groups or with a partner. Discuss strategies used and also how estimation and rounding can help with these calculations. C-5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Add, Subtract Multiply Divide Relate Explain Decimals to hundredths place Strategy Reasonings Using concrete models or drawings and strategies To a written method Apply Evaluating Build a room, design and plant a garden or landscaped area, buy groceries for a family or special event and divide the cost, etc. Remember that money is something our students usually understand well, use this pre-knowledge to enhance their skills with decimals.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity C-5.NF.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Solve Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions , e.g., by using visual fraction models and equations to represent the problem. Apply Papa John’s delivered 14 pizzas to the adult education class. Each student gets to eat 2/3 of a pizza. How many adults are in the class? 14 ÷ 2/3 = 21 Level C- Grade 5- Measurement and Data 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Measurement and Data Convert like measurement units within a given measurement system.
C-5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Convert among standard measurement units within a given measurement system and use these conversions in solving real world problems. Understand Apply Jonah needs 17 ounces of frozen peas, 1½ pounds of salad shrimp and 8 ounces of mayonnaise for a shrimp salad recipe. Peas are sold in ½ pound packages for $1.29, salad shrimp is .45 an ounce and 8 oz. of mayonnaise is $1.30. Other ingredients total $2 and weigh about 3 ounces. What is the cost of Jonah’s salad? Jonah has a plastic salad bowl he wants to use that will hold 3 lbs. of salad. Can he use this bowl to serve the salad? 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Represent and interpret data.
C-5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Recognize Understand volume as an attribute concepts of volume measurement. of solid figures Remember Understand Design a cereal box with 3 different sizes: regular size and mini-size. Calculate volume, and label dimensions. Which box do you think would be the best seller in your local market and why? C-5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Measure volumes By counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Evaluate Jorge wants to mail some treats to his aunt. He has two boxes (can give dimensions or give two sample boxes). Which box will hold the most treats? C-5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Relate Volume to the operations of and addition Analyze The Jaynes family is moving. They have a U-Haul truck as shown. (Show a diagram with a picture of a rectangular prism with one layer of boxes-either on the floor of the bed, or filling the front end of the container.) Assuming that the rest of their boxes are the same size and noting the boxes they have already loaded, how many boxes will fill the truck?
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity C-5.MD.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. Solve solve real world and mathematical problems involving volume Apply Cubic Corporation makes tiny paperweights that are 1” square (you can make paper boxes using nets). They are trying to decide the best value box for shipping the paperweights. Using the paper cubes, determine the volume of your group’s box. (Have the boxes cost different amounts, so we are looking for the highest volume/dollar ratio). Some students will intuit measuring the lengths of the sides of the boxes with the cubes. C-5.MD.5b Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems. Apply Formulas V = L x W x H and V = B x H for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths In the context of solving real world and math problems Apply Juan and Ming Lee are considering purchasing a swimming pool for their family. They are a little concerned about the cost of filling the pool, so they would like to know how much water the pool will hold. Find the volume of the swimming pool given the length, width and depth of the pool. Justin is storing feed for the winter feeding of his cattle. He has 500 cubic feet of food. Is his silo large enough to contain the food? Find the volume of at the silo given the diameter of the silo and the height of the silo.
Skills Included in Standard Concepts Included in Standard Through a Particular Context Levels of Thinking D-6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Use Ratio and rate reasoning To solve real world problems Understand Apply Tom and Diane start to race. Tom took 4 seconds to run 6 yards. Diane ran 5 yards in 3 seconds. If they continued to run at the same speeds, who would get to 30 yards first? Work with a partner and be prepared to explain how you figured it out. Who runs faster? How can you compare their speeds? D-6.RP.3a Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Make Find Plot Use Tables of equivalent ratios Missing values Pairs of values Tables With whole number measurements In tables On coordinate plane To compare ratios Apply Georgia has a family recipe for her salsa. When people ask for the recipe, she hands them a recipe card, but there is some information missing. She says she uses a combination of peppers and tomatoes to total 12 items in one of the following ratios: 3 peppers to 2 tomatoes 2 peppers to 3 tomatoes 3 peppers to 3 tomatoes 3 peppers to 4 tomatoes 1 pepper to 6 tomatoes Which is the correct ratio? How many peppers does she use? How many tomatoes? 1 2 3 4 5 6
Standards Skills Included in Standard Concepts Included in Standard Through a Particular Context Cognitive Demand/ Levels of Thinking Sample Activity D-6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve Unit rate problems Including pricing and constant speed Apply Ron needs to hire summer workers for his landscaping company. Megan can mow 7 lawns in 4 hours. In a 35 hour work week, how many lawns can Megan mow? At what rate (lawns/hour) does Megan mow lawns? If Paige can mow `8 lawns in 5 hours, who has a faster rate, Megan or Paige? D-6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Find Solve Percent of a quantity Problems As a rate per 100 Finding the whole, given a part and percent Apply Given the amount and percent of taxes added to your utility bill, find the total bill. D-6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Use Manipulate Transform Ratio reasoning Units appropriately To convert measurement units When multiplying or dividing quantities Apply Create a scale model of the classroom or a historic landmark, discuss how different scale measures yield different models.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. C-6.EE.1 Write and evaluate numerical expressions involving exponents. Write Evaluate numerical expressions numerical expressions involving whole-number exponents. Involving whole-number exponents. Remember Apply Calculate areas of square rooms for flooring and calculate volumes of cube-shaped rooms for installing air conditioning, dehumidifying or humidifying units. Show that exponents are a way of writing repeated multiplication. C-6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. Write Read Evaluate Expressions Expressions Expressions In Which Letters Stand for Numbers In Which Letters Stand for Numbers In Which Letters Stand for Numbers Apply Understand Evaluate Play, “I Have, Who Has” match items showing expressions in words and mathematical notation. Play matching games where expressions are matched with words. Practicing reading expressions out loud and explaining their meaning, for example explain why “5 less than y” is y-5, rather than 5-y. As student ticket to the skating show is $5 less than an adult ticket (t). Write an expression that could be used to determine the price of a student ticket. If the student ticket is $8, how much is an adult ticket? 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity C-6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Write expressions that record operations with numbers and with letters standing for numbers. Understand Marvo the Magician performs his act at children‘s birthday parties. He asks partygoers to, “Choose a number. Add 3. Multiply by 2. Subtract 4. Divide by 2. Subtract the original number. Add 1. What number do you always end up with?” Why does this work? Can you create other “tricks” for Marvo?
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Reason about and solve one-variable equations and inequalities. C-6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Understand Use solving an equation or inequality substitution as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? To determine whether a given number in a specified set makes an equation or inequality true. Understand Apply The local bagel store sells a baker’s dozen of bagels for $6.49, while the grocery store down the street sells a bag of 6 bagels for $2.50. Which store is the cheaper place to buy bagels? Hint – make a table of values for each store, then create a line graph on the same axis to determine which line is not as steep. C-6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Use Write variables expressions to represent numbers when solving a real-world or mathematical problem Apply Apply It costs $10 for 4 friends to rent shoes at High Rollers Lanes. Write an expression you could use to find the cost of renting shoes for each person. The friends do not want to spend more than $25 total for snacks and drinks while they are bowling, but agree they should each spend an equal amount. Write an inequality that you could use to determine how much each person could spend on snacks.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity C-6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Apply Lisa is cooking muffins. The recipe calls for 7 cups of sugar. She has already put in 2 cups. How many more cups does she need to put in? At a restaurant, Mike and his 3 friends decided to divide the bill evenly. If each person paid $13, then what was the total bill? Jenny wants to buy an MP3 player that costs $30.98. How much change does she receive if she gives the cashier $40? Note: Encourage students to use algebraic equations, even though many can solve these and similar problems through calculation. Encourage them to “see” the algebra in the calculation. As they work through these simpler one-step problems, multi-step problems will be understood more easily.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity C-6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write Recognize Represent inequality of the form x > c or x < c inequalities of the form x > c or x < c solutions of such inequalities to represent a constraint or condition in a real-world or mathematical problem. have infinitely many solutions on number line diagrams. Analyze Sal bought 4 DVD’s at the store. The cost of the first 3 movies was $12, $14, and $18. The average price he paid for a movie was no more than $15. What was the most money he could have spent on the 4th movie? A school has the following membership on their sports teams: football – 52, baseball – 28, basketball – 30 and soccer – s. The average number of students on a team is 41. What is the minimum number of students that could play on the soccer team?
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Geometry Solve real-world and mathematical problems involving area, surface area, and volume. C-6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. find apply area of triangles, special quadrilaterals and polygons finding area by composing and decomposing composing and decomposing real-world and mathematical Analyze apply Using a floor or landscape plan, with shapes included in concepts, use composing and decomposing to determine amounts of flooring, ceiling material, sod, etc. Level C - Grade 6- Geometry
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-6.SP.5 Summarize numerical data sets in relation to their context such as by: Summarize Numerical Data Sets in relation to their contexts Understand For all 6.SP.5: Using student-generated data sets use an online tool to create and manipulate various displays, box plots, etc. What happens to the mean, median and mode where there are a large number of outliers? What is the difference if the outliers are lower or higher than the median? Some examples of data sets could be sports team statistics such as free throw shots attempted and those made. Work production data, number of cars produced in a certain time period. Utilities cost per month- is it more economical to go on a prepaid amount plan? Several sites have free trials, such as: and D-6.SP.5a Reporting the number of observations. Report the number of observations in a numerical data set Understand D-6.SP.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement in a numerical data set Apply
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-6.SP.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Give Describe quantitative measures of center and variability any overall pattern and any striking deviations from the pattern context in which the data were gathered context in which the data were gathered Understanding Apply D-6.SP.5d Relating the choice of measures of center and variability to the shape of the data distribution and context in which the data were gathered. Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered Analyze
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. D-7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Compute Unit rates Associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in units. Apply If Jaxon runs ½ mile in each 1/12 hour, how fast is he running? (unit rate). If Eve runs ¾ mile in each ½ hour who is the faster runner? By how much? D-7.RP.2 Recognize and represent proportional relationships between quantities. Recognize Represent Proportional Relationships Proportional Relationships between Quantities between Quantities Understand Apply If two quantities are in a proportional relationship, the rate of change remains constant (y=mx)-create T-tables for x and y scenarios that show a pattern-create number patterns and graph them. Reagan works for a company resizing photographs for posters and banners. The T-table shows the sizes that can be made from a 4 X 6 print. Plot the sizes on the graph using the width as the and the length as the y-coordinate. Photographs should remain proportional so that the people or scenes being photographed do not become distorted. Reagan’s T-table got half-eaten by her cat, Trixie. A customer needs to know how long a banner would be that has a width of 26 inches. Can Reagan tell from the graph? Can you? Level D- Grade 7- Ratios and Proportional Relationships world
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. D-7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Apply Extend previous understandings of addition and subtraction represent addition and subtraction to add and subtract rational numbers; on a horizontal or vertical number line diagram. Apply The elevator in Kat’s office building that she usually uses is out of order today. She hops into the freight elevator and notices as the doors are closing that there are no numbers on the buttons. She got on at floor 3 and counts the floors as she goes down-5. There is a lobby and 3 floors above the lobby and 3 floors of parking below. Kat wants to get out at the lobby. Is that where she is? If not, should she go up or down and how many floors to get to the lobby? D-7.NS.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. Describe opposite quantities combine to make 0. combine to make 0. Evaluate George deposited $25 into his checking account on Tuesday morning and wrote a check Tuesday afternoon for $25. If he had $37 in his account before he made the deposit, how much is in his account after he writes the check?
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-7.NS.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Understand show Interpret p + q as the number located a distance |q| from p, number and its opposite sums of rational numbers in the positive or negative direction depending on whether q is positive or negative. have a sum of 0 (are additive inverses). by describing contexts. Understand Apply Understand The morning temperature is -5 F. The temperature drops 2 degrees. Is it colder or warmer? What is the temperature now? The next day begins at -2F and a warming trend increases the temperature by 10°. What is the current temperature? D-7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Understand Show Apply subtraction of rational numbers distance between two rational numbers principle as adding the additive inverse, p – q = p + (–q). on the number line is the absolute value of their difference in real-world contexts Understand Apply Apply D-7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers. apply Properties of operations Strategies to add and subtract rational numbers Apply Be familiar with the following properties: a + 0 = a a – 0 = a a – a = 0 a + b = b + a
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Apply Extend multiplication and division Of fractions to fractions to multiply and divide rational numbers Apply Use banking deposits and withdrawals of equal amounts for multiplying/dividing rational numbers. For example: Doreen’s bank account is debited $50 a month to repay a loan. What is the total amount withdrawn in a year? D-7.NS.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing contexts. Understand Interpret that multiplication is extended from fractions to rational numbers products rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products by describing contexts Understand Sam has 18 meters of rope. He cuts off 1/5 of the rope to make a leash for his dog, Rupp. How much rope did he use for the leash? (18 ÷ 5 = 3.6 OR 1/5 x 18 = 3 3/5 or 1/5 x 18 = 18/5)
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Solve Compare Word problems Algebraic and arithmetic solutions Word problem context leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers Word problems Apply Use annual budgets to determine how much is spent a month, a quarter, or for 6 months. D-7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Solve Graph and Interpret the solution word problems Solution sets of inequalities Word problems of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers Inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Apply Using various pay amounts with bonuses/overtime and budgets (could be real or contrived) determine how many hours a wage earner would have to work to meet their budget. Tell whether the pay amounts and/or hours are feasible.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Geometry Draw, construct, and describe geometrical figures and describe the relationships between them. D-7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. solve compute reproduce problems lengths and areas scale drawing in a different scale scale drawings of geometric figures scale drawings of geometric figures scale drawings of geometric figures apply Use student-generated floor plans of their dream rooms to plan for wall coverings, windows, flooring, etc. Have students reproduce a partner’s dream room in a different scale. 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. D-7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Know Use Give Formulas Formulas for the Area and of a Circle an Informal Derivation for Area and Circumference of a Circle to Solve Problems of the relationship between the Circumference and Area of a Circle Understand Apply Analyze Engage students in discovery activities that point to the formulas. Have them measure the radii, diameters, circumferences and approximate areas of circles (place on grid, use paper tiles to cover, etc.), of circular items, cylinders, etc. Chart the results and discuss the patterns seen to informally derive formulas. D-7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Use Write Solve Facts about Angles Simple Equations for an Unknown Angle in a Figure Simple Equations for an Unknown Angle in a Figure in a Multi-Step Problem in a Multi-Step Problem in a Multi-Step Problem Apply Apply Apply Use similar triangles, parallel lines with a transversal and vertical angles to illustrate complementary and supplementary angles. Try a site like The National Library of Virtual Manipulatives to create and manipulate angles.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Solve Problems involving area, volume and surface area of and objects composed of triangles, quadrilaterals, polygons, cubes and right prisms Real-World and Mathematical Apply Use nets to create, measure and calculate surface areas and volumes. Grade 7- Statistics and Probability 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Statistics and Probability Use random sampling to draw inferences about a population. dimensional
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Find Understand Probability of compound events Using organized lists, tables, tree diagrams, simulation Knowing Give a sample situation and have students work to solve in their own way before knowing the “formula.” Have students report out and discuss their methods for example: Liana is making a movie and needs to cast some actors. There are 2 actors interested in playing the female lead role, and 10 actors interested in playing the male lead role. How many different ways can Liana cast the film? 7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Understand Probability of compound event In sample space for which it occurs Understand Flip coins and roll dice to model compound events 7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. Represent Identify Sample space outcomes For compound events using lists, tables, tree diagrams In real-world events Apply Analyze Roll dice and flip coins to develop frequency tables and calculate the probability of (e.g.) rolling an even number on the die and getting heads on the coin flip. 1 Standards 2 3 4 5 6 Sample Activity
Skills Included in Standard Concepts Included in Standard Through a Particular Context Cognitive Demand/ Levels of Thinking 7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Design and use Simulation To generate frequencies for compound events Creating For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
Level D- Grade 8- The Number System 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Use rational approximations of irrational numbers numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., Apply In art and architecture, there is a shape called The Golden Rectangle. A golden rectangle is one whose side lengths are in the , . What is an approximation of this ratio? Level D- Grade 8- Expressions and Equations 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Expressions and Equations
to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the population is more than 20 times larger. of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. than Rhode Island’s or How much larger in area Texas is than Missouri. D-8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per for seafloor spreading). Interpret scientific notation that has been generated by technology. Perform Use Choose Interpret operations with numbers expressed in scientific notation scientific notation units of appropriate size for measurements of very large or very small quantities (e.g., use scientific notation that has been generated by technology including problems where both decimal and scientific notation are used Apply Apply Apply Analyze The speed of sound is 343.2 meters per second. Since the 1950’s planes have been flying faster than sound. The speed of light is 299,792,458 meters per second. What is the difference in these speeds expressed in miles per hour? How fast does an average commercial airliner fly? What is the difference between its speed and that of sound/ light?
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Understand the connections between proportional relationships, lines, and linear equations. D-8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Graph Compare proportional relationship, two different proportional relationships represented in different ways interpreting the unit rate as the slope of the graph Analyze Analyze Show two travelers’ rate, both by car, plane, mule etc. illustrating one with an equation and one with a graph to see which one is faster.
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity Analyze and solve linear equations and pairs of simultaneous linear equations. D-8.EE.7 Solve linear equations in one variable. Solve linear equations in one variable in one variable Apply Problems concerning a grocery or other budget that determine how much can be spent after bills are paid. How much water is left in a jug after 3 children drink x amount, etc.? D-8.EE.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Give Show examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results in one variable with one solution, infinitely many solutions, or no solutions. by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results Understand Understand How many hours of HD video can your DVR store? How many hours of SD video?
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Apply Explore linear relationships, such as miles per gallon, miles per hour, cost for a group of tickets or items. D-8.EE.8 Analyze and solve pairs of simultaneous linear equations. Analyze and Solve pairs of simultaneous linear equations. (understood to be in the coordinate plane) (understood to be in the coordinate plane) Analyze For all of 8.EE.8 Compare cell phone plans to determine if one is a better deal, or if there is a point at which both plans cost the same amount per month. Compare salary and bonus situations for two different jobs. Which one will get the employee a better income? Is there a point at which they are the same? See Lessons 8 and 9 in EMPower’s Seeking Patterns, Building Rules: Algebraic Thinking 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-8.F5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Describe Sketch functional relationship between two quantities a graph by analyzing a graph From a verbal description Analyze Apply Show graphs of increasing, decreasing values, linear and non-linear and have learners write situations to match the graphs. Level D- Grade 8- Geometry
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two figures, describe a sequence that exhibits the similarity between them. Understand Describe That two similar figures are similar if the second can be obtained from the first A sequence that exhibits similarity between two figures Through a sequence of rotations, reflections, translations, and dilations Given two similar two-dimensional figures Understand Evaluate Using student selected figures, have groups create a sequence of rotations, reflections, translations and dilations (at least one of each) and then, switching coordinate planes, have student groups describe other groups’ series of these types of transformations (these could be landscaped areas, patios, decks, floor plans, shadows, etc).
1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity D-8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Apply The Pythagorean Theorem to determine unknown side lengths in right triangles In real-world and mathematical problems in two and three dimensions Apply Have students find a situation on school grounds (poles with guy wires, the building of a ramp, braces for fence posts, etc.) in which the Pythagorean Theorem can be applied to determine unknown side lengths in in two and three dimensions. Following this, have students solve mathematical problems in which this theorem can be applied to find the unknown side lengths in the figures above. D-8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Apply The Pythagorean Theorem to find the distance between two points In a coordinate system Apply Vicki is laying a tile floor with square tiles at The Pythagorean Art Gallery.(show aerial view of floor with squares). She has been told that when she replaces the display cases they must be at least 8 ft. apart. If she placed cases A and B as shown (show two points on the floor on a diagonal from each other) are they far enough apart? How far away from each other are the two objects? Or use a map as a coordinate system to show the distance when a short cut is taken diagonally across a square or rectangle.
Level D- Grade 8- Statistics and Probability 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Levels of Thinking 6 Sample Activity Statistics and Probability Investigate patterns of association in bivariate data. D-8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Construct Interpret Describe Scatter Plots for Bivariate Measurement Data to Investigate Patterns of Association Scatter Plots for Bivariate Measurement Data to Investigate Patterns of Association Patterns such as Clustering, Outliers, Positive or Negative Association, Linear Association and Nonlinear Association between Two Quantities between Two Quantities Scatter Plots for Bivariate Measurement Data Create Analyze Analyze Use Excel or graphing calculators to create scatter plots or use the National Library of Virtual Manipulatives. As you vary the data, what happens? Use classroom collected data, such as number of books read in a month, number of pairs of shoes, etc. Does this vary by gender, for example? 1 Standards 2 Skills Included in Standard 3 Concepts Included in Standard 4 Through a Particular Context 5 Cognitive Demand/ Levels of Thinking 6 Sample Activity