BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals BIG IDEA 1:

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1 BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals Multiplying and Dividing Decimals Explain the difference between an exact answer and an estimated answer to a problem? Give an example. How does front-end estimation differ from the clustering method of estimation? When factors have decimals, where in the product is the decimal placed? How would you determine the reasonableness of an estimated answer? Convince your classmate. Write a rule for multiplying and dividing decimals numbers. Have a classmate test your rule. What is the relationship between a quotient, divisor and a dividend? Do your classmates agree? How would you determine which operation; division or multiplication is needed to solve a problem? What approach would you use when choosing the correct graphic representation of a multiplication or division problem involving decimals? Invent a real world problem involving multiplication or division of a decimal number. Does it make sense? MA.6.A.1.1, GR MA.6.A.1.3 MA. 6.A.1.2 BIG IDEA 1: Develop an understanding of and fluency with multiplication and division of fractions and decimals Multiplying and Dividing Fractions Compare and contrast the process of repeated addition and multiplication? What prediction can you make about the product of reciprocals? Does this prediction always hold true? Using a model, show how to multiply or divide a fraction by a fraction, whole and mixed number? How would you write a whole number as an improper fraction? How is multiplying by an improper fraction similar to multiplying by a mixed number? Give an example of a fraction and a whole number whose product is a fraction, whole or mixed number. Explain the steps involved in multiplying two mixed numbers or two improper fractions. How would you use the GCF to determine if a fraction is simplified? Can you think of a counter example? Show how you would use the distributive property when multiplying a whole number with a mixed number. How do you find the reciprocal of a mixed number? When you rewrite division as multiplication, for which number do you find the reciprocal? MA.6.A.1.1 MA.6.A.1.3 MA.6.A.1.2

2 BIG IDEA 2: Connect ratio and rates to multiplication and division Ratio and Rates What is a ratio? Describe three ways in which a ratio can be written. Give an example of each. What distinctions can you make between a ratio and a proportions How could you use equivalent ratios to solve proportions? How would you use multiplication or division to find equivalent ratios? Invent your own real world problem that can be solved using ratios How would you compare rates and ratios to solve real-world problems? Invent your own real-world problems that represent situations involving ratio and rate. Translate situations involving ratio and rate from real-world contexts to equations or expressions? When solving rate problems, why do you think finding the unit rate first is important? MA.6.A.2.1 MA.6.A.2.2, GR BIG IDEA 3: Linear Equations and Inequalities How would you describe a solution of an equation or an inequality? How are addition, subtraction, multiplication and division used to solve a one step equations and inequalities? Explain how you would solve a one or two step linear equation, inequality or formula? Write a rule for solving a one or two step linear equation or inequality. Let your classmate check your rule? How would you translate a real word situation into a mathematical equation or inequality? Present your steps to your class, and see if they agree. How would you approach choosing a representative graph for a given equation or inequality? Invent your own real world problem situations in which division, multiplication, addition or subtraction could be used to find the solution. Let a classmate find the solution of your equation. Make any adjustments necessary. MA.6.A.3.2 MA.6.A.3.4, GR

3 BIG IDEA 3: Linear Functions How would you describe a function? How would you identify a table, graph, or equation that represents a linear function or other simple relations? How would you analyze a table or graph to identify or describe a rate of change? How would you graph an equation or inequality? What information would you use? How would you represent a linear function using ordered pairs and a graph? How would you determine if a given ordered pair is a solution for a particular function? How would you identify representations of the same relationship, including translating among graphs, equations, tables and words? MA.6.A.3.6 BIG IDEA 3: Expressions Make a list of words which describes addition, subtraction, multiplication and division. Can you think of a counter example, when one of your words would actually describe something else? How would you determine an equation from an expression? How do you evaluate each? Make up your own algebraic expression that describes a real world situation. Let a class mate solve it. How do you know when to use a variable when translating words into mathematical expressions? Based on what you know, how would you explain what to do when writing phrases as numerical expressions and algebraic expressions? What information would you use to support the view that an expression can be written using different phrases? How would you determine if a given value of the variable is a solution for the expression? How would you use tables to translate expressions? MA.6.A.3.1 MA.6.A.33 /GR

4 BIG IDEA 3: SI XTH GR AD E Properties How does the Commutative Property of Multiplication compare to the Community Property of Addition? What do you know about the Associative Property of Addition? Of Multiplication? When do you use the Distributive Property? Why do you think it is called the Distributive Property? Explain What do you know about the Identity Properties of Addition and Multiplication? What do you know about the Inverse Properties of Addition and Multiplication? MA.6.A.3.5 SUPPORT IDEA 4: Geometry and Measurement Circles and Polygons How would you use the value of π to determine the approximate circumference and area of circles? How would you find the missing dimensions of composite two-dimensional, figures, given some of the dimensions, or the perimeter or area of the figure? How would you find the perimeter and areas of composite two dimensional figures made from convex and concave polygons, circles and semicircles? How would you find the area of a composite two dimensional figure? Describe how you would use formulas to determine a dimension of a plane figure or right prism, given its area or volume and the remaining dimensions? How would you establish the area of a plane figure or the volume of a right prism, given the dimensions? MA.6.G4.1 MA.6.G.4.2 MA.6.G.43 MA.6.A.3.4, GR

5 Equivalent Forms of Fractions, Decimals, and Percents SUPPORTING IDEA 5: Number and Operations Invent real world situations to represent the same number as a decimal, fraction, and a mixed number? How would you convert a decimal to fraction, a fraction to a decimal, or a mixed number to a decimal? Invent your own examples, using real world situations? Use a number line to order a group of fractions and decimal from least to greatest? Summarize your steps. How would you describe the relationship between a percent and the number 100? Use a 10 X 10 square grid to support your answer. Is that always true? Can you think of a counter example? Write a rule for converting percents to decimals and fractions. Does your rule always work? Can you use your rule to convert a decimal or fraction to a percent? Explain and adapt your rule if necessary. How would you find the missing value in a percent problem? Based on what you know about estimation, how would you use estimation to judge the reasonableness of the result(s) of computations with fractions, decimals and percents? MA.6.A.51 MA.6.A.52 MA.6.A.53, GR Measures of Central Tendency and Variability SUPPORTING IDEA 6 Data Analysis What approach would you use to find the mean, median, mode, and range of a group of numbers? Does this approach always work? Can you think of a counter example? Explain What is your opinion about the many different ways data can be presented (table, line plot, bar graph, double bar graph, or line graph)? Use data you have gathered and choose how it will be presented find the mean, median, mode, and range of your data. How would you identity which question can be answered given measures of central tendency or variability? How would you use real world data to make valid conclusions given measures of central tendency or variability? How would you find the missing data point in a set of data given the mean, median, or mode? MA.6.S.6.1, GR MA.6.S.6.2

TenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7

TenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7 EngageNY Module 1: Ratios and Proportional Relationships Topic A: Proportional Relationships Lesson 1 Lesson 2 Lesson 3 Understand equivalent ratios, rate, and unit rate related to a Understand proportional