Math in Focus Pacing Calendar 2013-2014 Course 1 (Grade 6)
August 15, 2013 Dear Math in Focus Users, We are excited to share our Math in Focus Pacing Guide calendars with you. Over the last several years of working with schools and districts to implement Math in Focus, we have received numerous requests for a pacing calendar to ensure that teachers focus on the major clusters of the Common Core State Standards. They are designed so that all the CCSS are thoroughly taught and that some Singapore material is left to the end of the year. These suggested calendars are intended as guides only and will have to be adjusted to your students needs and to the school schedules. They are primarily intended for the first couple of years of implementation after which it makes more sense to decide as a district on pacing suitable for your specific students. We welcome feedback and any other suggestions for improving the pacing of Math in Focus. Sincerely, Math in Focus Professional Services Andy Clark, Director of Math Partnerships Andy.Clark@hmhco.com Kelly Snyder, Director of Math in Focus Professional Development Kelly.Snyder@hmhco.com
From the Common Core State Standards: In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking. 1. Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates. 2. Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane. 3. Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities. 4. Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected. Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.
September 2013 Chapter 1 Positive Numbers and the Number Line: Chapter 1 is an important start to the grade 6 content. Be aware that students may need to spend time reviewing equivalent fractions, odd & even numbers and understanding of decimal place value. Students will work with number lines throughout the chapter; keep in mind the importance of students understanding that all rational numbers are a point on the number line. Students should also understand that whole numbers, fractions and decimals can be represented in multiple ways. Students may struggle with vertical number lines; try to make real world connections such as height and temperature. Chapter 2 Negative Numbers and the Number Line: This is a quick chapter! Students will continue to have experiences with number lines. A big idea for students is that negative numbers are the opposite of positive numbers. Students should understand the meaning of integers and compare integers. Students will also develop a secure understanding of absolute value and apply it to real world problem solving. Pay special attention to the sign which indicates directionality on the number line as well as an operation. *You may want to continue to practice fact fluency and operations with whole numbers for 5 minutes 3x a week 1 2 Labor 3 4 Chapter 5 6 7 Day 1 Positive Numbers and the Number Line 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Chapter 2 Negative Numbers & the Number Line 27 28 29 30
October 2013 Chapter 3 Multiplying and Dividing Fractions and Decimals: Chapter 3 is a very important chapter as students are completing their understanding of fractions and decimals and it is a CCSS big idea for grade 6. Students will be expected to use fractions and decimals throughout the grade 6 curriculum so extra days have been added to allow more time for students master the content in chapter 3. Use visual models and hands on activities to help build conceptual understanding. The progression moves students from considering whole numbers divided by proper fractions to larger fractions divided by fractions, and finally smaller fractions divided by larger fractions. Students look for a pattern as they find the solution to 1 a/b. *Fact Fluency and operations with whole numbers 5 minutes 3x a week 1 2 3 4 5 6 7 8 9 Chapter 3 Multiplying and Dividing Fractions and Decimals 10 11 12 13 14 Columbus Day 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
November 2013 Ratio and Rate are both critical chapters for grade 6. Additional days have been added; spend time here connecting ratio and rate to whole number multiplication and division. Also slow down and do the problem solving. Provide scaffolding for students who may have a more difficult time with some of the multi-step problems. Chapter 4 Ratio: Chapter 4 is a very important chapter for grade 6. The use of visual models is essential for the development of conceptual understanding. Students should be able to describe ratio relationships and their meaning. It is important to focus on part-to-part and part to whole ratio relationships. Students will also experience multi-step problem solving. If you need to go back, use grade 5, Chapter 7 for additional resources. You can use paper strips or cubes along with bar models to help students visualize ratio relationships. *Fact Fluency and operations with whole numbers 5 minutes 3x a week 1 2 3 4 5 6 7. 8 9 10 11 Chapter 4 Ratio 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Chapter 5 Rate 26 27 28 Thanksgiving 29 30
December 2013 Chapter 5 - Rate: Students should build on what they learned in Chapter 4, Ratio, to make connections between Ratio and Rate. In Chapter 5, students should understand that for a ratio a:b the unit rate is a/b. Additional days have been added to cover the deep problem solving in this chapter. You may need to briefly review converting measurements within systems. Be sure to point out how the visual model for unit rate connects to method 2 the formula often used. *Fact Fluency and operations with whole numbers 5 minutes 3x a week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
January 2014 Chapter 6 - Percent: This chapter continues to add depth of understanding of ratio and rate/unit rate. Students will explore percent of a number using multiple methods and visuals to support their understanding. Additional days have been added to allow time to problem solve. Spend most of the time on understanding percent, percent of a number and finding the whole given a part and the percent. Introduce students to percent of change, but understand you may not have time to spend as many days on this topic. Chapter 7 Algebraic Expressions: Chapter 7 is another very important chapter. Students will begin to build understanding that algebraic expressions can be used to describe situations. Use bar models and variables to represent unknown numbers and write algebraic expressions. Visuals can also be used to develop understanding of algebraic properties and how they can be used to produce equivalent algebraic expressions. 1 New Year s Day 2 Chapter 6 Percent 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 MLK Day 21 Chapter 7 Algebraic Expressions 22 23 24 25 26 27 28 29 30 31
February 2014 Chapter 7 Algebraic Expressions: Chapter 7 is also a CCSS major focus. Students will begin to build understanding that algebraic expressions can be used to describe situations. Use bar models and variables to represent unknown numbers and write algebraic expressions. Visuals can also be used to develop understanding of algebraic properties and how they can be used to produce equivalent algebraic expressions. Chapter 8 Equations and Inequalities: This is an important chapter! Students should have a very solid understanding of one-step equations and have the ability to write an equation to represent a real world situation. Days have been added to this chapter to allow for time to write, interpret, use and solve equations. Use models to help students make connections and form a visual representation. Spend time on inequalities after students have a solid understanding of algebraic expressions and equations. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Chapter 8 Equations and Inequalities 18 19 20 21 22 23 24 25 26 27 28
March 2014 Chapter 9 The Coordinate Plane: Students will graph points in all four quadrants. It is also important for students to solve problems involving the distance between two points on the coordinate plane. This is a great place to apply absolute value and make connections to geometry. 1 2 3 4 5 6 7 8 9 10 Chapter 9 Coordinate Plane 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Chapter 10 Area of Polygons
April 2014 Chapter 10 Area of Polygons: Extra days have been added into Chapter 10 to allow time to be sure that students have a strong understanding of area of triangles and how to find the base and height of all types of triangles. Students will use their understanding of the area of a triangle to calculate the area of other figures. Encourage students to make connections while exploring the formulas. It is important that students recognize how to decompose a shape and find the area of composite figures. Chapter 11 Circles: move to the end of the year as this is not a CCSS for gr. 6 Chapter 12 Surface Area and Volume of Solids: Focus on understanding volume and surface area and use cubes and nets to help visualize volume and surface area. Students will calculate volume using cubes and using the formula V=Bh. Give students time to explore some of the more complex problems. Provide scaffolding (graph paper, cubes, formulas, visuals) to help all students to access the problem solving. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Chapter 12 Surface Area and Volume of Solids 22 23 24 25 26 27 28 29 30
May 2014 Chapter 13 Introduction to Statistics: Begin to explore statistical variability. Discuss different types of statistical questions and the data produced. Summarize and collect data accurately and display data in line plots, dot plots and histograms. Spend time interpreting graphs and allow students time to share findings with the class or in pairs. Chapter 14 Measures of Central Tendency: As part of understanding statistical thinking students need to explore mean, median and mode to help summarize data. Slow down and discuss data, have students share their thinking. This is a great chapter to review numeracy skills. The focus in 6 th grade CCSS is on understanding the meaning o summary data as it relates to variability. Box and whiskers are mentioned ion CCSS, but will be examined fully in grade 7. 1 2 3 4 5 6 7 8 9 10 11 12 Chapter 13 Introduction to Statistics 13 14 15 16 17 18 19 20 21 22 Chapter 14 Measures of Central Tendency 23 24 25 26 27 28 29 30 31
June 2014 Add in Chapter 11 Circles, or go back to review the CCSS Big Ideas for Grade 6 Review Big Ideas from CCSS: In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking. 1 2 3 4 5 6 7 8 9 Review or Chapter Circles 10 11 12 13 14 1 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31