6th Grade - Gateway 1

The instructional materials reviewed for EdGems Math Grade 6 meet expectations for assessing grade-level content.

Each unit includes Form A and Form B Assessments as well as Tiered Assessments Form AT and Form BT, all of which include selected response and constructed response sections. Performance Tasks are also included with each unit. In addition, Gem Challenges are online, standards-based items for use after a standard has been addressed and are located after certain lessons. 

Examples of grade-level assessments include: 

• Lesson 2.5, Dividing Decimals, Online Gem Challenge 1, Problem 3: “Use the fact 9 x 324 = 2916.” “Find the exact product of 0.9 x 3.24.” (6.NS.3)
• Unit 3, Percents, Form B, Part II, Problem 10: “Gonzalez bought a new duffle bag that had a price tag of $28.00. He bought it in California which has an 8% sales tax. How much did Gonzalez pay for the duffle bag, including sales tax?”(6.RP.3c)
• Unit 5, Expressions, Form B, Part I, Problem 2: “Four friends went to dinner. The taxi ride to the restaurant cost $15. Each person ordered a hamburger for $6. Which of the following expressions would calculate the total cost of the outing? Circle all that apply. A. 4×6+15, B. 4(15+6), C. 15+6+6+6+6, D. 4+6+15, E. 4×6×15 ” (6.EE.3)
• Unit 7, Rational Numbers & the Coordinate Plane, Performance Task, Errand Run, “Lucy ran errands on Saturday. She wanted to create a map on a coordinate plane to illustrate the path she followed. She started at her home which was located at (2, −7). First, she went to the library to return some books. The library was located exactly 6 units north of her home on the map. She then went to the store to buy some milk. The store was located at (−5, −1). Before returning home, she went to the gas station to fill up her tank. The gas station was 6 units south of the store. Then she returned home.” Question 1. “Create a map for Lucy showing the path she traveled.” (6.NS.8) Question 2. “What shape best describes the shape that was formed by her path? Explain your answer.” (6.G.3) Question 3. “If each unit on the grid represents 0.5 miles, how many miles did she travel in all? Use words and/or numbers to show how you determined your answer.” (6.NS.8)
• Unit 6, One-Variable Equations, Form A, Part II, Problem 1: “Determine if the number given is the solution of the equation. y + 11 = 17; Is 6 the solution? Explain how you know.” (6.EE.5)

There are above grade-level assessment items that could be modified or omitted without impact on the underlying structure of the instructional materials. These items include:

• Unit 8, Form A, Part I, Problem 6: “Which of the graphs below show the equation ???? = 2x + 3?” Students find an equation in the form of y = mx + b from a line on a coordinate grid. (8.F.1,3)
• Unit 8, Form A, Part II, Problems 7 and 8: “Graph each equation. 7. y = 1 + 3x and 8. y = = 12 − 2x.” (8.F.1,3)
• Unit 3, Form A, Part II, Problems 12: “A scooter was originally priced $300. It went on sale for 20% off. It was still not selling so it was discounted an additional 20% off the sale price. Jules bought the scooter. How much did Jules pay for the scooter?” (7.RP.3)
• Unit 3, Tiered Assessment, Problem 10: “A purse costs $100. It went on sale for 40% off. Since it was still not selling, the store marked it down an additional 10% off the sale price. How much will the purse cost after the additional mark-down?” (7.RP.3)

The instructional materials reviewed for EdGems Math Grade 6 meet expectations for spending a majority of instructional time on major work of the grade. 

• The number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 10, which is 60%.
• The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 30.5 out of 49, which is approximately 62%.
• The approximate number of days devoted to major work (including assessments and supporting work connected to the major work) is 103 out of 150, which is approximately 69%. 

A day-level analysis is most representative of the instructional materials because this perspective includes all connections to major work and follows the recommended pacing suggestions for addressing major work. As a result, approximately 69% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for EdGems Math Grade 6 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards and clusters are connected to major standards and clusters of the grade, and lessons address supporting standards while maintaining focus on the major work of the grade. Examples of supporting work being used to support the focus and coherence of the major work of the grade include:

• Lesson 1.4 connects 6.NS.3 with 6.RP.3 as students divide decimals to compare unit rates. For example, “The Rodriguez family filled their car with gas while on vacation. They spent $45.60 and put 16 gallons in their car on Monday. On Friday, they spent $33.48 for 12 gallons of gas. On which day did they spend more per gallon? How much more?”
• Lesson 5.6 connects 6.NS.4 with 6.EE.3 as students find and use the greatest common factor or least common multiple to factor expressions. For example, “Factor each expression using the greatest common factor. a. 48 + 60  b. 6x − 9.”
• Lesson 9.1 connects 6.G.1 and 6.RP.3 as students find the area of rectangles and triangles and apply understanding of ratios to solve problems. For example, “Square A has side lengths of 8 inches. The ratio of Square A’s side lengths to Square B’s side lengths is 2:3. What is the area of Square B? Students must apply understanding of ratios to find the missing side length of Square B.”
• Lesson 9.2 connects 6.EE.2c and 6.G.1 as students substitute a value for a variable in order to determine the dimensions to find the area of a triangle. For example, “The base of a triangle is represented by 2y + 6 and the height represented by 2y + 3. When the value of y is 10, what is the area of the triangle?”

The instructional materials for EdGems Math Grade 6 meet expectations for being consistent with the progressions in the Standards. In general, the instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. In addition, the instructional materials give all students extensive work with grade-level problems.

Each Unit Overview describes how the work of the unit is connected to previous grade level work, for example:

• The introductory paragraph of the Unit 7 Overview, Rational Numbers and the Coordinate Plane, states, “In this unit, students will be introduced to the rational number system, which includes negative numbers. They will describe situations using positive and negative integers. They will find absolute values and compare rational numbers. Students will graph inequalities on a number line and write inequalities that model real world situations. Students will also be introduced to all four quadrants in the coordinate plane (as they have only graphed in the first quadrant previously). Vertices of quadrilaterals will be graphed on the coordinate plane. Students will use previous knowledge about different types of quadrilaterals to name figures on the coordinate plane and find the ordered pair for a missing vertex.”

Each Unit Overview includes Learning Progression, and each Learning Progression includes statements identifying what students have learned in earlier grades and what students will learn in future grades, for example:

Unit 1: Ratios and Rates, In earlier grades, students have…

• Interpreted a fraction as a division problem (5.NF.3)
• Multiplied fractions (5.NF.4-6)
• Converted measurements (4.MD.1)

In future grades, students will…

• Compute unit rates with ratios of fractions (7.RP.1)
• Recognize and represent proportional relationships (7.RP.2/8.EE.5)

In some units, the Unit Overview references connections to current, grade-level work that was addressed in prior units. Examples include:

• Unit 6, One-Variable Equations, the introductory paragraph includes, “Students will connect their understanding of percents from Unit 3 with the percent equation to find the whole when given the percent and a part.” 
• Unit 8, Two-Variable Equations, the introductory paragraph includes, “Connections will be made to ratios from Unit 1 and graphing ordered pairs in Unit 7.”

The instructional materials present opportunities for students to engage with grade-level problems within each Student Lesson, Explore activity, Student Gem (online activities to provide practice with the content), Online Practice & Gem Challenge (only in some lessons), Exit Card, and Performance Task. There are also additional worksheets in each lesson for Proficient Practice, Tiered Practice, and Challenge Practice. For example:

• In Lesson 7.5, students have multiple opportunities in the lesson to attend to each part of 6.NS.8. “Plot each set of points on a coordinate plane. Connect the points in the order given and connect the last point to the first point. Name the shape with all terms that apply (parallelogram, rectangle, rhombus, square and/or trapezoid). Exercise 6. (0, 4), (0, 0), (4, 0), and (4, 4).” Exercise 25. “Explain in words how to find the distance between (−4, 5) and (2, 5).”
• In Lesson 5.2, students, “Find the value of $$7 \times (8 - 5)^2 + 2$$.” During Tiered Practice, Problems 1 - 4, students “Number the operations in the order they should be performed:  _____ Grouping Symbols; _____ ; Addition & Subtraction _____; Multiplication & Division _____ Powers.” Proficient Practice, Problem 9, “Three friends go to the movies. Each ticket costs $7. They also buy popcorn for $6, candy for $4 and a drink for $2. The friends want to split the total cost evenly. Write a numerical expression to represent this situation and determine how much each friend owes.” Challenge Practice: “Insert the operations (×, ÷, +, -) in each box of the numerical expressions to make it equal to the stated amount.” Problem 8, “$$(10^2 \Box 2 \Box 1) \Box (3 \Box 4) = 7$$.” (6.EE.1)

The materials include two examples of off grade-level content that are not identified:

• In Lesson 3.4, Problem 20, students use proportional relationships to solve multistep ratio and percent problems (7.RP.3). “Elli wants a pair of jeans that were originally priced $44. They were marked down 25% and then an additional 10% of the sale price. How much do the jeans cost now?”
• In Lesson 8.3, students graph two-variable equations that are above grade level. In Exercise 17, “Graph the equation $$y = 2 + x^2$$” (8.F.3), and in Exercise 19, “Write the linear equation of a line that goes through the points (2, 5) and (4, 13).” (8.F.4)

Each unit includes a Parent Guide with Connecting Math Concepts, which includes, “Past math topics your child has learned that will be activated in this unit and Future math this unit prepares your child for.” For example, in Unit 4, Fraction Operations, Parent Guide, “Past math topics your child has learned that will be activated in this unit include finding and interpreting quotients of whole numbers less than 100 and multiplying fractions by whole numbers and fractions by fractions.” “Future math this unit prepares your child for includes applying and extending previous understandings of multiplication and division of fractions to multiply and divide rational numbers and solving equations with rational coefficients.”

Each Lesson Guide includes Teaching Tips, which often include connections from prior or future grades, for example:

• Lesson 1.2, Ratio Tables and Graphs, Teaching Tips section, “Students have graphed points in Grade 5 in the Common Core State Standards but they may need to review how to graph in the first Quadrant of the coordinate plane.” 
• Lesson 3.2, Percents, Decimals, and Fractions, Teaching Tips section, “In Grade 4 of the Common Core State Standards, students worked with decimal fractions to help them see the connections between the decimal name and the fraction. Use this knowledge to help students see decimals as a ratio compared to a power of ten, with the goal of having the denominator equal 100.”
• Lesson 7.4, The Coordinate Plane, connections to future grades are stated. “In Grade 6 Common Core State Standards, students are asked to find distances between points that have the same x-coordinate or the same y-coordinate. In Grade 8 standards, students find distances between points that do not fall on the same horizontal or vertical line using the Pythagorean Theorem.”

In each Lesson Guide, Warm Up includes problems noted with prior grade-level standards. For example:

• Lesson 3.1, Introducing Percents, Concepts and Procedure (4.NF.1), Question 27, Skill: Simplify each fraction.
• a. 25/100 
• b. 60/100
• c. 84/100
• d. 28/100
• e. 54/100
• f. 76/100
• Lesson 8.1, Input-Output Tables, Concepts and Procedure (3.OA.9), Question 26, Skill: Describe the operation used to calculate the next term in each list of numbers. Give the next two numbers in the list.
• a. 1, 4, 7, 10, _____, _____ 
• b. 40, 35, 30, 25, _____, _____
• c. 4-2/5 , 4, 3-3/5 , 3-1/5, ______, _____
• d. 2.4, 4, 5.6, 7.2, _____, _____
  

The instructional materials for EdGems Grade 6 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards.

Examples of learning objectives that are visibly shaped by CCSSM cluster headings include:

• The objective of Lesson 2.5, “I can find quotients of expressions involving decimals,” is shaped by 6.NS.B, Compute fluently with multi-digit numbers and find common factors and multiples.
• The objective of Lesson 4.3, “I can find quotients of expressions involving two fractions,” is shaped by 6.NS.A, Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• The objective of Lesson 9.5, “I can find the volume of rectangular prisms,” is shaped by 6.G.A, Solve real-world and mathematical problems involving area, surface area, and volume.

The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. Examples include:

• Lessons 5.3, 5.4, 5.5, and 5.6 connect 6.EE.A and 6.EE.B as students translate mathematical statements to write expressions using variables.
• Lesson 6.3 connects 6.EE.B with 6.NS.A as students write and solve equations using rational numbers requiring a fraction divided by a fraction. 
• Lesson 7.3 connects 6.NS.C and 6.EE.B as students write and graph inequalities.
• Lesson 7.5 connects 6.G.A with 6.NS.B as students use properties of quadrilaterals to find missing points in figures on a coordinate plane. For example, “Three of the four vertices of a square are at (4, 6), (2, 6) and (2, 4). What are the coordinates of the missing vertex?”
• Lesson 9.1 connects 6.G.A with 6.NS.B as students find the area of rectangles and triangles by multiplying multi-digit decimals.
• Lesson 10.7 connects 6.SP.B and 6.NS.B as students find absolute mean deviation involving decimal numbers.