6th Grade - Gateway 1

The materials reviewed for EdGems Math (2024) Grade 6 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Within the materials, print-based and digital assessments are included. Each unit has the following assessment types: Assessments that are available in two forms (A and B), Tiered Assessments available in two forms (AT and BT), Online Assessments available in two forms (A and B), and a Performance Assessment. 

Examples of grade-level assessments include: 

• Unit 2, Tiered Assessments, Form AT, Problem 8, “Amber walked 4 miles in 2 hours. At this rate, how far will she walk in 6 hours?” (6.RP.2 and 6.RP.3b) 

• Unit 7, Online Assessment, Form A, Problem 1, “Which pairs of numbers are opposites? Select all that apply. A) −10 and 10 B) 0 and 1 C) 10 and 100 D) −7 and 7 E) 50 and −0.50 F) \frac{3}{4} and \frac{4}{3}" (6.NS.5) 

• Unit 10, Assessments, Form A, Problem 12, “Kinsey delivers pizzas. His first six orders of the day cost: $26, $23, $12, $25, $24, $26. a. Find each measure of center. Mean =___ Median = ___ Mode = ___ b. Which measure of center best represents the data? Explain your reasoning.” (6.SP.3 and 6.SP.5)

There are above grade-level assessment items that could be modified or omitted without impacting the underlying structure of the materials. Examples include, but are not limited to:

• Unit 3, Assessments, Form A, Problem 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?” (6.RP.3c) (7.RP.3)

• Unit 8, Online Assessment, Form A, Problem 6, “Which of the graphs below show the equation y=2x+3?” Students are given the graphs of four lines on the coordinate plane. (6.EE.9) (8.F.1,3)

The materials reviewed for EdGems Math (2024) Grade 6 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each unit has a Storyboard that includes a Launch and a Finale. These tasks incorporate real-world applications and provide opportunities for students to apply unit concepts. Explore! activities provide students with an opportunity to discover mathematical concepts in a variety of methods. Teacher Gems are teacher-led activities that engage students with the main concepts of the lesson. Student lesson tasks fall into four categories (Practice My Skills, Reason and Communicate, Apply to the World Around Me and Spiral Review) in which students engage in grade-level content.

Materials engage all students in extensive work with grade-level problems to meet the full intent of grade-level standards. Examples include:

• In Unit 1, Lessons 1.6 and 5.6, students engage in extensive work with grade-level problems to meet the full intent of 6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers (1-100) with a common factor as a multiple of a sum of two whole numbers with no common factor. In Lesson 1.6, Exit Card, Exercise 3, students find the greatest common factor of two numbers in a real-world situation: Gina wants to sell 49 chocolate chip cookies and 35 sugar cookies. She is going to sell them on plates with equal amounts on each plate. Each plate needs to hold the largest number of cookies, without mixing types of cookies. How many cookies should Gina put on each plate? In Leveled Practice T, Exercise 7, students list multiples for two numbers, identify the common multiples, and determine the smallest of the common multiples: Find the least common multiple (LCM) for the numbers 4 and 8. a. List the first five non-zero multiples for the number 4: ___, ___, ___, ___, ___ b. List the first five non-zero multiples for the number 8: ___, ___, ___, ___, ___ c. What are the common multiples in your lists for the numbers 4 and 8? ___ and ___ d. Which of the numbers in part c is the smallest? This is the LCM of 4 and 8. ___.” In Lesson 5.6, Student Lesson, Exercise 10, students use the distributive property to rewrite an expression with a common factor: “Factor each expression using the greatest common factor. 10. 12 + 20.”

• In Unit 2, Lessons 2.2 and 2.3, students engage in extensive work with grade-level problems to meet the full intent of 6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems. In Lesson 2.2, Explore, Step 1, students complete a ratio table with missing values to form equivalent ratios: Terrance plays basketball for his middle school. His coach told him that his free throw ratio of shots made to shots missed is 5:3. Step 1: Ratio tables can be used to show equivalent ratios. Complete the table below to show equivalent ratios for Terrance’s free throw ratio.” A table is provided with values of 5, 15, and 20 for shots made and 3, 6, and 15 for shots missed. In Lesson 2.3, Explore, Step 5, students complete a double number line to show equivalent ratios: “A rate is a comparison of two numbers with different units. Below are ten rates for raffle tickets purchased during different fundraisers throughout the school year.” [Ticket rates are the following: $8.00/4 tickets, $10.00/2 tickets, $16.00/tickets, $25.00/5 tickets, $24.00/4 tickets, $12.00/4 tickets, $12.00/6 tickets, $6.00/1 ticket, $9.00/3 tickets, $24.00/3 tickets]. “A double number line can be used to show equivalent rates. Mika decided to buy the raffle tickets that were sold at the rate of $24 for 3 tickets. Complete a double number line to show the costs for different numbers of tickets.” An image of a double number line is given with labels of "$$$” and “Tickets,” with the values of 1, 3, and 8 for tickets completed and the corresponding value of 24 above the 3; the remaining boxes are blank. In the Student Lesson, Exercise 7, students create a double number line of equivalent ratios from a given rate. It states, “José spent $36 for 4 movie tickets. Create a double number line showing the prices for 1 to 5 tickets.” 

• In Unit 5, Lessons 5.3 and 5.4, students engage in extensive work with grade-level problems to meet the full intent of 6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers. In Lesson 5.3, Student Lesson, Exercise 14, students use variables to write an expression to represent a real-life situation: ”Francine’s Fruit Stand sells apples for $1.50 per pound and kiwis for $2 per pound. Write an expression to show the total cost for x pounds of apples plus y pounds of kiwis.” In Teacher Gems, Task Rotation, Rotation 4, students write and evaluate an algebraic expression to represent a real-life situation. It states, “Maison is putting together bouquets of flowers for the parent volunteers. The roses are $3.49 each and the peonies $1.89 each. There are 5 parent volunteers. Write two different variable expressions to represent how much Maison will spend to make each parent volunteer the same bouquet with r roses and p peonies.” In Lesson 5.4, Explore, students use variables to write expressions to represent a real-life situation. It states, “Step 1: The local zoo has different prices for entrance into the zoo. They charge $10 for adults and $6.50 for children. If a family has 𝑎 adults and 𝑐 children, what expression could the zoo use to calculate the total cost for a family to enter the zoo? Step 2: How could you use your expression in Step 1 to determine the cost for an extended family with 5 adults and 8 children to enter the zoo? What is the cost for this extended family? Step 3: For another family, 𝑎 = 2 and 𝑐 = 3. What is their cost to enter the zoo? Step 4: The train at the zoo charges the same rate for all ages. The zoo wants to create a display to show the cost of the train depending on the size of your group. For r riders, the train would cost 2.75r. Fill in the table below to help the zoo create their display.” A table is given with the title “Train Ride Sample Costs”. The left column heading is r, with the values 1,2,3,5. The right column is blank with the heading “Cost of Group with r riders (2.75r)”.

• In Unit 10, Lesson 10.1, students engage in extensive work with grade-level problems to meet the full intent of 6.SP.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. In Student Lesson, Exercise 5, students use responses to survey questions and explain why the survey results are not reliable: “Eliza writes for the school newspaper. She surveyed a group of her friends using the questions at the right. She called them late the night before her article was due to the newspaper. Some of her friends did not answer the phone. She drew the following conclusions for her article: Math is the favorite class of students at Happy Rock Middle School. Students have an average of five A’s in their classes. Students typically stay up until about 11 pm. a. Who did Eliza survey to get her data? How might this create bias? b. Why is the conclusion Eliza made from question #1 on her survey not reliable? c. Is Eliza’s data about the number of A’s that students are earning accurate? What bias might have been created when Eliza asked her friends this question? d. Eliza made her phone calls late at night. How could this have affected her survey results? e. If Eliza did her survey again, what recommendations would you give her to improve the accuracy of the results?” The survey questions given are as follows: “1. What is your favorite class? (choose one) _Science _Math _Music 2. In how many classes do you have an A? 3. How late do you stay up on school nights?” In Student Lesson, Exercise 8, students explain why one question would have more varied data than another question. It states, “Which statistical question will give data that is more varied? Explain. A. How many hours do students work per week? OR B. How many days do students work per week?”

The materials reviewed for EdGems Math (2024) Grade 6 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

When implemented as designed, the majority of the materials address the major clusters at least 65% of the time. Materials were considered from three perspectives; units, lessons, and instructional time (days).

• The approximate number of units devoted to major work of the grade is 7 out of 10, which is approximately 70%.

• The approximate number of lessons devoted to major work is 28.75 out of 48, which is approximately 60%.

• The approximate number of days devoted to instructional time, including assessments, of major work is 103 out of 159, which is approximately 65% of the time.

The instructional time (days) are considered the best representation of the materials because these represent the time students are engaged with major work, supporting work connected to major work, and include assessment of major work. Based on this analysis, approximately 65% of the instructional materials focus on the major work of the grade.

The materials reviewed for EdGems Math (2024) Grade 6 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Each unit contains a Unit Overview with information regarding standards correlation and how standards are connected in a unit. Specific examples are provided as well.

Materials connect supporting work to major work throughout the grade level, when appropriate, to enhance major grade-level work. Examples include:

• Unit 1, Lesson 1.2, Student Lesson, Exercise 14, connects the supporting work of 6.NS.3 (Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation) to the major work of 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems). Students multiply multi-digit decimals to solve a unit rate problem. An example is as follows, “Hakeem bought 4.2 pounds of almonds. They cost $2.45 per pound. How much did Hakeem pay for the almonds?”

• Unit 7, Lesson 7.5, Student Lesson, Exercise 12, connects the supporting work of 6.G.3 (Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.) to the major work of 6.NS.8 (Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate). Students plot points to form a polygon in the coordinate plane and find distances between the points. An example is as follows, “Uma went on a nature walk at a park with her family. The map of the park area was on a coordinate plane where each unit represented a meter. They started at their car, which was parked at (−30, −40). a. First they walked to a bird viewing station at (60, −40). How far did they walk? b. Next, they visited the duck pond at (60, 60). What is the total distance they have walked thus far? c. Finally, they went to the reptile center located at (−30, 60) and then back to their car. How far did they walk in all?”

• Unit 10, Lesson 10.3, Student Lesson, Exercise 7, connects the supporting work of 6.SP.4 (Display numerical data in plots on a number line, including dot plots, histograms, and box plots.) to the major work of 6.RP.3c (Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent.). Students find percentages of the number twenty and use the values to create a dot plot. An examples is as follows, “A police officer noted the following about the speed (in miles per hour) of twenty cars on a stretch of road on the interstate. Draw a dot plot that includes each description below. Half of the cars drove at least 65 mph. 20% of the cars drove over 70 mph. 30% of the cars drove 60 mph or slower. The most common speed traveled was 60 mph.”

The materials reviewed for EdGems Math (2024), Grade 6 meet expectations for including problems and activities that connect two or more clusters within a domain or two or more domains within a grade.

Each unit includes a Unit Overview with a section titled, Connecting Content Standards, which provides information about these connections as well as specific examples, where applicable.

Connections between supporting work and supporting work, as well as major work and major work, are made throughout the grade-level materials, when appropriate. Examples include:

• Unit 4, Lesson 4.4, Student Lesson, Exercise 14 connects the major work of 6.RP.A (Understand the concept of ratio and use ratio reasoning to solve problems) to the major work of 6.NS.A (Apply and extend previous understandings of multiplication and division to divide fractions by fractions). Students apply their understanding of rates to solve a real-world problem involving fraction division: “Chantal used liquid fertilizer for her garden. She used three tanks full of fertilizer. Each tank held three-fourths of a gallon. Her garden is 3\frac{1}{2} yards by 5 yards. How many gallons of fertilizer were used on each square yard?”

• Unit 6, Lesson 6.3, Student Lesson, Exercise 11 connects the major work of 6.NS.A (Apply and extend previous understandings of multiplication and division to divide fractions by fractions) to the major work of 6.EE.B (Reason about and solve one-variable equations and inequalities). Students explain their reasoning while solving a one-variable equation involving rational numbers: “Charissa claims that the division equation \frac{k}{5}=12 can also be written as a multiplication equation using the fraction: \frac{1}{5}k=12. Is she correct? Explain your reasoning.”

• Unit 9, Lesson 9.1, Student Lesson, Exercise 5 connects the supporting work of 6.NS.B (Compute fluently with multi-digit numbers and find common factors and multiples) to the supporting work of 6.G.A (Solve real-world and mathematical problems involving area, surface area, and volume). Students use decimal computation to calculate the base of a right triangle: “The height of a triangle is 12.2 centimeters. The area of the triangle is 48.8 square centimeters. What is the length of the base of the triangle?”

The materials reviewed for EdGems Math (2024) Grade 6 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

EdGems Math provides teachers with evidence that the content addressed within each unit is related to both previous and future learning. This information is first outlined in the Content Analysis section of the Unit Overview. The Unit Overview then provides a Learning Progressions table for each unit, illustrating the vertical alignment of the topics and standards present in the unit. This vertical progression of mathematical concepts and standards is further elaborated throughout each unit. Each unit includes a Readiness Check and Starter Choice Boards that focus on prerequisite skills. Each Readiness Check reviews three to five skills from a previous grade level, which represent prerequisite skills for the unit. The Unit Overview outlines the skills targeted within the Readiness Checks. Starter Choice Boards offer three options: "Storyboard," "Building Blocks," and "Blast from the Past." The Building Blocks warm-up focuses on a prerequisite skill that directly relates to the current lesson. The standards alignment for Building Blocks is provided in the Teacher Guide for each lesson. Finally, "Explore!" activities build upon students' prior knowledge and experiences to scaffold the discovery of grade-level concepts or skills. The Teacher Guide provides an overview of the activity, including connections to previous grades.

Materials identify content from future grades and relate it to grade-level work. Examples include:

• Unit 1, Planning and Assessment, Unit Overview, Readiness Check & Learning Progression, “In this unit, students will… Fluently divide with multi-digit numbers (6.NS.B.2), explore and develop fluency with the standard algorithm when computing with decimals (6.NS.B.3), and solve problems using GCF and LCM (6.NS.B.4),” connecting it to, “In the future, students will… Compute with integers and rational numbers (7.NS.A.1-3) and factor expressions using the GCF (6.EE.A.3, 7.EE.A.1).” Examples are given for each skill.

• “In this unit, students will… Convert between percents, fractions, and decimals (6.RP.A.3c), interpret finding the ‘percent of’ as multiplying a part by a whole (6.RP.A.3c), reason about parts out of 100 using various representations (6.RP.A.3c), and find the part when given the whole and the percent (6.RP.A.3c),” connecting it to, “In the future, students will… Recognize and calculate decimal forms of rational numbers (7.NS.A.2d), use proportions to solve multi-step percent problems (7.RP.A.3), and interpret and model exponential growth and decay (HS.F-IF.C.8, HS.F-LE.A.1).” Examples are given for each skill.

• Unit 6, Planning and Assessment, Unit Overview, Content Analysis, “In this unit, students will work with variables in an equation, experiencing situations in which the variable represents a specific number. In future years, students will work with increasingly more complex situations in which an equation may have no solution or many solutions.”

Materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples include:

• Unit 2, Lesson 2.1, Teacher Guide, Starter Choice Board Overview identifies prior grade-level skills with their standards: “Building Blocks: Simplify fractions (4.NF.A.1)” and “Blast from the Past: Compute with whole numbers in a real-world context (4.OA.A.3).” The Lesson Planning Guidance for Day 1 supports teachers in choosing the activity that best addresses the needs of their students: “In this lesson, the ‘Building Blocks’ task asks students to access background knowledge on creating equivalent (simplified) fractions. Use this activity if many of your students need support in recalling this skill. Consider using Expert Crayons to have students move around the room supporting each other. As an alternate option, choose the Starter Choice Board’s ‘Blast from the Past’ task to give students an opportunity to utilize problem-solving skills involving whole number operations.”

• Unit 4, Planning and Assessment, Unit Overview, Standards Correlation indicates that Lesson 4.1 connects to both 5.NF.B.4 and 5.NF.B.6. “The Focus Content Standards for this unit include current grade-level and prerequisite standards. Targeting standards 5.NF.B.4 and 5.NF.B.6 in the first lesson will lay the groundwork for the rest of the unit, as an understanding of fraction multiplication will be essential for students’ success as they explore fraction division concepts.”

• Unit 7, Planning and Assessment, Unit Overview, Content Analysis highlights prior grade-level skills, such as representing rational numbers on number lines and coordinate planes, as well as finding the area and perimeter of squares on the coordinate plane, aligned with standards 5.G.B.3 and 5.G.B.4. “In this unit, students will calculate the area and perimeter of squares and rectangles on the coordinate plane. They will also have opportunities to revisit the classification of quadrilaterals based on their properties from Grade 5.”