6th Grade - Gateway 1

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for assessing grade-level content.

The materials are organized by the Domains and Clusters delineated by CCSS. Each Cluster has a Milestone Assessment, and all assessments include multiple choice and/or multiple select. The assessments are aligned to grade-level standards, and examples include:

• In Milestone Assessment 6.NS.C, Question 11, “Which number sentence is true? a) $$-16 > -13$$
; b) $$3< -3$$
; c) $$-(-7) > 9$$
; d) $$-18 < -14$$.”

• In Milestone Assessment 6.EE.A, Question 16, “$$b + b + b + b$$ and $$4b$$ are equivalent expressions because: 
a) they both have b as a variable; b) they both have four terms; c) they both produce the same value no matter what number $$b$$ represents
; d) they both equal 4 when $$b = 1$$.”

• In Milestone Assessment 6.SP.B, Question 3, “Histograms, dot plots and box plots can all be used to display data. Which statement is true? a) Histograms show the distribution and the actual values of the data set; b) Dot plots show the distribution and the actual values of the data set; c) Box plots show the distribution and the actual values of the data set; d) Not enough information.”

• In Milestone Assessment 6.RP.A, Question 1, “Which statement correctly describes the image of clouds and suns? Select all the apply. a) For every three clouds, there are two suns; b) For every six clouds, there are nine suns; c) For every three suns, there are two clouds; d) For every two clouds, there are one sun.”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Materials present opportunities for all students to meet the full intent of grade-level standards through extensive work with grade-level problems. Each lesson addresses one grade-level standard with all standards addressed over the course of the year. Lessons are three to four days long. There are opportunities within each lesson to practice the content of the standards including: Math Simulator, one to four questions; Practice Printable typically has six to ten questions;  Additional Practice has four to ten questions; Clicker Quizzes include six questions; and the teacher can assign a specific domain in Test Trainer Pro. Examples where the full intent is attended to include:

• In 6.RP.A.3 Clone Wars, students 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. For example, Practice Printable Question 2, “Frankie is looking to add fish to his tank. He has done some research and found that different fish require a certain amount of space to thrive. Fill in the missing information in the ratio tables and then plot the ordered pairs on the coordinate plane. (Be sure to clearly label which line represents which fish.)”

• In 6.NS.A.1 Mr. Mung’s Ice Cream, students solve real-world problems with division of fractions by fractions. For example, Practice Printable Question 2, “Create a story context for 6¼ ÷ 1¼. Draw a visual fraction model to show the quotient.” 

• In 6.EE.A.4 ...And a Tin of Rice, students identify when two expressions are equivalent. For example, Practice Printable Questions 1-4, “Decide whether each pair of equations are equivalent. Explain how you know. Question 3: “2x + 3y and 5xy.”

The Test Trainer Pro and Simulation Trainer are also designed to provide additional, grade-level work.

• In Test Trainer Pro, primarily used as a daily warm-up, teachers can assign a specific domain, but not standards. Teachers have access to the question bank in order to see what the questions are, but cannot edit them.

• In Simulation Trainer, the content matches the lesson, but students can provide any number as an answer, then watch the steps worked out (no words) in a solution video. They’re presented with the same question again and can put in the correct answer, then watch the same solution again. If they get it correct the first time, they also watch the solution video. The next questions are not novel, but the same situation with new numbers. If students miss one, it resets them to the beginning, no matter where they were in the assignment. It is possible that some students would never complete a Simulation Trainer.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 125 out of 183, which is approximately 68%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 26 out of 37 lessons, which is approximately 70%.

• The number of weeks devoted to major work (including assessments and supporting work connected to the major work) is 26 out of 36, which is approximately 72%. 

A day-level analysis is most representative of the materials because this represents the class time that is devoted to major work of the grade including reviews, domain intensives, and assessments. As a result, approximately 68% of the materials focus on major work of the grade.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of connections between supporting content and major work of the grade include:

• 6.NS.B.2 Which Way connects to 6.RP.3b as students divide multi-digit numbers to find unit rates. In the Practice Printable, Question 4, “Carlos and Doug went on a road trip. They recorded how far they traveled each day in a travel journal. If they drove for a total of 30 hours, what was their average speed?” The journal provides the data: Day 1, 450 miles; Day 2, 300 miles; Day 3, 350 miles, Day 4, 400 miles. Additionally, the Immersion & Data and Computation portions of the lesson require students to use ratio reasoning to determine which route is fastest. 

• 6.G.A.2 River Rescue connects to 6.NS.A as students divide fractions by fractions to solve volume problems. In the Practice Printable, Question 6, “A right rectangular prism has a volume of $$20\frac{1}{4}$$ cubic units. The width is $$1\frac{1}{2}$$ cubic units, and the height is $$4\frac{1}{2}$$ cubic units. What is the length?” 

• 6.NS.B.4 The Castle Guard connects to 6.EE.3 as students use the Greatest Common Factor to produce equivalent expressions. In the Practice Printable, Question 3, “For each sum or difference, factor out the GCF, and rewrite the sum or difference.”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Examples include:

• 6.RP.A.3a Clone Wars “connects 6.RP.A to 6.EE.C as students can use ratio reasoning as a means to analyze the graph of the relationship between independent and dependent variables.” In the Practice Printable, Question 2 shows two types of fish and the space required based on the number of fish. Question 3 states, “Using the tables and graph from Question 2 , write a few sentences comparing the ratios of the amount of space needed for each fish. How is this shown in the graph?”

• 6.SP.A.3 Periodontal Pockets connects 6.SP.A and 6.NS.B as students compute with multi-digit numbers to “calculate and analyze the mean and the mean absolute deviation of a data set.” In Practice Printable, Question 2 states, “Tyrell is looking for a new place to keep his sailboat. He loves to sail and is looking for a location that will provide great sailing conditions year round. Tyrell’s ideal wind speed for optimal sailing conditions is around 10 knots. Below is some data he has gathered to help him make his final decision. (provided: a table with two different rivers and the average wind speed for each month) a) What is the mean wind speed of each location? b) What is the median wind speed of each location? c) Calculate the MAD for each set of data.”

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for clearly identifying content from future grades and relating it to grade-level work and explicitly relating grade-level concepts to prior knowledge from earlier grades.

Examples of clearly identifying content from future grades and relating it to grade-level work include:

• 6.RP.A.1 For Every Day states “This activity connects 6.RP to 7.RP.A and 8.EE.B, as unit rate is the basis for work involving constant of proportionality and slope of linear equations.”

• The game “Ko’s Journey” addresses several standards across grade levels. The Grade 6 standards include 6.RP.A.3a-c; 6.NS.B.3; 6.NS.C.6 and 8; and 6.G.A.2, though some of these have only one question. The game also addresses the Grade 4 concept of using a protractor and Grade 5 concepts including fractions, coordinate plane, and converting measurement units. The game introduces the Grade 8 concept of slope, though students are given formulas and directed through each equation.

Examples of explicitly relating grade-level concepts to prior knowledge from earlier grades include:

• 6.EE.B.7 The Sign of Zero states, “This activity connects 6.EE to 5.NF as students write and solve real-world problems involving multiplication of fractions and mixed numbers.”

• 6.G.A.4 Build a Better Box states, “This activity connects 6.G.A to 5.G.B in that students will draw nets and apply area formulas using their knowledge of classifying two-dimensional figures.”