6th Grade - Gateway 1

The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for assessing grade-level content. Overall, assessments are aligned to grade-level standards, and the instructional materials do not assess content from future grades. Each chapter has an End of Chapter Assessment in both Word and PDF formats.

Examples of End of Chapter Assessment items aligned to grade-level standards include:

• In Chapter 2, Item 3 states, “A basketball player makes 84 out of 100 free throw attempts.  a. Find the percent of free throws that the player makes.  b. At this rate, how many free throw attempts should it take to make 210 free throws?” (6.RP.3c)

• In Chapter 6, Item 1 states, “Write and evaluate: the sum of four to the third power and 35.” (6.EE.1)

• In Chapter 6, Item 4 states, “Use the numbers 48 and 30 to answer the following questions:  a. What is the greatest common factor of the two numbers?  b. Use the GCF to write the sum in the form __( __ + __ ).” (6.NS.4)

• In Chapter 7, Item 3 states, “Toby is driving 50 mph on the highway. He wants to know the relationship between how far he drives and how long it takes.  a. What is the independent variable? What is the dependent variable? How do you know?  b. Write an equation to represent the relationship between the two variables. Let x represent the independent variable and let y represent the dependent variable.  c. Create a table and graph. How do the values in the table and graph relate to the equation?” (6.EE.9)

• In Chapter 10, Item 1a states, “You want to create a study about the diet of cats. Write a statistical question for your study. Explain why it is a statistical question.” (6.SP.1)

The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. All lessons contain a Warm-Up, two or more activities, Extension Activities, Inline Questions, and Review Questions that are at grade level. Inline Questions range in number, and lessons generally contain around 10, which are used throughout the lesson to check for understanding. Also, there are Supplemental Questions and Extension Activities. These questions and activities are only seen in the Teacher’s Edition. The Review Questions are mostly multiple choice, and there are approximately 10 per lesson. Examples include:

6.RP.A, Understand ratio concepts and use ratio reasoning to solve problems.

• In Lesson 2.2, Activity 3 states, “Students can make up their own kind of sharks with a given number of rows and series of teeth. They can draw pictures of their sharks and give them names. In a small group, students can find the unit rates of teeth per shark and order the sharks from the greatest number of teeth to the least number of teeth.” (6.RP.2)

• In Lesson 2.9, Activity 1, Question 2 states, “A percent is a rate per 100. How would you write 95% and 105% as rates per 100?” (6.RP.3c)

6.NS.C, Apply and extend previous understandings of numbers to the system of rational numbers.

• In Lesson 5.4, Question 4 states, “ Find the distance between -23 and 13.” (6.NS.6a)

• In Lesson 5.10, Activity 2, Question 4 states, “Look at the points (3, 5) and (3, -5). The points have the same x-value, but they are located in different quadrants. How can you find the distance between the two points?” (6.NS.8)

• In Lesson 8.3, the Warm Up states, “Which movement would take you farther left, a vertical movement of -2 or a vertical movement of +2?” (6.NS.7a)

6.EE.B, Reason about and solve one variable equations and inequalities.

• In Lesson 7.1, Activity 2 states, “What variable can we use to represent the distance from each planet to the Sun?” (6.EE.5)

• In Lesson 7.4, Activity 3 states, “If you have \frac{1}{4} of a variable on one side and you add three more fourths to that side of the balance beam, what operation can be used to represent this?” (6.EE.7)

• In Lesson 8.6, Question 6 states, “Write the solution set for the inequality. Include at least three values in your solution set. y ≥ 3” (6.EE.8)

The full intent of the standards can be found in the progression of the chapters and lessons, for example:

• In Lesson 4.4, students are multiplying decimals using the standard algorithm. Activity 2 states, “Rachel has a motorized mini bike with a fuel tank that holds 0.32 gallons. The cost of gas in her neighborhood is $2.859 per gallon. Use the interactive to see how much it costs to fill Rachel's mini bike with gas.” (6.NS.2)

• In Chapter 9, there are multiple lessons on finding the area of various shapes, 9.3 Area of Quadrilaterals, Lesson 9.4 Area of Triangles, and Lesson 9.5 Area of Polygons. (6.G.1)

The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

• The approximate number of chapters devoted to major clusters of the grade is eight out of ten, which is approximately 80%.

• The number of lessons devoted to major clusters of the grade (including assessments and supporting clusters connected to the major clusters) is 79 out of 96, which is approximately 82%.

• The number of days devoted to major clusters (including assessments and supporting clusters connected to the major clusters) is 87 out of 107, which is approximately 81%. 

A day-level analysis is most representative of the instructional materials, because this calculation includes assessment days that represent major clusters. As a result, approximately 81% of the instructional materials focus on major clusters of the grade.

The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major standards/clusters of the grade. Lessons in Grade 6 incorporate supporting standards in ways that support and/or maintain the focus on major work standards. Examples of the connections between supporting and major work include the following:

• Lesson 2.4 connects 6.RP.3 and 6.NS.3. Students divide whole numbers by decimals and use the rate to solve problems. For example, in Activity 3, students find and compare rates, “Usain Bolt also known as ‘Lightning Bolt’, is the fastest sprinter of all time. He ran 100 meters in 9.58 seconds, and he ran 200 meters in 19.19 seconds. Which race was his fastest speed?”

• Lesson 6.9 connects 6.NS.B and 6.EE.4. Students factor expressions by finding a common factor and using the distributive property. For example, in Activity 3, Inline Question 5 states, “Look at the expression 12x + 20. Select the equivalent expression. a) 4(3x + 5),  b) 6x + 10,  c) 2(6x + 10),  d) 3x + 5.”

• In Lesson 9.2, students find the area by composing triangles into rectangles (6.G.1) and identifying what the formula would be with letters representing numbers (6.EE.2). In Activity 3, Inline Question 1 states, “In general, for a tangram with side length s, what is the area of all the pieces? a) 2s, b) 4s, c) 8s, d) s^2”. 

• Lesson 9.3 connects 6.G.1 and 6.EE.2. Students use written formulas to find the areas of parallelograms or trapezoids. An example is , “Area of a parallelogram = base x height, where height is the line that forms a right angle between the bases.” 

• Lesson 9.10 connects 6.G.4 and 6.EE.2. Students find the surface area by evaluating expressions with a letter representing a number. For example, in Activity 2, Inline Question 4 states, “If a cube has a side length of s units, which expression could be used to represent the surface area? a) 6s^2, b) (s^2)^6  c) 6s, d) 4s^2.”

The materials reviewed for CK-12 Interactive Middle School Math 6 for CCSS 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:

• Lesson 6.6 connects 6.EE.A with 6.EE.B as students evaluate expressions and examine how variables can be used in place of numbers. For example, in Activity 1, Inline Question 4, students use a variable in an expression, “Instead of writing out the number of reflected images, replace this phrase with r. Which expression can you use to find the measure between the two mirrors when there are r reflections? a. 360+r, b. \frac{360}{r}, c. 2r, d. \frac{r}{360}.”

• Lesson 7.9 connects 6.RP.A with 6.EE.C. Students solve problems involving ratios and identify how the variables are related. For example, in the Activity 3 Interactive, students see the ratio of the toys to actual size and determine what is the independent and dependent variable. The Interactive states, “Use the interactive below and your knowledge of equivalent ratio equations to complete the interactive. Remember that the ratio of the height of toys to the height of the characters is 1:5.”

• Lesson 9.7 connects 6.G.A with 6.NS.B as students solve volume problems using decimal operations. For example, in Activity 3, Inline Question 2 states, “(Fill in the Blank) Recall that the volume of the sandbox is 37.5 cubic feet and one bag of sand that fills 0.5 cubic feet costs $4.50. It will cost the school ____________ to fill the entire sandbox.”

• Lesson 10.4 connects 6.SP.A with 6.SP.B. For example, in Activity 2, Inline Question 3 states, “Here is the test score data again (in ascending order): 77, 83, 83, 85, 87, 90, 93, 94, 99. The median of the test scores is 88.5, since the middle two values are 87 and 90, and the average of those two is 88.5. What is the mean of the whole set?” In Activity 3, Discussion Question 1 states, “How can you use measures of center to describe a data set?”

In the Grade 6 materials, there is not a connection between 6.NS.A and 6.EE.B. In Chapter 3, students multiply and divide fractions, but students do not solve equations with variables. For example, in Lesson 3.10, the Inline Questions for Activity 1 are: “1) If Anna has two bottles of polish and each holds 15 ml, how many total ml of polish does Anna have? 30 2) How can Anna find the total number of manicures she can give with all the nail polish she has? Anna can __ the total number of mL of nail polish by the fraction of a mL it took to give one manicure. Highlight the word that goes in the blank: Reciprocal, Multiply, Divide, Subtract 4) If Anna uses \frac{9}{10} ml for one manicure and she has 30 ml nail polish, how many manicures can she give? a. \frac{3}{10}b. 30 c. 27 d. \frac{100}{3} 4) If Anna uses \frac{4}{5} ml for one manicure and she has 60 ml nail polish, how many manicures can she give? a. 60 b. \frac{1}{75}c. 75 d. 48.”