7th Grade - Gateway 1

The materials reviewed for CK-12 Interactive Middle School Math 7 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 1 states, “There is a wall in your living room that is 13 feet wide. Your TV is centered on the wall. You want to hang up two pictures on either side of the TV. Each picture should be 4.25 feet away from the center of the TV.  a. Label where the center of the TV is on the number line above.  b. Write two expressions to calculate where each picture will go. Then label their positions on the number line.” (7.NS.1)

• In Chapter 3, Item 4 states, “Gary’s birthday is coming up! He wants to book the party room at his favorite restaurant. The restaurant requires him to spend a minimum of $200 in order to book the party room. Each person’s meal costs $12.50. He also plans to buy a cake from the restaurant for $45.  a. Using the minimum requirement, write an inequality to represent the total amount he will spend at the restaurant for p people.  b. Solve the inequality for p. Graph the solution on a number line.  c. What is the least number of people you can have at your party? Show your Reasoning. Hint: Remember that you can’t have a fraction of a person.” (7.EE.4b)

• In Chapter 4, Item 2 states, “At a restaurant, a burger is $10.99 and a drink is $2.00.  a. The tax rate is 8.5%. What is the cost of a burger and drink including tax? Round your answer to the nearest cent.  b. If you want to tip your waiter 20% of the total cost, including tax, how much should you tip? Round your answer to the nearest cent.” (7.RP.3)

• In Chapter 7, Item 2 states, “Jessie is playing a game where a red ball, a blue ball and a gold ball are each placed under a cup. Then the three cups are shuffled around. If Jessie correctly guesses which cup has a gold ball underneath it she wins the game.  a. If Jessie has no idea which cup the ball is under, what is the probability that she guesses correctly? Write your answer as a fraction in simplest form. If Jessie plays the game 12 times, how many times would you expect her to guess correctly?” (7.SP.6,7)

• In Chapter 8, Item 1a states, “A news reporter wants to estimate how many of the 900,000 registered voters in Rhode Island plan to vote for the candidate Fiona Rodriguez in the state senatorial race. The reporter goes to a mall in a major city and surveys 50 people. He finds that 35% of people plan to vote for Fiona Rodriguez. Why might this sample not be representative of the population?” (7.SP.1)

The materials reviewed for CK-12 Interactive Middle School Math 7 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: 

7.RP.A, Analyze proportional relationships and use them to solve real-world and mathematical problems.

• In Lesson 1.6, Activity 1, Question 2 states, “If c = 0.79s is the equation that represents the proportional relationship in the interactive, what is k?” (7.RP.A)

• In Lesson 4.2, Activity 2, Question 2 states, “Jake also has a monthly car note of $575. About what percent of his income is this?” (7.RP.3)

7.NS.1, Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. 

• In Lesson 2.3, the Warm Up states, “Think about the three cases of integer addition: when the addends (the two numbers that are being added) are both positive, both negative, or one of each. Discuss how you approach an addition problem differently in each of these cases and what sign the answer has.” (7.NS.1)

• In Lesson 2.6, Question 7 states, “Solve -4 + 5 - 7” (7.NS.1)

7.EE.B, Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

• In Lesson 3.10, Activity 2 states, “Are there any values of n such that n + 1 < n?” (7.EE.4b)

• In Lesson 6.7, Activity 1, Question 4 states, “If you are looking at a square pyramid that has a base length of x, a slant height of y, and the pyramid height of z, which of the following are true?  a)The area of the base is 4x.  b) The area of the base is x^2.  c) The area of a triangular face is 12xy.  d) The area of a triangular face is 12xz.” (7.EE.4a)

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

• In Lesson 4.2, students solve multiple word problems related to percentages. For example, in Activity 1, Question 1, students identify how percent is found, “Which of the following can be used to find 60% of 450 customers?  A. 450 - (45 + 45 + 45 + 45)  b. 225 + 45  c. 45 + 45 + 45 + 45 + 45 + 45  d. 225 - 45”. In Activity 3, Question 1, students use ratios and percentages to solve the problems, “Jake pays $1625 per month in rent. He makes $6735 per month. Which equations can be used to correctly calculate the percent of Jake's salary on rent each month?” (7.RP.3)

• In Lesson 7.10, students solve multiple problems involving probability. In Activity 2, Question 4, students reason about the likelihood of probability by frequency. The question states, “The outcomes are not equally likely because the likelihood of getting a hit is less than 0.5. About one-third (0.333) of the time, the batter will hit the ball, and two-thirds of the time, he will not. Using a die roll to simulate an at-bat, what will the numbers 1 through 6 represent?” (7.SP.7)

The materials reviewed for CK-12 Interactive Middle School Math 7 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 four out of eight, which is approximately 50%.

• The number of lessons devoted to major clusters of the grade (including supporting clusters connected to the major clusters) is 53 out of 80, which is approximately 66%.

• The number of days devoted to major clusters (including assessments and supporting clusters connected to the major clusters) is 58 out of 88, which is approximately 66%. 

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 66% of the instructional materials focus on major clusters of the grade.

The materials reviewed for CK-12 Interactive Middle School Math 7 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 7 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 1.9 connects 7.G.1 and 7.RP.A. Students work with scaled drawings and solve problems with the use of proportions. For example, in Activity 1, the Teacher’s Edition directions are, “Discuss with students why scale drawings are proportional relationships. Why are they included in this chapter?... Also we can write the scale factor into an equation of proportionality.” Also, in the Activity 2 Interactive, students use proportions to create a scaled drawing. The problem states, “Tiana wants to rearrange the furniture in her bedroom. She knows that it is 12 feet by 10 feet, with a door and window on the opposite wall. In her bedroom, she needs her bed, a desk, bookshelf, dresser, and chair. She is drawing a scale mapping on graph paper and decides to make 1 foot = 2 squares (0.50 inch). Use the interactive to rearrange her furniture.”

• Lesson 4.10 connects 7.G.1 and 7.RP.3. Students use proportional relationships to solve problems involving scale and percent. For example, in Activity 1, Inline Question 1 states, “Which methods correctly convert a scale factor of 45 to a percent?” In Activity 2, students scale an image, “A scale model of a car was built at 12.5% scale. If the width of the model car is 9.75 inches, what is the width of the real car?”

• Lesson 7.6 connects 7.RP.2 and 7.SP.7. Students find the probability of possible outcomes with objects that have constant proportions. For example, in Activity 1 Interactive, students use the proportions of a dart board to predict probability. The problem states, “Below is a very basic dartboard, without a bullseye. There are 20 sections on the dartboard, and you have an equal likelihood of hitting any of them. The numbers around the circle represent the point values for each section if you are keeping score. Find probabilities for different sets of numbers (numbers less than 8, multiples of 3, etc) by clicking on the sections. The fraction will adjust accordingly.”

• Lesson 8.10 connects 7.SP.2 and 7.RP. Students examine samples to make generalizations using ratio understanding. The Warm Up states, “You will be using sample proportions to estimate the population proportions. A sample proportion is the ratio of members in the sample with a certain attribute to the total number of members in the sample.”

The materials reviewed for CK-12 Interactive Middle School Math 7 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 2.3 connects 7.NS.A with 7.EE.B. For example, in Activity 3, Stock Market states, “A particular stock started at $11.15 at the beginning of the day. After 3 hours, it was up $0.67 and at the end of the day it was down $2.25. What was the value of the stock at the end of the day? Use the number line interactive below to help you find the answer.” Also, Inline question 5 states, “On Monday, a stock rose $.50. On Tuesday, it dropped $.15. On Wednesday, it dropped $.12. Thursday it rose $.42. Friday it fell $.07. What was the overall loss?”

• Lesson 3.4 connects 7.EE.A with 7.EE.B. Students rewrite expressions in different forms while using variables to represent numbers. For example, Activity 3 Interactive states, “Your math teacher, Miss Nomer, gives you an extra credit problem to figure out her age. Half of her age three years ago is equal to one-third of her age nine years from now. How old is she currently? All the pieces to figure out Miss Nomer's age are in the box below. Your job is to make two equivalent expressions from the clues above. Set them equal to each other so you can determine her age and get extra credit.”

• Lesson 4.3 connects 7.NS.A with 7.RP.A. Students use operations to solve real-world problems involving percentages. For example, Warm-up Inline Question 1 states, “The original value of a house is $300,000. The house is now worth $600,000. Which of the following statements are true?  a. The new price is 200% of the old price.  b. The new price is 2 times the old price.  c. The new price is 300% of the old price.  d The amount of increase was $300,000.”

• Lesson 4.6 connects 7.RP.A with 7.NS.A. Students interpret and calculate percent error and absolute error. In Activity 1, Inline Question 3 states, “Which of the following statements are true about the distance between -4 and 7?”  Review Question 5 states, “A student determines the volume of a cube to be 4.6cm^3. What is the percent error if the correct volume of the crystal is 4.3cm^3?”