7th Grade - Gateway 1

The materials reviewed for STEMscopes Math Grade 7 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The curriculum is divided into 18 Scopes, and each Scope contains a Standards-Based Assessment used to assess what students have learned throughout the Scope. Examples from Standards-Based Assessments include:

• Scope 2: Addition and Subtraction with Rational Numbers, Evaluate, Standards-Based Assessment, Question 1, “A person has $45.75 in his checking account. He used his debit card for a $105.80 purchase. Which equation represents the transaction? 45.75+105.80=151.55; -45.75+105.80=60.05; 45.75+(-105.80)=-60.05; -45.75+(-105.80)=151.55.” (7.NS.1)

• Scope 5: Proportional Relationships, Evaluate, Standards-Based Assessment, Question 3, “The graph shows the price paid for a gym membership after each month.” Students see the first quadrant of a coordinate plane with the label of Months on the x-axis and Price Paid on the y-axis. There is a line graphed in the quadrant and the y-intercept is at 20.” Is the relationship between the price paid and the months attended proportional? Explain your reasoning. Enter your answer below.” (7.RP.2a)

• Scope 9: Equations, Evaluate, Standards-Based Assessment, Question 10, “Given the equation 0.25y+4=160, solve for y. Enter your answer below.” (7.EE.3)

• Scope 12: Angle Relationships, Evaluate, Standards-Based Assessment, Question 8, “Two supplementary angles have the measures of 6x-4 and 8x+16. Part A Which equation represents these angles? 6x-4=8x+16, 6x-4=2(8x+16), 6x-4+8x+16=90. 6x-4+8x+16=180” (7.G.5)

• Scope 16: Informal Inferences, Evaluate, Standards-Based Assessment, Question 3, “The mean weight of linemen on football team A is 280 pounds, with a mean absolute deviation of 10 pounds. The mean weight of linemen on football team B is 300 pounds, with a mean absolute deviation of 10 pounds. By how many multiples of the mean absolute deviation is the mean weight of team B greater than team A? ____ multiples.” (7.SP.3)

The materials reviewed for STEMscopes Math Grade 7 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials provide extensive work in Grade 7 as students engage with all CCSSM standards within a consistent daily lesson structure, including Engage, Explore, Explain, Elaborate, and Evaluate. Intervention and Acceleration sections are also included in every lesson. Examples of extensive work to meet the full intent of standards include:

• Scope 2: Addition and Subtraction with Rational Numbers, engages students in extensive work to meet the full intent of 7.NS.A.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.) Explain, Show What You Know - Part 1: Addition of Integers with Counters, students add integers. “Three friends are playing a card game. Each player is dealt 7 cards. The player whose cards combine to equal zero is the winner of the game. Find the total of each player’s cards by using counters to determine who (if anyone) won the game. Amy’s Cards are -2, 3, -4, 8, -5, -4, and 3, total ___; John’s Cards are 6, -2, 7, -8, -2, 4, and -5, total ___...” Show What You Know - Part 2: Addition with Number Lines, students write an addition sentence and use a number line to model it. “Aaron is playing a football game. His team gained 11 yards on their first play. For the next play, they lost 19 yards. How many yards have they gained or lost for these two plays? Write an addition sentence to represent this situation, and also use the number line to model your addition sentence. Addition sentence ___ Model: ___.” A number line is provided for the model.

• Scope 4: Rational Number Operations, Explore 1-Convert Fractions to Decimals, Show What You Know-Part 1: Convert Fractions to Decimals, engages students in the full intent of 7.NS.2d (Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.) Students are given four fractions and utilize long division to change each fraction to a decimal, then determine if the decimal is terminating or repeating. “Bryce is using fraction measurements to cut pieces of wood. He has to report his information in decimal form and needs to have exact measurements that don’t repeat. Find the measurements he can use by converting the fraction to a decimal using division. Determine whether they are exact measurements based on whether they terminate or repeat. \frac{1}{6}, \frac{5}{8}, \frac{2}{3}, \frac{3}{4}”

• Scope 5, Proportional Relationships, Explain, Show What You Know - Part 1: Proportional vs. Non-Proportional, presents opportunities for all students to meet the full intent of grade-level standards, 7.RP.2 (Recognize and represent proportional relationships between quantities.)  Students determine if a given relationship is proportional or not. “Mr. Smith is ordering pencils for his classroom and finds the two offers below.Determine if each offer is a proportional or non-proportional relationship. Each pencil costs 0.25. A table with two columns with title ‘Number of pencils” and “Cost.’ First column with entry, 0, 4, 10, and 20; the second column, $0.00, $1.00, $2.50, and $5.00; Use the chart above to create a graph. Is the relationship proportional or non-proportional? List two pieces of information that helped you determine whether the situation is proportional or non-proportional.”

• Scope 10: Solve Equations and Inequalities, engages students in extensive work to meet the full intent of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.) Explain, Show What You Know - Part 1: Construct Equations, students construct an equation and solve it for a given word problem. “Stephen is 4 times as old as Gianna. William is 5 years older than Stephen. William is 17 years old. Let a represent Gianna’s age. Use the space provided to write an equation to find Giannas age.” Show What You Know - Part 3: Construct Inequalities, students construct inequalities for a given word problem. “Tess is ordering jeans for her upcoming ski trip. Each pair of jeans costs 15. It costs 5 for shipping and she has 55 to spend. Write an inequality and solve the inequality to find the number of pairs of jeans Tess can buy.”

• Scope 17: Probability, Explore, Explore 1 - Probability, Math Chat and Show What You Know - Part 1: Probability, engages students in extensive work to meet the full intent of 7.SP.5 (Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring…) In the Math Chat, students discuss what they have learned about the probability of events occurring. (Each DOK question has sample answers after it.) “DOK–1 What is the range of likelihood for different events? The range is 0–1. Zero means an event will never happen. 1 means an event will always happen. \frac{1}{2} means an event will happen half the time. DOK–2 What are the numerical values of probability associated with each category of likeliness? Explain. Impossible – 0 because it has no chance of happening, Unlikely – between 0 and \frac{1}{2} because it should happen less than half the time, Equally likely -\frac{1}{2} because it should happen half the time, Likely – between \frac{1}{2} and 1 because it should happen more than half the time, Certain – 1 because it will happen every single time. DOK–3 Scenarios including which likelihoods would probably create the best games? Why? I think unlikely, equally likely, and likely are the scenarios that would probably create the best games because even if the likelihood of something happening is known, what is expected does not always happen in individual cases. That makes it exciting, fun, and unpredictable. Impossible and certain would be boring because everyone would know the outcome before it happened.” In Show What You Know, Student Handout, students are given a table with four events. They are to complete the table, indicating the probability of each event and circle Likely or Unlikely. “Pearl and her sister are going to play a game to decide who has to wash the dishes after dinner tonight. Pearl wants to play a game she has a better chance of winning. Determine the probability of each event and decide if each of the situations below is likely or unlikely to happen so that Pearl can choose which game she would like to play. Spinning an odd number on a spinner labeled 1–5, Rolling a composite number on a 6-sided die, Picking a 2 from a deck of cards, Spinning a composite number on a spinner labeled 1–5.”

The materials reviewed for STEMscopes Math Grade 7 meet expectations that, when implemented as designed, the majority of the materials address the major cluster of each grade.

The instructional materials devote at least 65% of instructional time to the major clusters of the grade:

• The approximate number of scopes devoted to major work of the grade (including assessments and supporting work connected to the major work) is 11 out of 18, approximately 61%.

• The number of lesson days and review days devoted to major work of the grade (including supporting work connected to the major work) is 118 out of 155, approximately 76%.

• The number of instructional days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 131 out of 180, approximately 73%.

An instructional day analysis is most representative of the instructional materials because this comprises the total number of lesson days, all assessment days, and review days. As a result, approximately 73% of the instructional materials focus on the major work of the grade.

The materials reviewed for STEMscopes Math Grade 7 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. Examples of connections include:

• Scope 11: Scaling, Explain, Show What You Know–Part 1: Scale Drawings, connects the supporting work of 7.G.1 (Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.) to the major work of 7.NS.3 (Solve real world and mathematical problems involving the four operations with rational numbers (extend the rules for manipulating fractions to complex fractions). Students identify the scale factor that involves rational numbers. “Bart is having a garage sale and is making posters to hang up around town. Each space to hang the posters is a different size, so he will need to make enlargements and reductions of the original poster. Help him identify which dimensions can be used to create the posters by circling them and identifying the scale factor (SF) used.” A rectangle is shown titled, “Original Sign,” with dimensions of 12 in x 5 in. In the work space two signs with dimensions 18in\times7\frac{1}{2}in and 8 in x 1in are shown.”

• Scope 12: Angle Relationships, Explore, Explore 3–Multi-step Angle Problems, Exit Ticket, connects the supporting work of 7.G.5 (Use facts about supplementary, complementary, vertical and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure) to the major work of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.) Students use their knowledge of angles to find missing information, represented by a variable or an equation. Students see 5 angles and a table they are to complete with measurements for some of the angles. “An adjustment to the nature trail proposal is shown below. Use the provided measurements to calculate the missing information by applying your knowledge of complementary, supplementary, vertical, and adjacent angles. \angle A, 95\degree, \angle F, x^0, \angle D, (2x+5)^\degree, Angle, Measurement, Justification and Equation, \angle F, \angle D”

• Scope 17: Probability, Explore, Explore 3–Probability Models, Procedure and Facilitation Points, connects the supporting work of 7.SP.6 (Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability) to the major work of 7.NS.3 (Solve real-world and mathematical problems involving the four operations with rational numbers.) Students work in groups of 4 to find the experimental and theoretical probability as they conduct experiments, create a model, and find the probability. “1. Read the scenario to the students: Your group is finishing up its last week of training at Famfun, the company that creates and manufactures family games. Your job this week is to prove that you understand probability models. If your group does well at this task, next week you get to test and tweak current games set for production to make sure they are exciting, fun, and surprising, rather than boring and predictable. 2. Give the Student Journal to each student. 3. Give a set of Probability Cards, a spinner, and the brown bags with the 20 color counters to each group. 4. Explain to students that they will apply their understanding of theoretical probability and experimental probability to find the probability of events. They will also use probability models to compare and predict probabilities. 5. Inform students that they will model two of the events with their groups and will select a probability model that their group will choose to develop. (If students select the brown bag with color counters, they do not have to use all 20 color counters; they can choose the number of counters that they would like to use for their models.) When students develop their models, they will need to create a table that includes a frequency column and a column that shows the frequency written as a fraction…”

The materials for STEMscopes Math Grade 7 meet expectations that materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. 

Materials are coherent and consistent with the Standards. These connections are sometimes listed for teachers in one or more of the three sections of the materials: Engage, Explore and Explain. Examples of connections include:

• Scope 6: Ratios, Rates, and Percents, Explore, Explore 1–Unit Rates with Ratios of Fractions, Procedure and Facilitation Points, connects the major work of 7.NS (The Number System) with the major work of 7.RP (Ratios & Proportional Relationships). Students analyze proportional relationships and use them to solve real-world and mathematical problems. Students compute unit rates associated with ratios of fractions in like or different units.  “1. Read the following scenario: Travis is a production assistant on the reality competition show Ready, Set, Bake. In this week’s episode, the contestants will be making cupcakes. The baker with the most delicious cupcake will win this round. Each baker has requested very specific ingredients that Travis is responsible for supplying. Your job is to help Travis decipher each baker’s recipe to determine how much flour each baker will need for a batch of cupcakes. 2. Review fraction, rates, and ratios with students. a. DOK-2 How is a fraction similar to a ratio? How is it different? b. DOK-1 What is a unit rate? 3. Give a Student Journal to each student. Give a set of Recipe Cards to each group. 4. Explain to students that they will be working with their small groups to determine the amount of flour that each baker will need for one batch of cupcakes. Students will use the various prompts in their Student Journal in order to find ratios and unit rates. 5. Complete page one of the Student Journal as a class. Guide the students with the following questions: a. DOK-1 According to the Recipe Card, how much flour is Kiana requesting? b. DOK-1 How can this be written as a ratio? c. DOK-1 If Kiana doubles both values, what will the new values be? d. DOK-1 How can you write these new values as a ratio? 6. Guide students to continue the double number line by extending the pattern created in the first two sections of the Student Journal. Encourage students to continue the pattern until they find the number of cups of flour needed for one batch of cupcakes. Assist as needed. 7. Allow students to work cooperatively with their small group to complete the remainder of the Recipe Cards and Student Journal, including the reflection questions. 8. Monitor and assess student understanding as each group collaborates by asking the following guiding questions: a. DOK-2 How do you determine when to increase your values or decrease your values when finding the unit rate? b. DOK-1 What operation does a fraction represent? c. DOK-2 In Neri’s calculations, why does it make sense to convert the decimal to a fraction for the complex fraction? d. DOK-3 How do you solve complex fractions? e. DOK-2 How do you know which value to place on the denominator of the complex fraction?”

• Scope 8: Expressions, Engage, Hook, Procedure and Facilitation Points, connects the major work of 7.EE.A (Use properties of operations to generate equivalent expressions.) to the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations.) Students work to create and solve algebraic expressions for scores on a video game between two players. (Sample answers are given after each DOK question.) “Part I: Pre-Explore, 1. Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. 2. Explain the situation while showing the video behind you. Steven is playing a video game against his best friend Jamaal. He is player 1 and Jamaal is player 2. At the end of the game, both of their scores were posted as expressions. Steven’s little sister Avery came in, looked at the scores, and asked who won. Steven and Jamaal need to decide whether the expressions are equivalent or not. If they are equivalent, it’s a tie. If not, the player with the greater score wins! Ask students the following questions: What do you notice? What do you wonder? Where can you see math in this situation? . Allow students to share all ideas… d. DOK-1 What is player 2’s score when simplified? e. DOK-1 Who won the video game and how can you tell? f. DOK-1 What would the scores be if x=1,000?”

• Scope 9: Equations, Explore, Explore 4–Solve Multi-Step Real-Life Problems, Exit Ticket, connects the Expressions & Equations domain to The Number System domain. Students solve real-life problems with algebraic expressions with fractions. “Ivy and her friends watched the fireworks that started at 9:00 p.m. Ivy and her party went home as soon as the fireworks display was done. Ivy and her mom got home by 10:30 p.m. 35% of the time was spent watching the actual fireworks. \frac{1}{4} of the time was spent saying goodbye to her friends and walking to the parking lot. The rest of the time was spent driving home. How long was the drive from the theme park to Ivy’s home? Show your work here. Total drive time:”

• Scope 15: Informal Inferences, Explain, Show What You Know–Part 3: Compare Data, connects the supporting work of 7.SP.A (Use random sampling to draw inferences about a population) to the supporting work of 7.SP.B (Draw informal comparative inferences about two populations). Students need to find the mean and range for a two dot plot and then make an inference based on the data. For example, “The double dot plot shows the number of points scored by Seth and Dave’s teams in 10 football games. Use the information provided to answer the questions that follow. Two dot plots. What is the mean for each team? Seth: ___, Dave: ___; What is the mean for each team? Seth: ___, Dave: ___; Which team's mean was the greatest? ___; What is the range for each team? Seth: ___, Dave: ___; Based on that information, which team is more consistent in their scores? ___.”

The materials reviewed for STEMscopes Math Grade 7 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.

Prior and future connections are identified within materials in the Home, Content Support, Background Knowledge, as well as Coming Attractions sections. Information can also be found in the Home, Scope Overview, Teacher Guide, Background Knowledge and Future Expectations sections. 

Examples of connections to future grades include:

• Scope 4: Rational Number Operations, Home, Scope Overview, Teacher Guide, Future Expectations connects 7.NS.A (Apply and extend previous understandings of operations with fractions.) to work in future grades. “Students will use their knowledge of rational numbers as they pertain to fractions that terminate and repeat in upcoming years. In 8th grade, they will build on these concepts to introduce irrational numbers. Students will approximate irrational numbers as they pertain to the number line and eventually functional graphs.”

• Scope 9: Equations, Home, Content Support, Background Knowledge, connect 7.EE.3 (Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically…) to future grades. “The concepts in this scope help students to create connections between numerical relationships as they continue to relate equations to functions in 8th grade. With greater knowledge of these methods, more complex problems will become easier and quicker to solve. The ideas behind rational numbers will expand as students begin to learn about irrational numbers and repeating decimals.”

• Scope 14: Circles, Home, Content Support, Coming Attractions connects 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.) to work in future grades. “Students will continue to find the area and circumference of circles throughout 8th grade and higher. They will learn to manipulate the formulas to find geometric pieces such as arcs, sectors, and radian measures. The understanding of new circle concepts will be expanded on in geometry classes in high school.”

Examples of connections to prior grades include:

• Scope 7: Percent Application, Home, Content Support, Background Knowledge connects 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems.) to work done in previous grades. “In sixth grade, students learned how to recognize proportional relationships and use ratios and unit rates to solve mathematical problems. This knowledge of proportions will be further explored as they discover the importance of proportional relationships within percent problems.”

• Scope 9: Equations, Home, Content Support, Background Knowledge, connect 7.EE.3 (Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically…) to prior grades. “In Grade 6, students learned how to solve equations that deal with nonnegative rational numbers through the use of order of operations. Students have prior knowledge of the value of negative numbers and how they are represented as the opposite of positive numbers. They are able to create real-world contexts from these positive and negative quantities.”

• Scope 11: Scaling, Home, Scope Overview, Teacher Guide, connects 7.G.A (Draw, construct, and describe geometrical figures and describe the relationships between them.) with work done in earlier grades. “In Grade 6, students determined the area of special quadrilaterals and parallelograms through the use of shape composition and decomposition skills. The students learned how to compute areas with given lengths as well as finding lengths from a given area. This background knowledge will be the framework that allows students to reproduce scale drawings at a different scale than the original.”