7th Grade - Gateway 1

The materials reviewed for i-Ready Classroom Mathematics, Grade 7 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Within the i-Ready Classroom Mathematics materials, the Unit Assessments are found in the Teacher Toolbox and include two forms for Unit Assessment, Form A and Form B. Both Forms contain similar problems for each unit. The Unit Assessments can be found at the end of each unit in the materials. 

Examples of assessment items in i-Ready Classroom Mathematics include:

• Unit 2, Unit Assessment, Form A, Problem 8, assesses 7.NS.1c as students use their understanding of subtraction of rational numbers as adding the additive inverse. “Why does -2.4-(-7) have the same result as -2.4+7? Explain your reasoning.”

• Unit 3, Unit Assessment, Form B, Problem 3, assesses 7.NS.3 as students solve real-world problems involving the four operations with rational numbers. “A baker adds baking powder onto a food scale by teaspoons. The scale has marks every \frac{1}{10}g. Each teaspoon of baking powder weighs 3.81g. Between which two marks on the scale will the weight be after the seventh teaspoon is added to the scale? Show your work.” 

• Unit 4, Unit Assessment, Form A, Problem 8, assesses 7.EE.4 as students use variables to represent quantities in a real-world problem. “Jameson Middle School gives bottles of water to teachers and students who are going on a field trip. The school orders 500 bottles of water. They plan to give 35 bottles of water to teachers. They ordered at least 2 bottles of water for each student. How many students could be going on the field trip? Show your work.” 

• Unit 5, Unit Assessment, Form B, Problem 4, assesses 7.RP.3 as students solve problems using box plots. “The box plots show the amount of rainfall, in inches, in two different towns during storms. Express the difference in the median amount of rainfall as a multiple of the IQR for each data set. Show your work.”

• Unit 6, Unit Assessment, Form A, Problem 14, assesses 7.G.6 as students solve problems involving volume of rectangular prisms. “Dawn has a plastic container filled with slime. The container is a rectangular prism with a base that measures 4 in. by 6 in. and a height of 3 in. She wants to put the slime in a new container that is a rectangular prism with a base that measures 10 in. by 3 in. and a height of 5 in. What is the height of the empty space in the new container after she adds all the slime? Show your work.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 7 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. In the materials, there are ample opportunities for students to work with grade level problems. This includes:  

• Lessons contain multiple opportunities for students to work with grade-level problems in the “Try It”, “Discuss It”, “Connect It”, “Apply It”, and “Practice” sections of the lessons. 

• Differentiation of grade-level concepts for small groups are found in the “Reteach”, “Reinforce”, and “Extend” sections of each lesson. 

• Fluency and Skills Practice problems are included in the Teacher Toolbox in addition to the lessons.

• Interactive tutorials for the majority of the lessons include a 17 minute interactive skill tutorial as an option for the teacher to assign to students. 

Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

• Unit 1, Lesson 2, Session 3, Apply It, Problem 2, students compute unit rates involving ratios of fractions (7.RP.1). “Amare runs \frac{1}{10} mile in \frac{2}{3} minute. What is his speed in miles per minute? Show your work.”

• Unit 2, Lesson 8, Session 2, Apply It, Problem 7, students apply properties of operations as they add and subtract rational numbers (7.NS.1). “A dragonfish is swimming at -900m relative to sea level. It rises 250m. What is the dragonfish’s new depth relative to sea level? Show your work.”

• Unit 3, Lesson 14, Interactive Tutorials provides extra problems in Equivalent Linear Expressions when students apply the distributive property to expand and factor linear expressions with rational coefficients. Students use the distributive property to write an equivalent expression (7.NS.3 and 7.EE.3). “$$3-(-4x+2)=3(-4x)+3(2)=-12x+6$$.”

• Unit 4, Lesson 16, Session 2, Practice, Problem 2, students analyze an expression in the context of situations and rewrite an expression in a different form to reflect a situation (7.EE.2). “Nathan is making blueberry and pineapple kebabs. Each kebab needs the same number of blueberries, b, and the same number of pineapple pieces, p. 

  a. Nathan wants to check if he has enough of each type of fruit to make 12 kebabs. How can the expression 12b+12p help him do that?

  b. Nathan’s sister, Linda, offers to help him make some of the kebabs. Nathan wants to set aside enough fruit for her to make 3 of the kebabs. How can you rewrite 12b+12p so that it shows the fruit for Nathan’s kebabs and the fruit for Linda’s kebabs separately?”

• Unit 5, Lesson 21, Session 2, Fluency and Skills Practice, students use proportional relationships to solve multistep ratio and percent problems (7.RP.3). “Find the percent change and tell whether it is a percent increase or a percent decrease. Problem 1, Original amount: 20  End amount: 15.” 

• Unit 7, Lesson 30, Session 2, Connect It, Problem 4, students understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. (7.SP.5) “What word describes the probability of rolling an integer on a standard number cube? How can you describe the same probability with a number? Explain why you can describe the probability both ways.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 7 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. Materials were analyzed from three different perspectives; units, lessons, and days. Each analysis includes assessments and supporting work connected to major work of the grade.  

• The approximate number of units devoted to major work of the grade is 4.5 out of 7 units, which is approximately 64%. 

• The number of lessons, including end of unit assessments, devoted to major work of the grade is 31 out of 47 lessons, which is approximately 66%. 

• The number of days, including end of unit assessments, devoted to major work of the grade is 98.5 out of 152, which is approximately 65%. 

A day-level analysis is the most representative of the materials because the number of sessions within each topic and lesson can vary. When reviewing the number of instructional days for i-Ready Classroom Mathematics Grade 7, approximately 65% of the days focus on major work of the grade.

The materials reviewed for i-Ready Classroom Mathematics, Grade 7 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Throughout the materials, supporting standards/clusters are connected to the major standards/ clusters of the grade. The following are examples of the connections between supporting work and major work in the materials: 

• Unit 1, Lesson 2, Session 3, Apply It, Problem 8, connects the supporting work of 7.G.1 to the major work of 7.RP.1 as students compute unit rates associated with ratios of fractions to solve problems involving scale drawings. “Nuru looks at a map on her phone. She zooms in until the map scale for centimeters to kilometers is 0.3:\frac{1}{5}. How many centimeters does the map use to show 1 kilometer? a. \frac{2}{3} b. \frac{3}{5} c. 0.06 d. 1.5.”

• Unit 4, Lesson 16, Session 3, Apply It, Problem 3 connects the supporting work of 7.G.6 with the major work of 7.EE.2 as students rewrite expressions in order to find the area of the flag. "The spirit club uses fabric to make school flags for students to wave at the pep rally. The club members want to find the amount of purple striped fabric, in square includes, that they need for one flag. Avery says they can use the expression 5(4) + 7(4). Pedro says they can use the expression (12\cdot8)\div2. Explain why both students are correct.”

• Unit 5, Lesson 23, Session 2, Apply It, Problem 7 connects the supporting work of 7.SP.2 with the major work of 7.RP.3 as students use proportional relationships to solve a multistep ratio problem to draw an inference about data. “A random sample of Grade 8 students at a school are asked whether they plan to take computer science in high school. Of those asked, 15 students plan to take computer science, 5 do not, and 7 are unsure. There are 326 Grade 8 students in the school. Based on the sample, about how many Grade 8 students in the school plan to take computer science in high school?”

• Unit 6, Lesson 28, Session 2, Apply It, Problem 7 connects the supporting work of 7.G.5 to the major work in 7.EE.4 as students construct equations to solve problems about angle measures. “$$\angle A$$ and \angle B are vertical angles. m$$\angle A=(4x+6)\degree$$ and m$$\angle B=(7x-66)\degree$$. What are m\angle A and m$$\angle B$$? Show your work.”

• Unit 7, Lesson 31, Session 1, Connect It, Problem 2c, connects the supporting work of 7.SP.6 to the major work of 7.EE.3 and 7.NS.2 as students determine the probability of an event and express it in fraction, decimal, and percent forms. “Each time Chantel selects a card from a bag, she performs one trial of an experiment. Chantel uses a box of marbles to conduct a different experiment. She selects a marble, records its color, and puts it back in the box. She does this several times. In all, she selects 5 red marbles, 3 blue marbles, and 2 yellow marbles. Chantel can use experimental probability to describe the likelihood of getting a particular result in an experiment. c. A probability can be expressed as a fraction, decimal, or percent. What is the experimental probability of selecting a red marble, expressed as a fraction? A decimal? A percent?”

The materials reviewed for i-Ready Classroom Mathematics, Grade 7 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 of problems and activities that serve to connect two or more major clusters or domains in a grade include: 

• Unit 2, Lesson 7, Session 2, Develop, Problem 1, connects the major work of 7.NS.A to the major work of 7.EE.B as students apply and extend understanding of adding and subtracting rational numbers and solve multi- step real work problems with positive and negative integers. “On the first play, Angel’s football team gains 5 yards from their starting position . On the second play, the team loses 7 yards. To find where the team is relative to its starting position, add 5 and -7. a. You can use integer chips to model 5 + (-7). Circle all the zero pairs. b. What is the value of the remaining chips? c. 5 +(-7). d. After the second play, where is Angel’s team relative to its starting position?”

• Unit 3, Lesson 14, Session 2, Practice, Problem 4, connects the major work of 7.NS.A to the major work of 7.EE.B as students find the value of a given expression involving fractions. “Consider the expression -6\frac{3}{5}-(-7\frac{4}{15})+2\frac{1}{5}. a. Estimate the value of the expression. b. Find the exact value of the expression. Show your work. c. Use your estimate to explain if your answer to problem 4b is reasonable.”

• Unit 4, Lesson 18, Session 2, Apply It, Problem 8, connects the major work of 7.EE.B to the major work of 7.NS.A as students solve algebraic equations involving rational numbers. “Solve -21=-\frac{1}{4}y+6. Show your work.”

• Unit 5, Lesson 20, Session 3, Connect It, Problem 4, connects the major work of 7.RP.A to the major work of 7.EE.A as students analyze an expression of a proportional relationship and identify equivalent expressions by using properties of operations. “Hiroaki uses the expression a+0.05a to represent an amount increasing by 5%. Allen uses the expression 1.05a . Explain why both Hiroaki and Allen’s expressions are correct.”

Examples of problems and activities that serve to connect two or more supporting clusters or domains in a grade include: 

• Unit 5, Lesson 24, Session 3, Apply It, Problem 8, connects the supporting work of 7.SP.A to the supporting work of 7.SP.B as students draw a comparative inference from random samplings of two populations. “River county has 15,000 likely voters. A survey of voters selected at random in River County finds that 60 plan to vote to re-elect the current governor. Lake County has 12,000 likely voters. A survey of 125 voters selected at random in Lake County finds that 90 plan to vote to re-elect the current governor. In which county can the current governor expect to get more votes? Show your work”

The materials reviewed for i-Ready Classroom Mathematics, 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. 

Each Unit contains the Teacher’s Guide which includes a Unit Flow and Progression video, a Lesson Progression, a Math Background, and a Lesson Overview that contains prior and future grade-level connections to the lessons in the unit. Examples include:

• Unit 2, Lesson 7, Overview, Learning Progression, prior grade learning is connected to understanding addition with negative integers. “In Grade 6, students learned that a negative number and its opposite are the same distance in opposite directions from 0 on a number line. They compared the values of negative numbers and placed them on horizontal and vertical number line diagrams. They also used positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.”

• Unit 3, Lesson 14, Overview, Lesson Progression, Use the Four Operations with Negative Numbers builds on Grade 6, Lesson 7, Add, Subtract, and Multiply Multi-Digit Decimals, 6.NS.3. This lesson prepares students for Grade 8, Lesson 23, Find Square Roots and Cube Roots to Solve Problems, 8.EE.2.

• Unit 4, Beginning of Unit, Math Background, Future Learning, describes the future work connected to the unit. “Students will move on to deepen their understanding of expressions and equations as they work with multi-step equations, systems of equations, and functions. Students will write and solve linear equations with variables on both sides of the equal sign; explore one-variable equations with zero or infinitely many solutions; write and solve systems of two-variable linear equations; use functions to model linear relationships.” (8.F.4, F.IF.9)

• Unit 5, Lesson 20, Overview, Learning Progression, describes the connected work of later grades. “In later grades, students will use their knowledge of percentages to solve problems in math, science, social science, and real-world situations.” (HSS.MD.B)

• Unit 6, Beginning of Unit, Math Background, Geometry, Prior Knowledge “Students should: be able to find the area of polygons by composing and decomposing them into triangles and rectangles, be able to use a net to find the surface area of a right prism or pyramid, be able to find the volume of right rectangular prisms, be able to draw an angle with a given measure, and be able to write and solve equations in one variable” and “be able to convert measurement units by multiplying and dividing.” (6.G.A and 6.EE.B) Future Learning states, “Students will draw images of translations, reflections, rotations, and dilations, explore relationships involving angles of triangles and angles formed by parallel lines and transversals, find the volume of cylinders, cones, and spheres, apply what they learned about the conditions that determine a unique triangle to explore triangle congruence, construct triangles and other figures using a compass and  straightedge, and use plane sections to justify volume formulas.” (8.G.A, G.CO.A, G.CO.B, and G.MD.A)