7th Grade - Gateway 1

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

The assessments are aligned to grade-level standards and do not assess content from future grade levels. Each unit has at least one quiz and one End Assessment, which comes in Forms A and B. Quizzes and End Assessments are available in print and digital versions. Examples of assessment items aligned to grade-level standards include:

• Unit 1, Quiz, Screen 9, Problem 5.1, assesses 7.G.1 as students 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. “Rectangle S is 3 units by 5 units. Sketch a scaled copy of rectangle S with an area of 60 square units. Label each side length of the copy.” An interactive graph where students can sketch a rectangle is included.

• Unit 2, End Assessment: Form A, Screen 10, Problem 7.3, assesses 7.RP.2d as students explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation. “A recipe for chocolate chip cookies uses 3 tablespoons of cookie batter for every 2 tablespoons of chocolate chips. Explain what the point (1, 1.5) means in terms of the situation.” A graph of the line representing this situation is included with the point (1, 1.5) on the line. In the previous (Problem, 7.2), students were asked to write an equation that represents this situation.

• Unit 3, End Assessment: Form B, Screen 3, Problem 2, assesses 7.G.4 as students use the calculation for the area of a circle to determine accuracy. “This circle has a radius of 6 units. Three students tried to calculate the area. Order their area from least accurate to most accurate.” Students are given a picture of a circle with a radius of 6 units and answer choices: 36\pi square units, 113.1\pi square units, 113.1 square units.

• Unit 7, Quiz, Screen 4, Problem 3, assesses 7.G.2 as students construct triangles from three measures of sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. “How many non-identical triangles can be made using these side lengths: 4 cm, 8 cm, and 14 cm?” Answer choices: “zero triangles, one triangle, more than one triangle.”

• Unit 8, End Assessment: Form A, Screen 10, Problem 6.2, assesses 7.SP.4 as students use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. “Rudra is wondering, "Should I start a petition for a longer lunch and longer school day?" They survey a random sample of 20 students and find that 12 of them agree. If the school has 250 students, about how many do you predict would agree?”

The materials reviewed for Desmos Math 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 opportunities for students to engage in extensive work and the full intent of all Grade 7 standards. Each lesson contains a Warm-up, one or more activities, an optional “Are You Ready for More?”, a Lesson Synthesis, and a Cool-Down. Each unit provides a Readiness Check and Practice Days. Readiness Checks provide insight into what knowledge and skills students already have. Practice Days provide opportunities for students to apply knowledge and skills from the unit. Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

• Unit 1, Lesson 7, Practice Problems, Screen 4, Problem 1.3, engages students with the full intent 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). Students are given a blueprint, a scale and the actual width of an object then asked to compute the scale size of that object. “The blueprint for Zahra’s new office measures 4 cm long and 2 cm wide. The scale for the blueprint is 6 cm to 15 ft. Zahra wants to put a couch in her office that is 3 feet wide. How wide would the couch be if it were drawn on the blueprint?”

• Unit 2, Lesson 4, Practice Problems, Screen 4, Problem 2.1, engages students with the full intent of 7.RP.2b (Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships). “A plane flew at a constant speed between Denver and Chicago. It took the plane 1.5 hours to fly 915 miles. Complete the table.” Students complete a table labeled time and distance. The time part of the table is hours and goes from 1 to t, while the distance only has 915 labeled on it. 

• Unit 5, Lesson 4, Student Worksheet, Problem 1, engages students with the full intent of 7.NS.1c (Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts). Students use a number line to explain a strategy. “Renata drew a number line diagram to help her think about Problems 3 and 4 from the warm up. Explain how you think Renata drew each number line.” Students are given two number lines and two expressions. One expression is 2-3 and the other expression is 2-(-3). Below each expression is a number line diagram Renata drew based on the expression. Students then explain Renata’s strategy. 

• Unit 6, Lesson 16, Screen 8, Help Chloe, engages students with the full intent of 7.EE.4b (Solve word problems leading to inequalities of the form px+q>r or px+q, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem).  Students work with inequalities to convince someone that their response is not correct. “Chloe is solving the inequality 25-4x<1. Chloe says the solutions to the inequality are x<6. Convince her that her response is not correct.”

While students engage with 7.RP.1 (Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units), there are limited opportunities for students to engage with fractions to meet the full intent of grade-level standards.

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

To determine the amount of time spent on major work, the number of topics, the number of lessons, and the number of days were examined. Practice and assessment days are included. Any lesson marked optional was excluded.

• The approximate number of units devoted to major work of the grade (including supporting work connected to the major work) is 5 out of 8, which is 63%.

• The approximate number of lessons devoted to major work (including assessments and supporting work connected to the major work) is 90 out of 122, which is approximately 74%. 

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 93 out of 127, which is approximately 73%.

A day-level analysis is most representative of the instructional materials because this contains all lessons including those that are more than one day. As a result, approximately 73% of the instructional materials focus on major work of the grade.

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

In most cases, materials are designed so supporting standards/clusters are connected to the major standards/clusters of the grade. Examples of connections include:

• Unit 1, Lesson 3, Screen 8, Settle a Dispute, 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.RP.2 (Recognize and represent proportional relationships between quantities). “Here is one student’s sketch. Sasha thinks the student used a scale factor of 2. Randy thinks the student used a scale factor of 1.5. Who is correct?” Students are given a drawing of two trapezoids of different sizes, one labeled “Original” and the other “Student’s Sketch.” Answer choices: Sasha, Randy, Both or Neither.

• Unit 3, Lesson 7, Screens 2 and 3, Circle Area and Radius vs. Area, connects the supporting work of 7.G.4 (Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle)to the major work of 7.RP.2 (Recognize and represent proportional relationships between quantities). “The graph shows some of the areas your classmates gathered. Do you think there is a proportional relationship between the radius and the area of a circle?” On Screen 2, students are given a tool allowing them to collapse or expand a circle. As students manipulate the circle the radius of the circle is given in units. “Drag the point to make a circle.  Then determine the area of your circle.” On Screen 3, students are provided a graph with five points already plotted, the x-axis is labeled “Radius (units)”, and the y-axis is labeled “Area (sq.units)”. 

• Unit 7, Lesson 4, Practice Problems, Screens 5 and 6, Problem 3.1 and 3.2, 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 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). Screen 5, “Write an equation that represents the angle relationships in this diagram.” The diagram shows a straight angle that is divided into four angles. One angle is labeled 132\degree. The other three are each labeled x\degree. Screen 6, “Solve your equation.”

• Unit 8, Lesson 3, Screen 10, Cool-Down, connects the supporting work of 7.SP.2 (Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions) to the major work of 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems). “A new mystery bag has 5 blocks. Some are red and some are blue. The table shows outcomes from a repeated experiment. Based on these results, how many blocks are red?”

The materials reviewed for Desmos Math 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. 

There are multiple connections between major clusters and/or domains and supporting clusters and/or domains. Any connections not made between clusters and/or domains are mathematically reasonable. Connections between major clusters or domains include:

• Unit 4, Lesson 5, Screen 5, Calculate #2, connects the major work of 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems) to the major work of 7.EE.A (Use properties of operations to generate equivalent expressions). “Each new rectangle is 21% longer than the original. Complete the table with the length of each new rectangle.” Students are given three tape diagrams; 120cm, 50cm and 150cm indicating they are the original 100%. Each diagram indicates an additional 21% has been added. 

• Unit 5, Lesson 5, Screen 3, Puzzle #2, connects the major work of 7.NS.A (Apply and extend previous understandings of operations with fractions) to the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations). “Make true equations by dragging and flipping the cards. Try to use as few flips as possible.” Students are provided an equation tool with the following equations: an unknown plus 5 is equal to an unknown, and an unknown subtracted from an unknown is equal to 9. The original card choices are: 1, 2, 3, 4, -5, -6, -7 and -8. All cards can be flipped from positive to negative and vice versa.

• Unit 6, Practice Day 1, Student Worksheet, Problem 5, connects the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations) to the major work of 7.NS.A (Apply and extend previous understandings of operations with fractions). The materials tasks the students with solving the following equation,  2(11-x)=40.

Connections between supporting clusters or domains include:

• Unit 1, Practice Day 1, Task Cards, Fix It!, Problem 2, connects the supporting work of 7.G.A (Draw construct, and describe geometrical figures and describe the relationships between them) to the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume). “Mayra created a scaled copy of figure C using a scale factor of 2. They said, “Figure C has an area of 28 square units, so the scaled copy must have an area of 56 square units.” Convince Mayra that the area of the scaled copy is not 56 square units. Ready for More? Use any strategy to calculate the area of Mayra’s scaled copy.” Students are given a diagram of figure C drawn on a grid.

• Unit 8, Lesson 13, Screen 12, Cool-Down, 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). “Omari wants to know the median height of all 200 students in his dance school. He sampled 20 students on three different days and recorded their heights. Predict the median height for all students. Explain how accurate you think your prediction is for all the students at Omari's dance school.” Students are provided a diagram with three box plots, each one representing the heights of the students recorded on the different days.

The materials reviewed for Desmos Math 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.

Content from future grades is identified and related to grade-level work. These references can be found within many of the Unit Summaries, Unit Facilitation Guides, and/or Lesson Summaries. Examples of connections to future grades include:

• Unit 2, Unit Facilitation Guide, Section 3: Proportional Relationships in Graphs (Lessons 8-10), connects 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems) to the work of 8th grade. “Students explore graphs of proportional relationships and use graphs to determine constants of proportionality. This work supports students with the study of slope in Grade 8.”

• Unit 4, Lesson 13, Summary, About This Lesson, connects 7.NS.A (Apply and extend previous understandings of operations with fractions) to the work of 8th grade. “Students convert fractions to decimals using long division. This builds on their understanding of using decimals in equations to represent percent increase and decrease. The skills that students build in this lesson lay the foundation for a series of lessons on rational and irrational numbers in Math 8.”

Materials relate grade-level concepts from Grade 7 explicitly to prior knowledge from earlier grades. These references can be found within many of the Unit Summaries, Unit Facilitation Guides, and/or Lesson Summaries. Examples of connections to prior knowledge include:

• Unit 5, Unit Facilitation Guide, Connections to Prior Learning, connects 7.NS.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) to work in 6th grade. “The following concepts from previous grades may support students in meeting grade-level standards in this unit: Using positive and negative numbers to represent quantities in real-world contexts. (6.NS.C.5), Plotting positive and negative numbers on a number line. (6.NS.C.6)”

• Unit 7, Lesson 11, Summary, About This Lesson, connects 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume) to work in 6th grade. “In this lesson, students extend the work they did in Lesson 10 to calculate the volume of more complicated prisms. Students use a variety of strategies to determine the areas of complicated bases, including decomposing into more familiar shapes or surrounding and subtracting (MP 7). Students developed these strategies in Grade 6 and revisited them in Grade 7, Unit 3.”