7th Grade - Gateway 2

The instructional materials do not meet the expectation for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics without losing focus on the major work of each grade. Overall, there is little evidence of the opportunity to work with engaging applications of the mathematics. There are few non-routine problems throughout the year. Word problems are present in the materials, but the context has limited bearing on the mathematics. However, there are ten Problem Solving Lessons designed to help students "isolate and focus on [problem solving] strategies."

Cluster 7.RP.A expects students to use proportional relationships to solve real-world and mathematical problems. The parts of this cluster that relate to applications, 7.RP.3 in particular, are primarily focused on in Teacher Resources Part 2 Unit 2, so the following evidence comes from that Book and Unit.

• In Lessons 31 and 32, students write proportions to solve problems involving percents. Both lessons are structured so that exercises for students to complete immediately follow examples that the teacher does which are exactly like the exercises. Many exercises also include contexts like the teacher-led examples. In the exercises where different contexts are presented, the wording of the exercises is very similar to the examples, so students still have a procedure for how to solve the problem in the new context.
• In Lessons 34 and 35, students solve mathematical problems involving proportional relationships, but none of the problems involve a context. Also, the problems are routine because students complete exercises that follow the process used in teacher-led examples.
• In Lesson 37, students are shown how to use tape diagrams to solve problems involving percent discounts and markups. The exercises that students are asked to complete are routine because, as in previous lessons, they immediately follow and are the same as teacher-led examples.

Standard 7.NS.3 sets an expectation that students solve real-world and mathematical problems involving the four operations with rational numbers.

• In Lessons 28 and 29 of Unit 7 in Teacher Resources Part 1, students are presented with few opportunities to solve real-world problems involving the four operations with rational numbers, and the few problems they are given are routine as they follow exercises with which they are very similar. Also, the contexts for the problems do not vary.
• In Lessons 30 and 31 of Unit 7 in Teacher Resources Part 1, students are presented with numerical expressions involving the four operations that they are supposed to simplify. The students do not create any of the expressions, and contexts are not presented with the expressions.
• In Lessons 39 and 44 of Unit 1 in Teacher Resources Part 2, students are presented with some word problems that require them to multiply or divide rational numbers, but these problems are routine. They follow exercises with which they are similar, and the contexts do not have bearing on them.

Standard 7.EE.3 includes solving problems with rational numbers using tools strategically, applying properties of operations to calculate with numbers, converting between different forms of numbers as appropriate, and assessing the reasonableness of answers. This standard is primarily addressed in Unit 5 of Teacher Resources Part 1.

• In Lessons 17 through 25, students are given some opportunities to solve problems with rational numbers, but the problems are routine, and tools are given to students. For example, in Lesson 23 students are shown how to use tape diagrams for solving problems that involve percents and told to use tape diagrams when completing the exercises. In Lesson 25, there are some exercises at the end of the lesson where the context could have a bearing on the students solving a problem, but these exercises at the end are routine because they have the same format and use the same wording as the preceding exercises in the lesson. For example, there are a series of exercises where students work in the context of the ratio of boys to girls in a classroom and are supposed to use a tape diagram to help them answer the exercises , but these follow a teacher-led example that also uses the context of the ratio of boys to girls in a classroom and a tape diagram.

In Problem Solving Lesson PS7-5 students are presented with two problem solving strategies: using tape diagrams and using algebra to solve multi-step ratio problems. The teacher-led exercises scaffold students through the strategies in a variety of applications. In one instance in the lesson, teachers are prompted to ask students what is the same between the two strategies. The Problem Bank provides students opportunities to work independently on routine tasks that are similar to the exercises. Students were directed to use both strategies learned in the lesson. Teachers were guided to ask students which strategy they prefer and why but were not guided to connect application of the strategies to the mathematics.

The instructional materials reviewed for Grade 7 do not meet the expectations for carefully attending to the full meaning of each practice standard. The publisher rarely addresses the Mathematical Practice Standards in a meaningful way.

The materials identify examples of the Standards for Mathematical Practice (MPs), so the teacher does not always know when a MP is being carefully attended to. MPs are marked throughout the curriculum, but sometimes the problems are routine problems that do not cover the depth of the Math Practices. Many times the MPs are marked where teachers are doing the work.

Examples where the material does not meet the expectation for the full meaning of the identified MP:

• MP1: In Teacher Resources Part 1 Unit 8 Lesson 6, students are asked to make an organized list from an already completed tree diagram and a separate list from a chart. Both of these exercises resemble examples that are completed by the teacher immediately preceding the exercises. Another example is in Teacher Resource Part 1 Unit 8 Lesson 8. A task asks students to, “Check that the numbers in Part C actually add to 1,000 and that the numbers in the Bonus question add to 10,000 or that their percents add to 100%.” These are not examples of MP1 as they do not require students to make sense of problems or persevere in solving them.
• MP4: In Teacher Resources Part 2 Unit 3, Lesson 18 asks students to choose two variables and write an equation, and this exercise does not show the full meaning of modeling with mathematics. Also, in Teacher Resources Part 2 Unit 1 Lesson 32, students are asked to determine if a recipe will turn out by multiplying two fractions. These exercises follow teacher-led examples exactly like them, and there is not an opportunity for students to say what changes would need to be made if they determine the recipe will not turn out.
• MP4: While the publisher attaches MP4 to many lessons, there are occasions when the activities students are completing do not have them model with mathematics. For example, in Teacher Resources Part 1 Unit 3 Lesson 6, there are exercises with instructions to "write a subtraction expression for the change (in dollars) from $20 as the price of a CD is ...". From the instructions, students are told to subtract from 20 and that the units will be dollars. Although, the answer is a mathematical model, the directions give the format of the model to the students, and by giving the units, students are not able to identify any important quantities. Also in Lesson 6, students are to complete three exercises where an algebraic expression is given to them, and they are to evaluate the expression by substituting a given value for the variable. In these exercises, students do not have the opportunity to make assumptions or approximations in a complex situation, identify important quantities and represent their relationships, draw conclusions, or interpret the results of a problem and make improvements if needed.
• MP5: In Teacher Resources Part 1 Unit 5, Lesson 16 says, “Explain that you can use estimation to check the answer.” There is no choosing of tools. In Teacher Resources Part 1 Unit 8, Lesson 9 has the teacher telling students “it can be tedious to find theoretical probabilities of compound events using a tree diagram, chart, or organized list.” This does not require the students to use tools strategically.
• MP7: While MP7 is indicated in many lessons, sometimes the structure is found in the standard itself and not the indicated exercise or a rule is being provided. For example, in Teacher Resources Part 2 Unit 6 Lesson 28, students are finding the surface area of composite shapes. The teacher then guides them through the process of separating prisms and each of their corresponding calculations. In this exercise, students are not discerning anything about the decomposition of three-dimensional composite shapes; they are simply following the teacher and the instruction given.