The instructional materials reviewed for Grade 5 partially meet expectations that materials carefully attend to the full meaning of each practice standard (MP). Although the instructional materials attend to the full meaning of some of the MPs, there are some MPs for which the full meaning is not developed.

At times, the instructional materials only attend superficially to MPs. The following are examples:

• The Unit 2 Session 2.1 Math Practice Note lists MP5 and has students determining the volume in cubic centimeters of a small prism. The Math Practice Note states that “students might use centimeter cubes or a centimeter ruler to find the dimensions.” In this activity, students are told which tools to use.
• The Unit 7 Session 1.1 Math Practice Note lists MP1. The teacher states, “Earlier in the year you worked on adding and subtracting fractions, and in the last unit you worked on adding and subtracting decimals. In this unit you will be multiplying and dividing fractions and decimals. We are going to begin with multiplying fractions.” The Math Practice Note discusses that part of making sense of problems is being able to connect unfamiliar work with prior learning. However, the statements to be made by the teacher explicitly guide students to where connections could be made, and the session itself does not assist the teachers or students to make or discuss these connections.
• The Unit 7 Session 2.1 Math Practice Note lists MP1 and has students making sense of the problem by recognizing that different pathways to a solution may yield answers that look different even if they are equivalent. However, they are not persevering in solving the problems given.
• The Unit 7 Session 2.2 Math Practice Note lists MP5 and has students identifying decimal and fraction equivalence through the use of a calculator. The Math Practice Note states that in this activity, students explore how to use a calculator to determine the records of several basketball players. This activity tells students which tool to use.

At times, the instructional materials fully attend to a specific MP. The following are examples:

• The Unit 1 Session 2.6 Math Practice Note lists MP5 and has students reminded of the various tools, such as story contexts and arrays, that they can use to represent not only the problem but also the steps of their solutions to solve multiplication problems. They are never specifically told which tool to use and are able to choose the tool that is most appropriate for them and the lesson.
• The Unit 4 Session 1.1 Math Practice Note lists MP6 and has students describing and comparing strategies used to solve multi-digit multiplication problems. The Math Practice Note specifically calls out that in the discussions students need to explain the steps of their solution, name the strategy used, and question classmates making sure to develop clear explanations and concise notation for their work.
• The Unit 7 Session 1.5 Math Practice Note lists MP6 and asks students to make a conjecture about what happens when they multiply a number by a fraction smaller than 1. The Math Practice Note discusses that articulating conjectures requires that students attend carefully to the language they use and to state all components of their reasoning.

The instructional materials reviewed for Grade 5 partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade level mathematics.

When MP3 is referenced, students are often asked to solve and share solutions. The independent work of the student is most often about finding the solution to a problem without creating a viable argument. Students often listen to peer solutions without being asked to critique the reasoning of the other student. Much of the student engagement in the class discussion is teacher prompted without giving students the opportunity to create their own authentic inquiry in the thinking of others.

• In Unit 6 Session 1.2 students neither construct an argument nor critique the arguments of others when the materials reference MP3 and direct students to “make sure that they think about how many parts out of 1,000 are shaded.”
• In Unit 6 Session 1.5 MP3 is referenced when students are asked to “share their responses and justifications with the whole class.” The students are not required to analyze the arguments of others.
• In Unit 7 Session 1.1 MP3 is referenced when students are asked to share their solutions and equations for Problem 1 on Student Activity Book page 421.

At times, the materials prompt students to construct viable arguments and analyze the arguments of others.

• In Unit 1 Session 1.2 students are told “[Hana] and [Yumiko] say that all these numbers are multiples of 12 and that any solution to this number puzzle will be a multiple of 12. Do you agree? Why or why not?”
• In Unit 6 Session 1.7 the following guided exchange supports students in critiquing the arguments of others: “[Stuart] says that we can’t play the card because, in the bottom row, we’ve already played 825 thousandths and 975 thousandths, and this card goes in between them. Are there any comments? [Shandra] disagrees. she says that we could play it in the last spot in the middle row because it’s greater than 6 tenths and goes between 45 hundredths and 975 thousandths in the last column. Are there any comments? [Shandra] is right; we can play the card there. Remember the rules: the decimals have to be in order from left to right and from top to bottom, but it’s all right if the last card in one row is bigger than a card in the first one or two spaces of the next row.”

The instructional materials reviewed for Grade 5 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

Most of the time when MP3 is referenced, teachers are asked to have students share or explain their solutions. Teachers are also directed to have students ask questions but are not supported in focusing those questions toward critiquing the arguments of others.

• In Unit 3 Session 3.3 students are playing a game, and the teacher says, “a player wins a round if the sum of his or her two cards is greater than the sum of the other player’s cards. Who has the greater sum? How do you know?” These questions would prompt students to construct their own argument, but there are no other questions or prompts to help students who are not able to construct an argument. There are also no questions or prompts for students to analyze the arguments of others.
• In Unit 5 Session 1.4 there are a series of scaffolded questions for teachers that would assist them in having students construct arguments from graphs about the height and age of two people. There are no questions or prompts for teachers to assist them in having students analyze others’ arguments when different interpretations might arise.
• In Unit 8 Session 2.3 students are asked to explain their thinking about how the perimeter and area of rectangles change when each dimension is doubled. There are question that assist the teacher with engaging students in constructing their own arguments, but there are no questions or prompts to assist teachers with having students analyze the arguments of others.

The materials assist teachers, at times, in engaging students in constructing viable and analyzing the argument of others.

• In Unit 3 Session 1.1 teachers are prompted to provide the students with questions such as, “How did you know how many marbles to circle in Problem 5a?....Deon says that since there are 12 marbles, ⅓ is four marbles. Deon , how do you know that? Who has another way to think abou this problem? I noticed in Problem 7 that almost everyone agrees ⅔ is greater than 2/6, but who can explain why this is true?” The Math Practice Note tells teachers to ask students to paraphrase each other’s explanations or to ask one another questions to encourage students’ working to make sense of each other’s approaches.