1st Grade - Gateway 2

The instructional materials reviewed for Grade 1 partially meet the expectations for balance of the three aspects of rigor within a grade. Although the instructional materials meet expectations for each aspect of rigor, these aspects of rigor are often addressed in separate parts of the Sessions. Materials targeting application are often scaffolded, detracting from the balance of rigor. Overall, the three aspects of rigor are most commonly treated separately.

In general, conceptual understanding, procedural skill and fluency, and application are addressed in the Sessions; however, for the most part they are addressed in separate sections of the instructional materials. Conceptual understanding is typically addressed in the Discussion and Math Workshop portions of the Sessions. Procedural skill and fluency is typically introduced in separate Sessions and then practiced in the Daily Practice portion of sessions. Application consists of routine word problems in the instructional materials. As a result, all aspects of rigor are almost always treated separately within the curriculum including within and during Sessions, Practice, and Homework.

The instructional materials reviewed for Grade 1 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 1 Session 1.1 Math Practice Note lists MP1 and has students learn the activity "Start With/Get To." The students are being shown a strategy to help them through making sense of a problem; however, the students are never actually having to engage in any of the MP themselves.
• The Unit 1 Session 2.3 Math Practice Note lists MP1 and is introducing students to story problems and is establishing the routine for working on them in the whole group. The Math Practice Note states that story problems will be a central component of students’ mathematical studies for many years and that this session students learn how to enter into a problem. This session does allow students to make sense of certain problems, but it does not have them persevere through any.
• The Unit 2 Session 2.2 Math Practice Note lists MP5 and has students play a game called Triangle Connect-the-Dots. This game has students draw triangles on dot paper. Students are not able to choose a tool in this session.
• The Unit 8 Session 1.1 Math Practice Note lists MP5 and has students look at a set of geometric solids while the teacher explains that the shapes are 3-dimensional. In this session students are not able to choose a specific tool, only looking at the given geometric solids and a chart with 2-dimensional flats.

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

• The Unit 6 Session 2.2 Math Practice Note lists MP4 and has students representing and interpreting data in three categories. Students take a survey on which they like the best. The teacher models how the responses will be recorded, and there is a brief discussion on the results. Then students complete an activity on their own in the Student Activity Book making sure to ask themselves if the representation communicates the information appropriately. The students are working with a real-world problem and making a model of their choice to represent the information.
• The Unit 7 Session 3.1 Math Practice Note lists MP5 and has students playing a game that introduces adding tens. The students are only using cubes in tower form and have the ability to use Ten Frame Cards if they choose. The Math Practice Notes say that students can represent the numbers with either cubes in towers of 10 or Ten Frame Cards. In this session students are able to choose between the two different tools which at this grade level is appropriate.

The instructional materials reviewed for Grade 1 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 into the thinking of others.

• In Unit 1 Session 3.2 students are asked to compare their strategy for solving a problem to others that are shared with the class, and the students are asked to raise their hand for the strategy that was closest to their own. There are no prompts or questions for students to construct their own argument or to analyze the strategies presented that are different from theirs.
• In Unit 3 Session 4.6 the students discuss with a partner, before joining a whole-class discussion, what the missing number could be when playing a game. Some students share their explanations with the class, but all students do not get to necessarily share their argument. There are no prompts or questions for students to analyze the arguments of others.
• In Unit 8 Session 1.4 students are asked to pick blocks that match pictures presented to them. After viewing other students’ selections, students can change their original picks. Students are asked how they made their final decision, but there are no specific prompts that have them analyze the selections of other students.

There are a few places where the materials prompt students to construct viable arguments and analyze the arguments of others.

• In Unit 6 Session 1.3 students are prompted with a set of questions to help them make sure they have a viable representation of a set of data. Then the students participate in a whole-class discussion and are instructed to “Look at your classmates’ representations. What do you notice that is the same or similar in many of your representations? How are your representations different?”

The instructional materials reviewed for Grade 1 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. Overall, teachers are instructed to have students share or explain their solutions and occasionally ask questions of other students, but these questions or prompts generally do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

• In Unit 2 Session 2.4 students examine six shapes in order to determine how each of them may or may not be grouped with two triangles. The teacher is prompted to “encourage students to share their thinking and to respectfully disagree with one another, insisting that they explain their reasoning as they are trying to name shapes.” This assistance prompts students to construct an 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 students are playing a game called Tens Go Fish, and the teacher is reminded to “ask students to share their strategies for playing the game. Then have students use cubes to model their strategies for classmates.” This prompt is one method for the teacher to assist students in constructing an argument, but no other possible methods are discussed. There are also no questions or prompts for students to analyze the arguments of others.
• In Unit 7 Session 2.1 teachers are prompted to say, “Does it make sense that (two students) got the same number even though they counted in different ways?” This question could prompt a student to construct an argument, but there is no other assistance for teachers if students don’t answer on their own. The teachers are also reminded to ask their students if they agree with their classmates explanations, but there are no other questions or prompts to assist in analyzing those arguments.

There are a few places where the materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.

• In Unit 3 Session 3.6 the teacher leads a whole group discussion about determining which equations are true and which ones are false. As students give their explanations, the teacher is prompted to encourage kids to think about what mistakes the students could have made and share their thoughts. The teacher is also provided with possible explanations that students could give which would assist students in analyzing the arguments of others.