2nd Grade - Gateway 2

The instructional materials reviewed for Grade 2 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 2 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 2.7 Math Practice Note lists MP5 and has students play "Quick Images." This is a game that uses Ten Frames instead of coins. The Math Practice Note talks specifically about the Ten Frame that highlights the structure of 10, combinations of ten, teen numbers as ten plus some amount, and 2-digit numbers as groups of ten and some number of ones. Students are not able to choose a tool in this session.
• The Unit 1 Session 3.1 Math Practice Note lists MP1 and has students work together to figure out how many children are in the class. They solve the problem in two different ways. The teacher asks students if she will get the same answer if she adds the number of boys to girls and if she adds the girls to the boys and encourages students to explain their thinking. The students are encouraged to explain their thinking and discuss if their answer makes sense. They are not having to persevere through this problem.
• The Unit 8 Session 1.1 Math Practice Note lists MP4 and introduces students to comparison problems with a smaller unknown. The teacher displays a story problem on the board and then draws a sketch to show what is being seen. She draws two bars to show the students number of stickers from the problem. In this session the teacher is doing all of the work, the student is not engaged in modeling with mathematics on their own.
• The Unit 8 Session 2.8 Math Practice Note lists MP1 and has students breaking up a hundred and some tens. The following question is posed: If a student started with 235 stickers and needs to take away 158, with 150 being taken away so far, how many stickers are left to take? The students are taken through this problem step-by-step and work on this as a whole group. This discussion of the activity does not have a student persevere or make sense of the problem.

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

• The Unit 4 Session 2.2 Math Practice Note lists MP1 and has students in pairs discuss and decide how they will collect their data about the number of teeth lost by students in other classes. They perform the same task with teeth lost in their classroom first. The Math Practice Note explains to the teacher that the step prior to collecting data is to devise a plan. Students are engaging in perseverance if they need to devise a plan and be clear about the question they will ask to be able to gather accurate data for their survey.
• The Unit 4 Session 2.3 Math Practice Note lists MP4 and has students predicting the number of teeth lost by students in other classrooms. They are asked to collect the data, make predictions about the data, and display the data. The representation of data students collected allowed them to make the predictions about the other classrooms. This is a real-world problem that uses a model to express the data.

The instructional materials reviewed for Grade 2 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 2 Session 2.2 students are asked to sort shapes into two categories, 4 sides with 4 right angles or 4 sides but not 4 right angles. The materials state, “If there is a disagreement, have students explain how they determine whether an angle is a right angle or not, and have them show how they “measure” the angles of the shape with the square tile?” This is an opportunity for students to construct their own viable argument, but there are no specific prompts or questions for analyzing the arguments of others, just agreeing or disagreeing.
• In Unit 5 Session 2.2 students are playing a game where they determine what number should be added to 79 in order to obtain a sum of 100, and the students are prompted to consider how they would answer this question knowing that 80 + 20 = 100. The students are prompted to construct other strategies besides the one that is presented, but there is not an opportunity for students to analyze the alternative strategies that are presented.
• In Unit 8 Session 1.2 students are prompted to construct arguments that support why certain subtraction expressions have a difference of 10. In this example, students are also prompted to construct their arguments in a specific way, and there are also no opportunities for students to analyze other arguments that might be presented.

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

• In Unit 1 Session 1.6 students are asked to figure out what part of the counting strip is incorrect, and they are supposed to discuss what is wrong, how they know, and how they could fix it. Students are also supposed to include why someone might have made the errors.

The instructional materials reviewed for Grade 2 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.

• The Unit 3 Session 2.4 Math Practice Note states, “When students notice a numerical pattern such as this one- that when 10 is added to a number, the tens place increases by 1 and the ones place stays the same- it is important that they explain why this pattern holds. Does this happen only for the numbers we have looked at, or will it happen for other numbers, too?” This note assists teachers in helping students construct viable arguments, but there is no assistance for analyzing the arguments of others.
• In Unit 6 Session 1.2 while students are comparing measurements with different units, the teacher is directed to ask, “(Holly’s) number is higher than anyone else’s? Does that mean that (her) jump was the longest? Why does (Holly) have the highest number?” These questions and the accompanying Math Practice Note assist teachers in engaging students in constructing an argument, but there are no questions or prompts to assist teachers in having students analyze the arguments of others.
• In Unit 8 Session 2.4 students are asked to examine three different strategies for adding two three-digit numbers, and the teacher is prompted to have “students share their understanding of why the two problems (one of the three strategies) are equivalent.” Through this prompt, students could begin to construct a viable 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.

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 1 Session 3.1 teachers are prompted to lead a discussion with the following: “First let’s see what people have for an answer to this problem. [Katrina] thinks 12. Who has a different answer?...Did anyone have another answer? People found a few different answers to this problem. Let’s hear how some of you solved the problem and see whether we can figure out why there are different answers. Last year, some of my students used the number line or the 100 chart to solve Enough for the Class? problems. How do you think they used these tools?” These questions assist the teacher in prompting students to construct their own argument, and they also provide different strategies that the students could use in analyzing the arguments of others.