Kindergarten - Gateway 2

The materials reviewed for Kindergarten partially meet the expectations for teachers and students spending sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade. Overall, the materials reviewed partially engage students in activities that require application.

Practice with the application of the major work of K.OA.2, solve addition and subtraction word problems, and add and subtract within 10, by using objects or drawings to represent the problem, can be found in 2 units of instruction.

• Unit 4 Session 2.2 during “Two Story Problems” students visualize, represent, and solve addition and subtraction story problems with result unknown; however, it is scaffolded with the teacher directing the students through this entire activity. During Session 2.3 “Acting Out Story Problems” students act out word problems and use strategies to solve. After solving both problems, they are asked to compare what is the same about the two problems and what is different. This session asks the students to apply their understanding of addition or subtraction by having them compare two word problems. During Session 2.5 “More or Less at the End” students visualize, represent, and solve addition and subtraction story problems with result unknown; however, it is scaffolded with the teacher directing the students through this discussion.
• Unit 6 Session 2.2 includes a whole-group classroom routine called “Story Problems.” This classroom routine requires students to apply what they know in order to solve the word problems. Students compare what is the same and different. The Focus Points of the routine are visualizing, representing, and solving addition word problems with result unknown and solving a set of related problems. Students are presented with two different word problems one at a time. Students are not told whether or not the word problem involves combining or removing. After solving the problem, students are asked, “Is this a problem about separating or taking away one group from another?” After solving both problems, they are also asked to compare what is the same about the two problems and what is different.

Some sessions listed as addressing K.OA.2 in the Content Guide do not require students to solve addition and subtraction word problems. This is found in Unit 4 Sessions 1.6, 1.7, 1.8, 1.9, 1.10, and 2.4. Also, the word problems that are given throughout the material are often routine.

The instructional materials reviewed for Kindergarten partially meet the expectations for balance of the three aspects of rigor within a grade. Although the instructional materials meet expectations for conceptual understanding and procedural skill and fluency, the three aspects of rigor are often addressed in separate parts of the Sessions. Materials addressing 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 all 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 Sessions. Procedural skill and fluency is typically introduced in separate Sessions and then practiced in the 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 Kindergarten 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.

The following are examples of how the materials do not develop the full meaning of some MPs:

• The Unit 1 Session 3.1 Math Practice Note lists MP1 and has students matching attributes. Students are asked to look at a chart asking “Are you a girl or boy?” The teacher walks them through counting the number of boys and girls in the class. The Math Practice Note states that developing the habit of double-checking will serve students throughout their mathematical studies. This session guides students through checking to make sure the information makes sense but does not have them persevere through a problem.
• The Unit 2 Session 1.7 Math Practice Note lists MP5 and has students play a game to be introduced to the Ten Frame. The Math Practice Note talks specifically about the introduction of the Ten Frame and how this tool will allow students to become familiar with numbers less than 10. This activity only has students learning about Ten Frames and does not allow them to choose any other tool.
• The Unit 4 Session 2.3 Math Practice Note lists MP4 and has students playing a one more or one less game with pennies and a number cube. Though they are using money, which is a real-world concept, the game itself is not actually modeling a real-world problem that could arise in everyday life, society, or the workplace.
• In Unit 5 Session 1.1 students are looking at 3-D shapes. The students are only using the set of eight shapes that the teacher has been informed to assemble. This session does not allow them to choose any other tool as is intended by MP5.

The following are examples of how the materials attend to the full meaning of some MPs:

• In Unit 6 Session 3.3 the Math Practice Note lists MP5 and has students making the number six. Students are encouraged to use cubes or their fingers to solve the problems given; however, they are not directly told to use any one specific tool and are able to choose a tool that works best for them and the problem.
• In Unit 7 Session 1.1 the Math Practice Note lists MP1 and has students matching and sorting during their Math Workshop time. Students are working in pairs to find attribute blocks that share at least one attribute. The Math Practice Note informs teachers that if students aren’t making sense of the problem that they should ask them questions to get them started. They are also prompting students to stay with the problem and persevere. This session attends to the full meaning of the MP 1.

The instructional materials reviewed for Kindergarten 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 5 Session 1.2 students work with partners exploring geoblocks, and in the activity, students discuss the size, shape, and position of the geoblocks relative to each other. The teacher is instructed to watch students work to see if students explain their ideas to their partner and then listen to their partner’s ideas. The teacher is instructed to ask other students in the class if their block looks like the chosen block and students answer. There is no direction for the students to explain their own descriptions or to analyze the descriptions of their partners.
• In Unit 7 Session 1.1 students are supposed to stand next to the teacher based on whether or not they meet a certain characteristic. There are no questions or prompt that have students explain or justify why they did or did not stand next to the teacher, and there are no opportunities for students to analyze the other's arguments.
• In Unit 8 Session 2.5 students are prompted to explain how they knew to correctly fill in their ten frame card while playing a game. There are no questions or prompts for the students to analyze other students’ explanations when multiple explanations are possible.

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

• In Unit 4 Session 2.7 students are asked to compare the sums of two pairs of numbers. Students are prompted to explain which sum is bigger, and multiple strategies for explaining their choice are shared throughout the class. All students are asked to analyze the explanations of others as they are prompted to indicate which of the shared strategies theirs is most alike.

The instructional materials reviewed for Kindergarten 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 3 Session 2.7 students are playing a game called Fill the Hexagons. Teachers are instructed to tell the students, “Before we discuss what you found out, take a minute to compare the hexagons you made with those of a person sitting near you. Did you find the same combinations? Did you find any that were different?” These instructions assist teachers in starting a dialogue between the students, but there is no specific assistance that could assist students in constructing their own argument about playing the game or analyzing the arguments of others when different combinations are discussed.
• In Unit 6 Session 1.1 the teacher is instructed to say the following prompt during a class activity that requires the measurement of body parts using cubes: “We found that my hand was nine cubes long, and (Mary’s) hand was five cubes long. Whose hand was longer? How do you know?” There are no questions or prompts that would assist the teacher in engaging students in analyzing the arguments of others.
• In Unit 8 Session 1.3 the teacher is instructed to say, “We have several different stories for the problem three minus two. Do you think these problems have the same answer or different answers? Why?” These questions prompt 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.

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 2 Session 1.5 the teacher is told to “ask students to describe what they noticed (while the teacher counted) and to suggest strategies that may help (the teacher) count more accurately.”