Kindergarten - Gateway 2

The instructional materials for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials do not include non-routine problems. Students do not have the opportunity to demonstrate the use of mathematics flexibly. Pictures accompany word problems, and students are prompted often to use specific methods, such as number bonds, to solve the problems. For example:

• In Activity Book B, Lesson 12.4 pages 44-46 there are six story problems. Each of these problems are partially illustrated for the student. The first group is depicted in the illustration. The students use cutouts to add to the picture in order to find the total. Students use the model to solve routine problems.
• In Textbook B, Lesson 12.6 page 61, students make up a story to describe the picture on the page. The picture shows a fox eating and a fox with no food.
• In Textbook B,Lesson 13.1 page 69, the teacher gives situations for each of three problems. “Ask, ‘There were 5 balloons. 1 burst. How many balloons are still here?’” Each problem is illustrated with the original number of balloons. Students cross out the burst balloons and write the answer in the box. This is a routine application problem.
• In Activity Book B, Lesson 13.2 pages 51-52, there are four story problems centered around the nursery rhyme, Jack and Jill. All the rhymes start with “Jack and Jill went up the hill to fetch (total number of pails of water). Jack carried (set number) of pails. How many pails did Jill carry?”
• In Textbook B, Lesson 13.8 page 83, the Development section states, “Give each student linking cubes in two different colors. Tell the students to form a rod using two colors. Tell them they must use eight cubes altogether. Ask, 'How many cubes are there altogether? How many of them are red? How many of them are blue?'” This is the one opportunity students are provided for both addends in an unknown problem type.

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

• In Teacher’s Guide, Lesson 2.4 pages 29-30, MP3 is identified. However, when following the lesson plan, there is no opportunity for students to “construct a viable argument or critique the reasoning of others.” Students are instructed to work with others in the conclusion of the lesson. The directions state, “Have students work in groups to create a story that has sets of 1, 2, 3, 4 and 5 objects. Students can then share or act out their story to the rest of the class.”
• In Teacher’s Guide B, Lesson 11.2 page 49, MP1 and MP5 are listed in the Lesson Plans. When following the Lesson Plan, there is no opportunity for students to choose appropriate tools.
• MP1 is identified in Lesson 9.1. Students are given few opportunities to make sense of problems on their own. In the Textbook, page 2, the teacher is instructed, “Direct students’ attention to the first triangle in the top row on Textbook, page 2. 'What number is 1 more than 3?' Have them count the dots in the next triangle to confirm the answer. Guide them to say, “1 more than 3 is 4.”
• MP5 is identified in Chapter 11. In these lessons, students connect cubes and number bonds. The Teacher’s Guide does not identify opportunities for students to choose their own tools; rather, they are guided by the teacher and the drawings in the Textbook and Activity book to use specific tools. For example, in Teacher’s Guide, Lesson 11.3 page 51, and Textbook page 39, the teacher is directed, “Provide five linking cubes, two blue, and three red for each student. Have them use the cubes to show the number of lions and lionesses.” On Textbook page 39, students are shown two lions and three lionesses and a number bond that shows two connecting cubes in one part, three connecting cubes in the other part, and five connecting cubes in the whole.

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The student edition textbook and activity book do not have questions or problems where students justify their conclusions, communicate them to others, and respond to the arguments of others. Many questions presented in the content elicit one answer.

There are few prompts for students to construct viable arguments.

• MP3 is identified in Lesson 1.1. In this lesson, students compare objects to determine if they are the same or different (teacher edition page 3). The teacher is directed to “Show students the red and blue cup. Ask, ‘What can you tell me about these?’ Have students use their own words before modeling the language structure, ‘They are not exactly the same.’ Have students tell you why the cups are not exactly the same."
• MP3 is identified in Teacher’s Guide A, Lesson 1.2 page 6. The teacher asks the question, “Are these the same?” In the conclusion, the students are to “tell their partner about objects in the classroom that are the same but are placed differently.”
• MP3 is identified in Teacher’s Guide A, Lesson 1.5 pages 11-12. In Activity Book A, page 6, students choose one animal out of a line of four that is different from the others. Students are to give their reasons for their answers. Students explain their reason for picking an animal, but there is no mathematical reasoning required.
• MP3 is identified in Teacher’s Guide, Lesson 7.7 pages 158-159. Students use sentence frames to compare the number of shoes in the picture. “Guide students to say, ’The number of shoes with buckles is greater/fewer than the number of shoes with laces.’ and ‘There are more/fewer shoes with buckles than shoes with laces.’” There is no evidence of students constructing a viable argument or critiquing the reasoning of others in this lesson.

Students are not given opportunities to look at another student’s work and critique their solution or strategy. There are also no opportunities for students to look at two samples of work and justify which is correct.

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Teacher directions do not include prompts to lead discussions around the construction of viable arguments or to analyze the arguments of others. Materials do not give opportunities for teachers to present problems to the class that require students to develop arguments.

• Other than listing the Mathematical Practice in the beginning of these lessons, there is no other specific instruction to help the teacher engage students in constructing viable arguments or critique the reasoning of others.
• Teacher’s Guide A, Lesson 1.1 page 3 lists MP3 as the Mathematical Practice focused on in the lesson. The directions in the Teacher’s Guide state, “Ask, ‘What can you tell me about these?’ Have students use their own words before modeling the language structure, ‘They are not exactly the same.’“ These questions do not lend themselves to students justifying their mathematical thinking.
• Teacher’s Guide A, Lesson 1.5 pages 11-12 identifies MP3. “Teachers ask, ‘Are these two colored the same way?” Elicit the response, ‘No.'” Follow-up questions for teachers are not provided nor is there an opportunity for students to share their thinking.
• Teacher’s Guide A, Lesson 2.5 page 31 identifies MP3. Students show five fingers then bend some fingers. Teachers are prompted to ask, “'Are all their fingers different? Do any of them have the same finger form?' Elicit responses from students using ‘same’ and ‘different.’” No prompts are provided for the teacher to lead the students in a mathematical discussion.
• In Teacher’s Guide A, Lesson 8.10 page 180, students compare objects that are heavy and light. The teacher holds a dictionary in one hand and a pencil in the other. The teacher is prompted to, “Ask, ‘Which do you think is more difficult to carry?’ Say, ‘The dictionary is more difficult to carry. It is heavy.’ Guide students to say, ‘The dictionary is heavy.’ Say, ‘The pencil is easier to carry. It is light.’ Guide students to say, ‘The pencil is light.’" Students are prompted to give specific answers, and the teacher explains most concepts to the students.
• In Teacher’s Guide B, Lesson 13.7 page 104, the teacher asks, “How many insects are there altogether? How many of them are red? How many of them are green?” There is no follow-up question that asks students to justify their reasoning.

The instructional materials reviewed for Earlybird Kindergarten Mathematics Common Core Edition do not meet expectations for attending to the specialized language of mathematics.

• Materials do not always use accurate vocabulary. For example, in Teacher’s Guide, Lesson 8.9 page 179 and Student Materials page 186, students compare three bears using the terms big, bigger than, and biggest, and small, smaller than, and smallest. Another example can be found in Teacher’s Guide, Lesson 5.4 page 108. A rectangular prism is referred to as a rectangular block.
• Vocabulary words are listed at the beginning of each lesson but are not always explained/used within the lesson. For example, in Teacher’s Guide, Lesson 8.2 page 165, students compare the length of objects using the terms short and long. The words length, long, and short are not explained within the lesson nor in the previous lesson. Workbook page 67, which corresponds to Lesson 8.2, uses the words height and tall, and these words are also not explained.
• Vocabulary is not introduced in the chapters on addition and subtraction. Addition is introduced in Unit 11: Number Bonds. There is one vocabulary word included in this unit, which is number bond in theTeacher’s Guide, Lesson 11.3 page 51. Vocabulary such as add, addition, total, and sum are not included in the unit.
• Unit 12 introduces students to equations and the + and = symbols. This is not labeled as vocabulary within the lesson plans or introduced to the students within the lesson plan script. There is one vocabulary word included in this unit within Lesson 12.5, number line on page 79.
• Teachers Guide B, Unit 12, Lesson 1 page 67 states, “Have the students say, ‘2 and 3 make 5’ while you point at the numeral 2, then +, 3, and =. Hence, write the number 5 in the addition equation.“ Correct vocabulary is not shared with or explained to the students.
• In Teacher’s Guide, Unit 13, Lesson 13.5 page 99, subtraction sign and subtraction equation are listed in the lesson plans. Instruction is not given to the teacher or students for these vocabulary words. “Show students three balloons. Write the numeral '3' on the board. Have a student burst two balloons. Then, write the subtraction sign and ‘2’ to show ‘3-2’ on the board. Ask, “how many balloons are left? As you point to the remaining balloon. Finally, complete the subtraction equation to show 3 - 2 = 1”

An example where vocabulary is introduced and explained is in Unit 5. Unit 5 introduces students to cubes, cones, rectangular blocks, spheres, cylinders, circles, rectangles, squares, triangles, and hexagons.