Kindergarten - Gateway 1

The instructional materials reviewed for Achievement First Mathematics Kindergarten meet expectations for assessing grade-level content. Above-grade-level assessment questions are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

The series is divided into nine units, and each unit contains a Unit Assessment available online in the Unit Overview document and can also be printed for students. The Unit Assessments contain written and interview questions. Some units contain suggestions for use of Post-Unit Assessment questions as Pre-Unit Assessment questions. Teachers are directed to adjust instruction according to the Pre-Assessment results. 

Examples of assessment questions aligned to grade-level standards include:

• In Unit 2, Geometry Interview Questions, Task 1 states, “Put a triangle above a square and ask, ‘Where is the triangle in relation to the square?’” (K.G.1)
• In Unit 5, Counting & Comparing Unit 5 Assessment, Question 2 states, “Look at the slices of pizza, (picture of five slices of pizza). Circle the group of ice cream cones that has more than the slices of pizza, (picture of one group of eight ice cream cones and another picture of six ice cream cones).” (K.CC.6)
• In Unit 6, Counting Unit 6 Assessment, Question 9 states, “There were 10 cupcakes on the table. Jamaine ate 4 cupcakes. How many cupcakes are on the table now?” (K.OA.2)
• In Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 3 states, “Draw a picture and write a number sentence to show 17 as tens and ones.” (K.NBT.1)

There are examples of above-grade-level assessment questions. In Unit 8, four of the seven questions assess above-grade-level content. The Guide to Implementing AF Math: Grade K states, “Teachers should remove these items or use them for extension purposes only.” For example:

• In Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 4 states, “How many tens are in the number 37? A. 3 B. 37 C. 7 D. 73.” The Unit 8 Scoring Guide identifies this as a Grade 1 standard, 1.NBT.2. However, K.NBT.1 requires students to work with numbers between 11-19 to gain foundations for place value. 
• In Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 5 states, “Keisha drew sticks and dots to show how many blocks she had. How many blocks does Keisha have? A. 34 B. 7 C. 43 D. 44.” A picture representing 43 is between the question and answers. The Unit 8 Scoring Guide identifies this as a Grade 1 standard, 1.NBT.2. However, K.NBT.1 requires students to work with numbers between 11-19 to gain foundations for place value. 
• In Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 6 states, “Gloria wants to draw a picture to represent the number 26 as tens and ones. What could she draw to show the number 26 as tens and ones?” The Unit 8 Scoring Guide identifies this as a Grade 1 standard, 1.NBT.2. However, K.NBT.1 requires students to work with numbers between 11-19 to gain foundations for place value. 
• In Unit 8, Two-Digit Numbers Unit 8 Assessment, Question 7 states, “Use sticks and dots to show 42.” The Unit 8 Scoring Guide identifies this as a Grade 1 standard, 1.NBT.2. However, K.NBT.1 requires students to work with numbers between 11-19 to gain foundations for place value.

The instructional materials reviewed for Achievement First Mathematics Kindergarten meet expectations for spending a majority of instructional time on major work of the grade. 

• The approximate number of units devoted to major work of the grade, including assessments and supporting work connected to the major work, is 6 out of 9, which is approximately 67%.
• The number of lessons devoted to major work of the grade, including assessments and supporting work connected to the major work, is approximately 124 out of 163, which is approximately 76%. 
• The instructional block includes a math lesson, math stories, and math practice components. The non-major component minutes were deducted from the total instructional minutes resulting in 9,420 major work minutes out of 13,855 total instructional minutes. As a result of dividing the major work minutes by the total minutes, approximately 68% of the instructional materials focus on major work of the grade. 

A minute-level analysis is most representative of the instructional materials because the minutes consider all components included during math instructional time. As a result, approximately 68% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Achievement First Mathematics Kindergarten meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The publishers identify connections between supporting content and major work within the lesson plan in the “Standards in Lesson” section, as well as in the Guide to Implementing AF Math: Grade K. Additional connections exist within the materials, although not always stated by the publisher. In addition, the publisher identifies the CCSSM clusters at the top of each lesson plan. However, in some cases, supporting clusters are misidentified as major clusters. For example, in Unit 2, Lesson 3, the publisher incorrectly identifies the Geometry Clusters as the major work of the grade. Examples of the connections between supporting work and major work include:

• In Unit 1, Lesson 5, Introduction, students engage with the supporting work of K.MD.3, classify objects into categories, and the major work of K.CC.5, count to answer “how many” questions. In Step 4, students sort pattern blocks by shape, then answer, “How Many? We need to figure out how many are in each group.”
• In Unit 2, Lesson 3, Exit Ticket, students engage with the supporting work of K.G.2, correctly name shapes, K.G.5, model shapes in the world by building shapes from components, and the major work of K.CC.5, count to answer “how many” questions. Students count sides and vertices and build them using geoboards. Problem 3 states, “Circle the shape that has 4 corners.” Students are shown pictures of a hexagon, a circle, a triangle, and a square. 
• In Unit 2, Lesson 12, Understand: Introduce the Problem, students engage with the supporting work of K.G.4, analyze and compare two-dimensional shapes, and the major work of K.OA.2, solve addition word problems. Students are asked to visualize the shapes being mentioned. The teacher says, “Get ready to make a mind movie! Close your eyes and turn on your ears!” The teacher poses the problem by reading it 2-3 times, “Noah has three shapes. Noah has one square. Noah has one rectangle. Noah has one triangle. Noah counts all the corners of each shape. How many corners does Noah count all together? Show and tell how you know.” After the problem is read, students create a drawing of the three shapes based on their knowledge of their attributes. They then count the corners to add them, and represent the addition with an equation. In this lesson K.G.4 is the only standard identified, not K.OA.2.
• In Unit 4, Lesson 5, Introduction, students engage with supporting work of K.MD.2, compare two objects to see which holds “more of”/”less of” the attribute, and the major work of K.CC.6, count to determine which group holds more. Students play a game called “Which holds more?” where they compare two objects and determine which holds more scoops of rice. The teacher asks, “How can we figure out which object has a larger capacity or holds more?” Students might say, “We can put in scoops of rice and count each to compare.” 
• In Unit 9, Lesson 5, Workshop engages with the supporting work of K.MD.3, classify objects into categories, count the number of objects in each category, and sort the categories by count; and the major work of K.OA.3, compose and decompose numbers less than or equal to 10 in more than one way while finding multiple combinations of 10 pink and blue beads to make groups of 10. The Workshop worksheet states, “Introduction: Linda has pink beads and blue beads. Linda has some bags. Linda wants to put 10 beads in each bag. Some must be pink and some must be blue. How many different ways can Linda put pink beads and blue beads in bags? Show all of your mathematical thinking.”
• Kindergarten Practice Workbook A, students engage with the supporting work of K.MD.3, classify objects into given categories, and the major work of K.CC.5, count the number of objects to answer “How many?” Problem 1 states, “Color each group of 3.” The directions are followed by a picture of three rectangles, five triangles, three circles, and four squares.

The instructional materials reviewed for Achievement First Mathematics Kindergarten meet expectations that the amount of content designated for one grade-level is viable for one school year. The Guide to Implementing AF, Grade K includes a scope and sequence which states, “Not every lesson is entirely focused on grade level standards, and, therefore, some lessons can be used for either remediation or enrichment.” As designed, the instructional materials can be completed in 163 days. One day is provided for each lesson and one day is allotted for each unit assessment.

• Nine units with 155 lessons in total.
• The Guide to Implementing identifies lessons as either R (remediation), O (on grade level), or E (enrichment). There are 22 lessons identified as E (enrichment), 1 identified as R (remediation) and 132 identified as O (on grade level).
• Eight days for unit assessments. Unit 9 does not have a unit assessment. 

The publisher recommends 85 minutes of mathematics instruction daily.

• There are two lesson types, Game Introduction Lesson or Task Based Lesson. Each lesson is designed for 45 minutes. 
• Math stories are designed for 25 minutes. 
• Calendar/practice is designed for 15 minutes.

The instructional materials reviewed for Achievement First Mathematics Kindergarten meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. The publisher identifies the CCSSM clusters at the top of each lesson plan. However, in some cases, supporting clusters are misidentified as major clusters. For example, in Unit 2, Lesson 3, the publisher incorrectly identifies the Geometry Clusters as the major work of the grade. 

The materials include learning objectives, or Aims, that are visibly shaped by CCSSM cluster headings. Examples include: 

• In Unit 2, Lesson 2, Aim is shaped by K.G.A, identify and describe shapes and K.G.B, analyze, compare, compose, and create shapes. The materials state, “SWBAT identify 2D shapes (triangle, square, rectangle, circle, hexagon) by noticing their attributes (sides and corners). SWBAT create 2D shapes (triangle, square, rectangle, hexagon) by noticing their attributes.”
• In Unit 3, Lesson 5, Aim is shaped by K.CC.B, count to tell the number of objects. The materials state, “SWBAT represent a quantity 5-15 pictorially by using a strategy to keep track of the count.”
• In Unit 5, Lesson 3, Aim is shaped by K.CC.C, compare numbers. The materials state, “SWBAT determine if groups are equal or which group has more and which has less by arranging the cubes (building towers or matching 1:1) and comparing directly.”
• In Unit 6, Lesson 2, Aim is shaped by K.OA.A, understand addition as putting together and adding to, and subtraction as taking apart and taking from. The materials state, “SWBAT find the total of two groups of objects and represent with an addition equation.”
• In Unit 8, Lesson 6, Aim is shaped by K.NBT.A, work with numbers 11-19 to gain foundations for place value. The materials state, “SWBAT compose teen numbers by looking at a group of ten ones and some more ones and using a strategy that works for them (count all, count on, just know).” 

Materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. The publisher identifies the CCSSM Clusters at the top of each lesson plan. However, in some cases, supporting clusters are misidentified as major clusters. For example, in Unit 2, Lesson 8, the publisher incorrectly identifies the Geometry clusters as the major work of the grade. Examples of connections include:

• In Unit 3, Lesson 24, Exit Ticket, students engage with K.CC.B, count to tell the number of objects, and K.NBT.A, work with numbers 11-19 to gain foundations for place value, as they count a number represented in two ten frames. Problem 1 shows two tens frames with ten and six ones and states, “How many are there?”
• In Unit 2, Lesson 8, Workshop, students engage with K.G.A, identify and describe shapes, and K.G.B, analyze, compare, create, and compose shapes, as they match the faces of 3D solids to 2D shapes. The Student Workshop Worksheet states, “Makkelle had a can of soup. She wanted to put a label on it that would cover the whole top face. What shape would the label be? A. (insert a picture of a rectangle) B. (insert a picture of a circle) C. (insert a picture of a triangle).” Students are provided with a cylinder to represent the can of soup.
• In Unit 8, Lesson 7, Workshop, Exit Ticket, students engage with K.NBT.A, work with numbers 11-19 to gain foundations for place value, and K.OA.A, understand addition as putting together and adding to, and understand subtraction as taking apart and taking from, as they make drawings to decompose teen numbers into ten ones, and some more ones. Problem 1 states, “Write a number sentence to show the number 13 as a group of ten ones and some more ones.”
• Practice Workbook B, students engage with K.G.A, identify and describe shapes, and, although not stated, K.G.B, analyze, compare, create, and compose shapes, as they draw shapes in relation to one another. Problem 2 states, “Look at the star. Draw a circle below the star. Draw a triangle above the star. Draw a rectangle next to the star.”