1st Grade - Gateway 1

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. Above-grade-level assessment questions are present but could be modified or omitted without a significant impact on the underlying structure of the 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. Unit Assessments 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. Some parts of the assessment may be read to the students or done orally in small groups. 

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

• Unit 2, Geometry Unit Assessment, Question 2, “Cross out the shapes that have 4 corners.” Pictures of a variety of two-dimensional shapes are given. (1.G.1)

• Unit 3, Story Problems 1 Unit Assessment, Question 1, “Maya had 3 books. Sean had 5 books. How many books did they all have?” (1.OA.1)

• Unit 5, Addition & Subtraction Unit Assessment, Question 5, “a. Sally had 4 stickers in her sticker collection. Her teacher gave her some more. Now she has 12. How many stickers did her teacher give her? b. What subtraction problem could you use to solve this story problem?” (1.OA.6) 

• Unit 6, Two-Digit Numbers 1 Unit Assessment, Question 2, “Shanaya had 47 cubes. How many towers of ten could she make and how many single cubes would be left over?” (1.NBT.2)

• Unit 8, Measurement Unit Assessment, Question 1, “Which shows the flowers in order from shortest to tallest?” The item is followed by four choices, each displaying three flowers in different order by height. (1.MD.1)

There are examples of above-grade-level assessment questions. The Guide to Implementing AF Math: Grade 1 and the assessments do not consistently align questions to the same standards. The Guide to Implementing AF Math: Grade 1, “Teachers should remove these items or use them for extension purposes only.” For example:

• Unit 8, Measurement Unit Assessment, Question 4, “Steven’s foot is two inches shorter than Jason’s foot. Jason’s foot is 7 inches long. How long is Steven’s foot?” According to the Guide for Implementing AF Math: Grade 1, “Problems 4, 9, and 10 align with standard 2.MD.5.”

• Unit 8, Measurement Unit Assessment, Question 9, “Trout keepers are 10 inches long. Kim caught a trout that was 7 inches long. How much longer would her trout need to be to be a keeper?” According to the Guide for Implementing AF Math: Grade 1, “Problems 4, 9, and 10 align with standard 2.MD.5.”

• Unit 8, Measurement Unit Assessment, Question 10, “Julie’s bike is longer than Dave’s bike. Sarah’s bike is shorter than Dave’s bike. Whose bike is longer Julie’s or Sarah’s?” According to the Guide for Implementing AF Math: Grade 1, “Problems 4, 9, and 10 align with standard 2.MD.5.”

• Unit 9, Two-Digit Numbers 2 Unit Assessment, Question 7, “67-22.” In Grade 1, students subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (1.NBT.6). This question aligns to 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction).

• Unit 9, Two-Digit Numbers 2 Unit Assessment, Question 8, “88-54.” In Grade 1, students subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (1.NBT.6). This question aligns to 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction).

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. 

Each unit consists of lessons that are broken into four components: Introduction, Workshop/ Discussion, Independent Practice, and Exit Ticket. In addition to lessons, there are Math Stories “to enable students to make connections, identify and practice representation and calculation strategies, and develop deep conceptual understanding through the introduction of a specific story problem type in a clear and focused fashion with deliberate questioning and independent work time,” and Math Practice (Practice Workbook) for students “to build procedural skill and fluency.” Examples include:

• Unit 2, Lesson 3, Exit Slip, students engage with 1.G.1 as they build and draw shapes that possess defining attributes. Students experience the full intent of 1.G.1 as they draw three-sided shapes with defining attributes. “Rule: Shapes with exactly 3 corners. In the shape draw a circle that meets the rule. Outside the circle, draw a shape that does not meet the rule.”

• Unit 6, Lesson 17, Workshop, students engage with 1.NBT.5 as they are given a two-digit number and asked to mentally find 10 more or 10 less than the number, without having to count and explain the reasoning used. Students practice the skill of mentally finding 10 more or 10 less through a card game of Leapfrog. Students roll dice telling them how many spaces to move forward on a game board, then draw a card telling them how many tens to leap ahead. The Workshop includes Check for Understanding questions such as “How did you solve? Why? Why does that work?” The full intent of the standard is met as students explain their reasoning. In the Exit Ticket, Problem 2, “Solve. 58 + 30 = ______.” 

• Unit 8, Lesson 7, students engage with 1.MD.1 as they order three objects by length and compare the lengths of two objects indirectly by using a third object. Students are provided with extensive work with this standard including five problems during Workshop, two problems within Practice Workbook D and eight problems within the Exit Tickets. Exit Ticket, “On the lines below, write the names of the objects in order from shortest to longest.” Students are shown images of a cup, a sneaker, and a ball.

• Unit 5, Lessons 18-23, students engage with 1.OA.7 to understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. There are six lessons addressing this standard. As a result, the full intent of the standard is met for all students. The lessons focus on students matching expressions that are equal, asking the question “are they the same amount?”, determining if an equation is true or false by asking “are both sides of the equal sign the same value, by creating true equations using what they know about the equal sign, and revising false equations to make them true. In Lesson 20, Introduce the Math, “Yesterday we learned what the word equal means. What does equal mean? (Equal means the same.) In math, we have a special symbol to show that two amounts are equal. Raise your hand if you know what it is. (The equal sign.)...Today, we will learn more about the equal sign and how it works in equations by playing a game called True or False Sort. In this game, you will see lots of equations...Some will be true and some will be false like the one we just saw. It’s our job to figure out which is which.”

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of units devoted to major work of the grade, including assessments and supporting work connected to the major work, is 6.5 out of 9, which is approximately 72%.

• The number of lessons devoted to major work of the grade, including assessments and supporting work connected to the major work, is approximately 113 out of 150, which is approximately 75%. 

• 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 9,200 major work minutes out of 12,750 total instructional minutes. As a result of dividing the major work minutes by the total minutes, approximately 72% of the materials focus on major work of the grade. 

A minute-level analysis is most representative of the materials because the minutes consider all components included during math instructional time. As a result, approximately 72% of the materials focus on major work of the grade.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations that supporting content 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 1. 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 as the “CC Clusters in Unit.” However, the major clusters listed are not consistent throughout the unit, and, therefore, it is unclear how the publisher identified clusters connected to the unit. For example, in Unit 5, Lesson 7, the publisher identifies 1.OA.A, represent and solve problems involving addition and subtraction, as connected to Unit 5. However, the 1.OA.A standards are not identified in any Unit 5 lesson. Examples of the connections between supporting work and major work includE:

• Unit 2, Lesson 7, Exit Ticket, students engage with the supporting work of 1.G.2, compose two-dimensional shapes or three-dimensional shapes to create a composite shape and the major work of 1.OA.1, use addition and subtraction within 20 to solve word problems by having students determine how to use the fewest pattern block shapes to fill a larger shape, complete a table, and add to find the total number of shapes used. Problem 2, “Elijah is trying to figure out a way to fill the same pattern using more than 4 pattern blocks. What is a way that he can fill the shape that uses more than 4 pattern blocks? Fill in the table to show how you fill the shape.” The table provided includes pictures of the different pattern blocks available, a place to record the number used, and a place to provide the total number of blocks used. 

• Unit 4, Lesson 4, Exit Ticket, students engage with the supporting work of 1.MD.4, interpret data with up to three categories and answer questions about the total number of data points. This lesson also addresses, although not stated, the major work of 1.OA.2, adding three whole numbers whose sum is less than or equal to 20. A bar graph is shown representing the favorite sport of 3rd graders. Problem 3, “How many kids took the survey?” 

• Unit 7, Lesson 6, Exit Ticket, students engage with the supporting work of 1.MD.3, tell and write time in hours and half-hours and with the major work of 1.NBT.1, read and write numbers to 120. In this lesson, students tell and write time in hours and half-hours using analog and digital clocks. In Problem 1, students are shown a digital clock showing 10:30 as the time. They are given a clock face without hands on it and asked to, “Draw the hands to show the time.” 

• Practice Workbook E, students engage with the supporting work of 1.MD.4, interpreting data up to three categories, and the major work of 1.OA.2, solving word problems that call for addition of three whole numbers whose sum is less than or equal to 20. 1.MD.4 is the only standard identified for this problem. In Problem 2, students are presented with a table that shows the types of shoe ties with three categories: “velcro, laces, no ties.” Students are asked, “Write a number sentence to show how many total students are asked about their shoes.”

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.  Examples of connections include:

• Unit 3, Lesson 7, Exit Ticket, students engage with 1.OA.B, understand and apply properties of operations and the relationship between addition and subtraction, and 1.OA.C, add and subtract within 20, as they are provided different strategy options to solve and write an addition equation. Problem 1, “Solve for the unknown. Write an addition equation that shows the parts and whole (You may use the number line but do not have to.)” Students are provided with a number bond with 8 and 5 in two of the circles, a space to write the addition equation, and a number line to use. 

• Unit 5, Lesson 18, Workshop, students engage with 1.OA.B, understand and apply the properties of operations and the relationship between addition and subtraction, 1.OA.C, add and subtract within 20, and 1.OA.D, work with addition and subtraction equations. During Workshop, students play a game called “True Match” in which they use the strategies explored in recent lessons to solve efficiently. They have two sets of cards with equivalent matches and are to use the following strategies: solve for the total by counting on, solve for the total by making ten, just know the total, and just know the equivalent expression without solving either expression (compensating). 

• Unit 6, Lesson 5, Workshop, students engage with 1.NBT.B, understand place value, and 1.NBT.A, extend the counting sequence, as they draw numbers 10-90 using sticks and dots and write the numeral. Exit Ticket, Problem 2, “If you have 4 tens and 2 ones, how many do you have? Represent with sticks and dots and write the numeral.”

• Unit 7, Lesson 5, Worksheet Packets engage students with 1.MD.B, tell and write time, and 1.G.A, reason with shapes and their attributes, as they identify a clock with a given time. Problem 1, “Circle the correct clock. 1. Half past 10 o’clock.” Students are provided with three clocks (10:30, 11:30, and 12:30).

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 

The Unit Overview supports the progression of First Grade standards by explicitly stating connections between prior grades and current grade level work. Each Unit Overview contains an Identify the Narrative component that identifies connections to what students learned before this First Grade unit and/or concepts previously learned in Kindergarten. 

Each Unit Overview also contains an Identify Desired Results: Identify the Standards section that makes connections to supporting standards learned prior to the unit. In addition, some lessons make connections to previous grade-level learning in the Narrative section. Examples include: 

• Unit 1, Lesson 2, Narrative, What is new and/or hard about the lesson?, “Students will be familiar with counting by tens and ones from kindergarten, and many will recall that it is useful to group objects into sets of tens and ones from their work with teen numbers.”

• Unit 2, Geometry Unit Overview, Identify the Narrative, “Throughout the unit, students identify the defining characteristics, or attributes, of two- and three-dimensional shapes, building on their Kindergarten experiences of sorting, analyzing, comparing, and creating various two- and three-dimensional shapes and objects (1.G.1).”

• Unit 3, Story Problems Unit Overview, Identify Desired Results, “K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings (no detail), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations,” and “K.OA.5 Fluently add and subtract within 5” as previous grade level standards related to “1.OA.1 Use addition and subtraction within 20 to solve world problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol of the unknown number to represent the problem.”

• Unit 5, Addition and Subtraction Unit Overview, Identify the Narrative, “Make 10 is a valuable strategy in the base-ten system because it allows students to work flexibly with numbers to solve more challenging problems by breaking them down into easier problems that they can solve fluently. The building blocks for the make ten strategy are built in Kindergarten, as students become familiar with number partners for numbers 1-10, decompose teen numbers into a group of ten and some more ones. If students are struggling to use the make ten strategy, teachers should ensure that the students solidly understand K.OA.4, K.OA.3, and K.NBT.1 because they are foundational for the make ten strategy.” 

• Unit 8, Measurement Unit Overview, Identify Desired Results: Identify the Standards, 1.MD.2 (Express the length of an object as a whole number of length unit, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.) is identified as a Unit 8 standard. The Kindergarten standard identified as foundational is K.MD.1 (Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.) 

The Unit Overview documents contain an Identify the Narrative component that looks ahead to content taught in future grades. In addition, the Linking section includes connections taught in future grades, units, or lessons. Evidence of prior and future grade-level work supporting the progressions in the standards is identified. Examples include: 

• Unit 1, Counting Unit Overview, Identify the Narrative, Linking, “Continuing through the rest of elementary school, students will use the counting sequence in all grades. In 2nd grade they’ll be using the counting and place value patterns to count to 1,000 and add and subtract within 1,000. This becomes fluent in 3rd grade. By fourth grade, they’ve generalized the counting and place value patterns to all numbers and can add and subtract any size and number.”

• Unit 3, Story Problems Unit Overview, Identify The Narrative, Linking, “In the rest of elementary school, students will continue to work with story problems following the protocol taught and practiced in this unit. In second grade, students will master the start unknown, compare-bigger unknown-fewer, and compare-smaller unknown-more problem types that they were exposed to in this unit, and they will begin to solve two-step story problems. They will continue to expand their bank of representation and solution strategies.”

• Unit 5, Addition and Subtraction Unit Overview, Identify the Narrative, Linking, “Looking ahead to the remainder of first grade, students will continue to use the strategies taught in this unit to efficiently solve addition and subtraction problems and story problems within 20. They will build on these strategies to solve problems beyond 20 and up to 100, especially using count on and count back to add and subtract multiples of 10 to two-digit numbers.”

• Unit 8, Measurement Unit Overview, Identify The Narrative, Linking, “In the remainder of first grade, comparing lengths of objects help support students in understanding and solving compare-difference unknown story problems. Moving into second grade, students begin to use standard units of measurements such as rulers, yardsticks, meter sticks, and measuring tapes to measure and estimate length. They relate the length of a unit of measurement to the length of the object being measured with that unit. (For example, students recognize that a table would be more inches long than feet because inches are shorter than feet.) Second graders also build on the compare work they did in first grade to determine how much longer one object is than another, expressing the difference in terms of a standard length unit.”

• Unit 9, Two Digit Numbers 2 Unit Overview, Identify the Narrative, Structural Overview outlines the concepts of addition and subtraction across grades K to 4. The visual shows that addition and subtraction within 10 occurs in Kindergarten, while within 100 occurs in First Grade and within 1,000 occurs in Second through Fourth Grades. It also identifies that Properties of Addition and Subtraction are learned from First Grade through to Fourth Grade, while the Standard Algorithm for addition and subtraction is taught in Fourth Grade.