1st Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 92% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
The instructional materials reviewed for Achievement First Mathematics Grade 1 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focus by assessing grade-level content and spending at least 65% of instructional time on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.
Criterion 1.1: Focus
The instructional materials reviewed for Achievement First Mathematics Grade 1 meet expectations for not assessing topics before the grade level in which the topic should be introduced.
Indicator 1a
The instructional materials reviewed for Achievement First Mathematics Grade 1 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. 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:
- In Unit 2, Geometry Unit Assessment, Question 2 states, “Cross out the shapes that have 4 corners.” Pictures of a variety of two-dimensional shapes are given. (1.G.1)
- In 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)
- In Unit 5, Addition & Subtraction Unit Assessment, Question 5 states, “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)
- In Unit 6, Two-Digit Numbers 1 Unit Assessment, Question 2 states, “Shanaya had 47 cubes. How many towers of ten could she make and how many single cubes would be left over?” (1.NBT.2)
- In Unit 8, Measurement Unit Assessment, Question 1 states, “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 states, “Teachers should remove these items or use them for extension purposes only.” For example:
- In Unit 8, Measurement Unit Assessment, Question 4 states, “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.”
- In Unit 8, Measurement Unit Assessment, Question 9 states, “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.”
- In Unit 8, Measurement Unit Assessment, Question 10 states, “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.”
- In Unit 9, Two-Digit Numbers 2 Unit Assessment, Question 7 states, “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 subtraction).
- In Unit 9, Two-Digit Numbers 2 Unit Assessment, Question 8 states, “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 subtraction).
Criterion 1.2: Coherence
Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
The instructional materials reviewed for Achievement First Mathematics Grade 1, when used as designed, spend approximately 72% of instructional time on the major work of the grade, or supporting work connected to major work of the grade.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Achievement First Mathematics Grade 1 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 6.5 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 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 72% of the instructional materials focus on major work of the grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Achievement First Mathematics Grade 1 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The materials also foster coherence through connections at a single grade.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Achievement First Mathematics Grade 1 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 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 the following:
- In 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 states, “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.
- In 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 states, “How many kids took the survey?”
- In 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.”
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials reviewed for Achievement First Mathematics Grade 1 meet expectations that the amount of content designated for one grade-level is viable for one school year. The Guide to Implementing AF, Grade 1 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 150 days. One day is provided for each lesson and one day is allotted for each unit assessment.
- Nine units with 141 lessons in total.
- The Guide identifies lessons as either R (remediation), O (on grade level), or E (enrichment). There are 10 lessons identified as E (enrichment), 0 identified as R (remediation), and 131 identified as O (on grade level).
- Nine days for unit assessments.
When reviewing the materials for Achievement First, Grade 1, a difference in the number of total instructional days was found. Although the publisher states the curriculum will encompass 151 days, there are 150 days of lessons and unit assessments. The Grade 1 Unit Overview for Unit 6 shows 24 days for the unit while the Guide to Implementing AF, Grade 1 provides 23 days for the unit. The unit has 23 lessons including the 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.
Indicator 1e
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
The instructional materials reviewed for Achievement First Mathematics Grade 1 partially meet expectations for being consistent with the progressions in the Standards. Overall, the materials do not provide all students with extensive work on grade-level problems. The instructional materials develop according to the grade-by-grade progressions in the Standards. Content from future grades is clearly identified and relates to the grade-level work. The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier units. Within the overview for each unit, there is “Identify the Narrative” component, which provides a description of connections to concepts in prior and future grade levels.
The lessons follow a workshop model, including a Math Lesson, Math Stories, and Calendar/Fluency. Most lessons do not provide enough opportunity or resources for students to independently demonstrate mastery. The lessons include teacher-directed problems that the class solves together. Math stories are intended to occur every day there is a lesson, however there are insufficient math stories for each lesson day. In addition, many practice workbook pages are repeated across multiple units.
The materials develop according to the grade-by-grade progressions in the Standards. The Unit Overview documents contain an Identify the Narrative component that looks back at previous content or grade level standards and 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:
- In Unit 1, Counting Unit Overview, Identify the Narrative, Linking states, “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.”
- In Unit 3, Story Problems Unit Overview, Identify The Narrative, Linking states, “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.”
- In Unit 5, Addition and Subtraction Unit Overview, Identify the Narrative, Linking states, “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.”
- In Unit 8, Measurement Unit Overview, Identify The Narrative, Linking states, “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.”
- In 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.
Overall, the materials do not provide all students with extensive work on grade-level problems. The majority of the lessons implement 45 minutes of math workshop with a whole group introduction, workshop in pairs or small groups, mid-workshop interruption, whole group discussion, and closing with an exit slip. As it is unclear if students are working together or individually, workshop lessons may not provide enough opportunity for students to independently demonstrate mastery. The Guide to Implementing AF, Grade 1, describes the workshop component as, “Collaborative processing time to continue to develop understanding of prioritized concept and strategy.” The lessons include a teacher-directed introduction to the workshop “game” and follows up with students tasked to participate in the “game.” Most lessons include an exit ticket with one or two questions for the students to complete individually.
Beyond the lesson component of the math time, the Guide to Implementing AF Math, Grade 1 suggests 15 minutes of daily calendar and practice. Each unit indicates the Grade 1 Practice Workbook pages to be implemented during this time. However, the practice workbook pages contain a limited number of practice items and are recommended to be used repeatedly in different units. As a result of the limited number of opportunities to practice grade-level standards, the materials do not give students extensive work with grade-level problems.
Examples where the full intent of a standard is not met and/or extensive work is not provided include:
- In Unit 2, Lesson 13, Task (labeled Lesson 12 task in the lesson), students engage 1.G.1 as they build and draw shapes to possess defining attributes. Students do not experience the full intent or extensive work of 1.G.1 because they are only asked to draw four-sided shapes. Within the six Exit Tickets, students are not asked to independently build or draw shapes that possess defining attributes. For example, “Leah is learning about shapes. Leah makes for different shapes on her paper. The shapes are different colors and sizes, but all the shapes have four corners. What four different shapes can Leah make on her paper? Show all your mathematical thinking and be ready to explain your answer.”
- Unit 3, Lesson 11 is the only lesson students engage with the standard 1.OA.2 and practice solving word problems that call for addition of three whole numbers. The independent practice can be found on the Exit Ticket. The Practice Workbook for the grade-level provides zero problems to provide additional independent practice for this standard outside of the Exit Ticket. Extensive work is not provided for 1.OA.2. It is part of the major work of the grade, but is only addressed in 1 of the 141 lessons. In the Exit Ticket, Problem 1 states, “Chardae was drawing pictures of dogs. She drew 2 brown dogs, 3 black dogs, and 2 spotted dogs. How many dogs did she draw?”
- In Unit 5, Lesson 22, Workshop, students engage with 1.OA.8 as they determine the unknown whole number in an addition or subtraction equation relating three whole numbers. Students find the unknown numbers to make addition and subtraction equations true. This standard is addressed in only three lessons, and 16 Practice workbook problems. Exit Ticket states, “Fill in the blank to make the equations true. $$10 -$$ ____ = $$8 - 2$$, $$2 +$$ ____ $$= 3 + 4$$, $$4 + 5 = 5 +$$ ____”.
- In Unit 6, Lesson 17, Workshop, students engage with a portion of 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 do 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. However, the lesson does not address the full intent of the standard because students are not asked to explain their reasoning, as is part of the standard. In the Exit Ticket, Problem 2 states, “Solve. $$58 + 30 =$$ ______.”
- In Unit 7, Lesson 3, Workshop and Practice Workbook E, students engage with 1.G.3 as they partition circles and rectangles into two and four equal shares. However, only three lessons address the standard, 1.G.3, with four Exit Ticket problems and six Practice Workbook problems to independently practice partitioning. While students experience some practice during Workshop using the words halves, fourths, and quarters, they do not experience the use of the phrases “half of,” “fourth of,” and “quarter of.” As a result, students do not have the opportunity to meet the full intent of the standard. In addition, there are only three lessons that address 1.G.3 with limited independent practice; therefore, students do not get extensive work with this standard. During Workshop, students solve a story problem comparing halves and fourths of two same sized pies to determine who gets the biggest piece of pie.
- In Unit 8, Lesson 6, 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 only provided four problems within Practice Workbook D and three Exit Tickets to meet the full intent of this standard. All other independent work does not require students to use three objects to compare lengths. This is not sufficient to meet extensive work of the standard. The Exit Ticket states, “Shaquan’s crayon was shorter than Tyra’s crayon. Jesse’s crayon is longer than Tyra’s crayon. Whose crayon is longer - Jesse or Shaquan? How do you know?”
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:
- In Unit 1, Lesson 2, Narrative, What is new and/or hard about the lesson? states, “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.”
- In Unit 2, Geometry Unit Overview, Identify the Narrative states, “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).”
- In Unit 3, Story Problems Unit Overview, Identify Desired Results states, “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.”
- In Unit 5, Addition and Subtraction Unit Overview, Identify the Narrative states, “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.”
- In 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.)
Indicator 1f
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to 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 instructional materials reviewed for Achievement First Mathematics Grade 1 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 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 connect to each lesson.
The materials include learning objectives, or Aims, that are visibly shaped by CCSSM cluster headings. Examples include:
- In Unit 2, Lesson 4, Aim is shaped by 1.G.A, reason with shapes and their attributes. The materials state, “SWBAT decompose a shape by asking, Which smaller shapes could be put together to make the larger shape?”
- In Unit 4, Lesson 6, Aim is shaped by 1.MD.C, represent and interpret data. The materials state, “SWBAT solve comparison problems using a data set by using the graph as a representation or creating their own representation to match the graph.”
- In Unit 5, Lesson 10, Aim is shaped by 1.OA.B, understand and apply properties of operations and the relationship between addition and subtraction. The materials state, “SWBAT solve subtraction problems by decomposing a number leading to a ten.”
- In Unit 7, Lesson 6, Aim is shaped by 1.MD.B, tell and write time. The materials state, “SWBAT show time to the half hour by drawing the hour hand and minute hand.”
- In Unit 9, Lesson 4, Aim is shaped by 1.NBT.C, use place value understanding and properties of operations to add and subtract. The materials state, “SWBAT add a two-digit and a one-digit number with regrouping by using a strategy that makes sense to them (count on-cubes, sticks and dots, fingers… make ten).”
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. Examples of connections include:
- In 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 states, “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.
- In 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).
- In 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 states, “If you have 4 tens and 2 ones, how many do you have? Represent with sticks and dots and write the numeral.”
- In 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 states, “Circle the correct clock. 1. Half past 10 o’clock.” Students are provided with three clocks (10:30, 11:30, and 12:30).