5th 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 5 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 5 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 5 meet expectations for assessing grade-level content. Each unit of instruction contains a Post-Assessment which is a summative assessment based on the standards designated in that unit. Examples of assessment items aligned to grade-level standards include:
- In Unit 1, Common Core, Item 23 states, “What is 43.98 rounded to the nearest tenths place?” (5.NBT.4)
- In Unit 4, Unit Assessment, Item 3 states, “A rectangular garden has an area of 400 square meters. If the garden has a width of 5 meters, how long is the garden?” (5.NBT.2)
- In Unit 5, Unit Assessment, Item 1 states, “At a Sand Castle building contest, the tallest tower was 2 yards tall and the shortest tower was 1 foot and 4 inches tall. How much taller was the tallest tower than the shortest tower?” (5.MD.2)
- In Unit 8, Post-Assessment, Item 4 states, “Anthony has 12 marbles if $$\frac{3}{4}$$ of the marbles are clear, how many clear marbles does Anthony have. Draw a model to show your answer.” (5.NF.4)
Achievement First Mathematics Grade 5 has assessments linked to external resources in some Unit Overviews; however there is no clear delineation as to whether the assessment is used for formative, interim, cumulative or summative purposes.
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 5, when used as designed, spend approximately 88% 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 5 meet expectations for spending a majority of instructional time on major work of the grade.
- The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 88 out of 132, which is approximately 67%.
- The number of days devoted to major work (including assessments and supporting work connected to the major work) is 113 out of 143, which is approximately 79%.
- The instructional minutes were calculated by taking the number of minutes devoted to the major work of the grade (11,365) and dividing it by the total number of instructional minutes (12,870), which is approximately 88%.
A minute-level analysis is most representative of the instructional materials because the units and lessons do not include all of the components included in the math instructional time. The instructional block includes a math lesson, math stories, and math practice components. As a result, approximately 88% 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 5 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 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. There are opportunities in which supporting standards/clusters are used to support major work of the grade and are connected to the major standards/clusters of the grade. Examples include:
- In Unit 3, Lesson 2, Independent Practice, Ph.D Level Problem 1 states, “Carol sells bracelets and pairs of earrings at a craft fair. Each item sells for $8. Write an expression to show how much money Carol makes if she sells 23 bracelets and 17 pairs of earrings, but pays $25 to rent her booth.” This problem connects the major work of 5.NBT.5, fluently multiply multi-digit whole numbers, to the supporting work of 5.OA.A, writing and interpreting numerical expressions, as students write an expression and solve the problem.
- In Unit 5, Lesson 5, Exit Ticket, Problem 2 states, “Valerie uses 12 fluid oz of detergent each week for her laundry. If there are 5 cups of detergent in the bottle, in how many weeks will she need to buy a new bottle of detergent. Explain how you know.” This problem connects the major work of 5.NBT.B, perform operations with multi-digit whole numbers and with decimals to the hundreths, to the supporting standard 5.MD.1, convert among different sized standard measurement units within a given measurement system, as students perform a conversion and utilize at least one of the four operations to solve the problem.
- In Unit 10, Cumulative Review 10.1, Problem of the Day, Day 3 states, “This year, the managers of the farm will change the fraction of the budget for housing to $$\frac{1}{8}$$ but will leave the fraction of the budget for food and medical care the same. Again, the remaining portion of the budget will be for maintenance expenses. What is the difference between the fraction of the budget for maintenance this year and last year?” This problem connects the major work of 5.NF.1 to the supporting cluster 5.MD.B, as students represent and interpret data while solving a multi-step problem involving adding and subtracting fractions with unlike denominators.
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 5 meet expectations that the amount of content designated for one grade-level is viable for one school year. As designed, the instructional materials can be completed in 143 days.
- There are 10 units with 132 lessons total.
- There are 11 days for Post-Assessments.
According to The Guide to Implementing Achievement First Mathematics Grade 5, each lesson is designed to be completed in 90 minutes. For example:
- The math lessons are divided into three structural lesson types: conjecture-based lesson, exercise-based lesson, and error analysis lesson. The materials state, “On a given day students will be engaging in either a conjecture-based, exercise-based lesson or less often an error analysis lesson.”
- Four days of the instructional week contain a Math Lesson (55 minutes) and Cumulative Review (35 minutes). The Cumulative Review is broken down into different parts:
- Three days of Cumulative Review include Fluency (10 minutes), Mixed Practice (15 minutes), and Problem of the Day (10 minutes).
- One day of Cumulative Review includes Fluency (10 minutes) and Reteach/Quiz (25 Minutes).
- One day within the instructional week contains a Math Lesson (55 minutes) and Reteach Time Based on Data (35 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 5 partially meet expectations for being consistent with the progressions in the Standards. Content from prior or future grades is identified and connected to grade-level work. However, there is inconsistency across the materials in the identification of content and all students are not given extensive work with grade-level problems.
Overall, the materials develop according to the grade-by-grade progressions in the Standards. However, content is not consistently connected to future grades within each Unit Overview. Each Unit Overview contains a narrative that includes a “Linking” section that describes in detail the progression of the standards within the unit. Examples include:
- In Unit 2, Overview, Identify the Narrative states, “Following this unit, students study multi-digit whole number computation to develop fluency with standard algorithms for whole number in multiplication and division, before moving into fraction and decimal operations.” The materials further state, “In later grades students continue to leverage this work when forms of rational numbers (grade 6), operating with all forms of rational numbers (grades 6 and 7), understanding ratios and rates of changes (grade 6-8), creating probability models (grade 7), working on coordinate grids (grades 5-8), and creating graphs to represent data (grades 5-8).”
- In Unit 4, Unit Overview, Identify the Narrative states, “Throughout elementary school students are also writing simple expressions or equations to represent and solve word problems (2.OA.1, 3.OA.3, 4.OA.2). They use bar models to make sense of, think about, and solve simple real-world applications of multiplication. In fifth grade, students will leverage early work in Operations and Algebraic thinking to represent and solve real-world problems, and to write and evaluate mathematical expressions using the order of operations (5.OA.1, 5.OA.2).”
- In Unit 7, Unit Overview, Identify the Narrative states, “In 5th grade, students will progress to adding fractions and mixed numbers with unlike denominators. In 4th grade and Unit 1 in 5th grade, scholars learned to find equivalent fractions using models and the identity property. This skill will be a crucial prerequisite to this unit. Additionally, scholars also learned how to add and subtract fractions and mixed numbers with like denominators by using fraction tiles, drawing models, and using the standard algorithm. In fourth grade, this included some regrouping, which is typically where scholars struggle the most. It is recommended to assess prior knowledge/skill for adding and subtracting mixed numbers (with like denominators) where regrouping is required to determine how to best target pre-existing gaps while progressing in this unit.”
The instructional materials in Achievement First Mathematics Grade 5 do not provide opportunities for all students to engage with grade-level problems. Each unit consists of three types of lessons: conjecture based lessons, exercise based lessons, or an error analysis lesson. All three of these lessons types provide dedicated times for Partner Practice and Debrief, Independent Practice and Debrief, and Exit Tickets. The materials include Bachelor Level, Master Level, and Ph.D. Level specific tasks for Partner Practice and Independent Practice. As a result, all students are not provided with the opportunity to engage with grade-level problems to meet the full intent of the standard. Examples include:
- 5.NBT.2: According to the Implementation Guide, this standard is identified as being taught in two lessons: one in Unit 1, and the other in Unit 4; with 17 independent practice questions for Bachelor Level students, nine for Master Level students, and 11 for Ph.D Level students. While all students are provided with the opportunity to solve problems with exponents, students at the Bachelor Level do not have an opportunity to explain the patterns. For example, Unit 4, Lesson 8, Independent Practice, Bachelor Level, Problem 3 states, “Ms. Jenkins decided it was time to donate and sell all of her old books. She has 1,042 books. She donated 300 and sold the rest. A used book store let her drop off the books she was selling in boxes of 80. How many boxes did she have to drop off?”
- 5.OA.1: There are not opportunities to solve problems with brackets or braces. According to the Implementation Guide, this standard is identified as being taught in two lessons in Unit 3; with 11 independent practice questions for the Bachelor Level students, nine for Master Level students, and nine for Ph.D students. However, students at the Bachelor Level are not provided with the opportunity to solve problems with brackets or braces. For example, Unit 3, Lesson 1, Independent Practice, Bachelor Level, Problem 2 states, “Evaluate $$15 × (7 - 7) + (5 × 2) - 3$$.”
- 5.OA.2: According to the Implementation Guide, this standard is only identified and present in Unit 3, Lesson 2, with one independent practice question for Bachelor Level students, zero independent practice questions for Master Level students, and two independent practice questions for Ph.D students. For example, Unit 3, Lesson 2, Independent Practice, Ph.D Level states, “Carol sells bracelets and pairs of earrings at a craft fair. Each item sells for $8. Write an expression to show how much money Carol makes if she sells 23 bracelets and 17 pairs of earrings, but pays $25 to rent her booth.”
- 5.MD.1: There are not opportunities for students at all levels to solve multi-step word problems. According to the Implementation Guide, this standard is identified as being present in five lessons in Unit 5 and one lesson in Unit 6, with 24 independent practice questions for the Bachelor Level students, 22 for Master Level students, and nine for Ph.D students. At the Bachelor Level, students are not provided with the opportunity to solve multi-step problems and problems are focused mainly on conversions. For example, Unit 5, Lesson 2, Independent Practice, Bachelor Level, Problem 1 states, “___ pounds = 160 ounces.”
Achievement First Mathematics Grade 5 relates grade-level concepts explicitly to prior knowledge from earlier grades. Each unit has a Unit Overview and a section labeled “Identify Desired Results” where the standards for the unit are provided as well as a correlating section “Previous Grade Level Standards/Previously Taught & Related Standards” where prior grade-level standards are identified. Examples include:
- In Unit 2, Unit Overview, Identify Desired Results: Identify the Standards lists 5.NF as being addressed in this unit and 4.NF.1, 4.NF.2, and 4.NF.3 as Previous Grade Level Standards/ Previously Taught & Related Standards connections. The materials state, “Starting in 3rd grade, students learn to recognize fractions as numbers (3.NF.A). They learn to represent fractions concretely and pictorially using unit fractions, on a number line and with equivalent fractions. They also learn to reason about relative sizes of fractions that have the same numerator or denominator. In 4th grade, students extend their understanding of fractions to compare and order fractions using equivalent fractions (4.NF.A), add and subtract fractions with like denominators, and multiply fractions and whole numbers (4.NF.B).”
- In Unit 6, Unit Overview, Identify the Narrative connects the work of this unit to prior work in 3rd and 4th grades. The materials state, “Unit 6 draws heavily from Geometry and Numbers in Base Ten content learned in grades 3 and 4. In grade 3, students develop an understanding of area and relate the concept to both multiplication and addition. They also apply the concept to explore number properties (commutative and distributive) (3.MD.C). In fourth grade, students solidify their understanding of area and learn to apply the area formula fluently when measuring the area of rectangles (4.MD.3). These understandings and skills are useful moving into 5th grade as the concept of volume is developed concretely, pictorially and abstractly by making connections between volume and base-area using unit cubes, pictures and formulas as well as addition and multiplication to calculate the volume of a right rectangular prism. (5.MD.3,4,5).”
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 5 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.
The materials include learning objectives, identified as Aims, that are visibly shaped by the CCSM cluster headings. The instructional materials utilize the acronym SWBAT to stand for “Students will be able to” when identifying the lesson objectives. Examples include:
- In Unit 1, Lesson 8, the Aim states, “SWBAT explain the effect of multiplying or dividing by powers of ten on the location of digits in a number,” which is shaped by 5.NBT.A, “Understand the place value system.”
- In Unit 3, Lesson 2, the Aim states, “SWBAT write simple numerical expressions that record calculations with numbers and interpret numerical expressions without evaluating them,” which is shaped by 5.OA.A, “Write and interpret numerical expressions.”
- In Unit 6, Lesson 2 the Aim states, “SWBAT explore volume by building 3D figures and counting with unit cubes,” which is shaped by 5.MD.C, “Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.”
The 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 include:
- In Unit 6, Lesson 5, students connect 5.MD.C, understand concepts of volume and relate volume to multiplication and addition, to 5.NBT.B, perform operations with multi-digit whole numbers and decimals, as they determine unknown values for measurements based on a given volume. In Exit Ticket, Problem 2 states, “Bernard is packing a box with a volume of 96 cubic inches. Enter a possible base area and height for his box below.”
- In Unit 8, Cumulative Review 8.3, Problem of the Day, Day 3 connects 5.NBT.A, 5.NBT.B, and 5.OA.A, as students use their understanding of the place value system to evaluate a multi-step problems involving decimals, giving the answer in various forms. The materials state, “A.) Evaluate and express your answer in the three given forms: $$[(15×2)+(2×4)]+[12.06-(3×4)]$$; Standard Form, Expanded Form, Word Form.”
- In Unit 9, Cumulative Review 9.3, Problem of the Day, Day 2 connects 5.NBT.B with 5.NF.B, as students perform operations with multi-digit whole numbers and fractions. For example, “A chocolate factory produced 5,301 pounds of chocolate every day for 31 days in the month of January and 4,592 pounds of chocolate every day for 28 days in the month of February. Of their total chocolate produced, $$\frac{5}{8}$$ was milk chocolate. How many ounces of non-milk chocolate did the factory produce?”
- In Unit 11, Lesson 5, students connect 5.MD.B, represent and interpret data to 5.G.A, graph points on the coordinate plane to solve real-world and mathematical problems, as they generate data and develop a coordinate graph. In the Independent Practice, Bachelors Level states, “There is a $25 annual fee for membership at the gym. It also costs $5 per visit to use the gym. Fill in the table to show the total cost of $$\frac{5}{8}$$ visits to the gym. A. Write the ordered pairs, and graph the data on the coordinate graph. B. Write the ordered pair that represents 6 visits to the gym. Explain what the ordered pair means. C. If Amaya can only spend up to $50 in one month, how many times can she visit the gym? Explain.”