3rd Grade - Gateway 1

The materials reviewed for Achievement First Mathematics Grade 3 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. Each unit 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: 

• Unit 3, Post-Assessment, Item 1, “Round 452 to the nearest ten.” (3.NBT.1)

• Unit 5, Post-Assessment, Item 10, “Mark and his family were eating pizza for dinner. The pizza was split into 8 parts. Mark, his mom and his dad each ate one slice. What fraction of the pizza was NOT eaten?” (3.NF.1)

• Unit 7, Post-Assessment, Item 1, “Tyshio spent $48 on gifts for her friends. She bought gifts for 6 friends. How much did each gift cost?” (3.OA.3)

• Unit 8, Post-Assessment, Item 3, “Mike runs 2 miles a day. His goal is to run 25 miles. After 5 days, how many miles does Mike have left to run in order to reach his goal?” (3.OA.8)

There is one above grade level assessment item that can be omitted or modified without impacting the underlying structure of the materials. For example: 

• Unit 4 Post- Assessment, Item 2, “Ophelia had 64 ounces of milk. She wants to pour an equal amount of milk into 8 glasses for her children. How many ounces will Ophelia pour into each glass?” (4.MD.1) 

Achievement First Mathematics Grade 3 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.

The materials reviewed for Achievement First Mathematics Grade 3 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 4, Lessons 4 and 5, Independent Practice, students use addition, subtraction, multiplication, and division to solve one-step word problems involving masses or values that are given in the same units (3.MD.2). Most items require students to use addition and subtraction, though practice is provided for all operations. Lesson 5, Independent Practice, Problem 6, students are shown a picture of a scale balance with a mass of 18g on one side and two oranges on the other. “Julian placed two oranges on the balance scale below with the weight shown. What is the weight of one orange?” 

• Unit 5, Lesson 2, Independent Practice, students partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole (3.G.2). Students practice partitioning fraction strips or shapes constructed with pattern blocks and record a specified portion as a fraction in 13 problems. In the Exit Ticket, Problem 2, students “Build the shaded shape below with your pattern blocks, tiles, or fraction strips. Then identify the unit fraction that represents the piece below that the arrow is pointing to.” An additional 13 items are provided in Practice Workbook D (pages 65-69) addressing this standard. 

• Unit 7, Lesson 4, Workshop, students fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations (3.OA.7). During Independent Practice, students solve multiplication facts using the number 9. The Exit Ticket also provides an opportunity to engage with 3.OA.7 as students solve four more problems. Problem 4, “Carter thinks that the product of 9×8 is 63. Use what you know about patterns of multiples of 9 to explain why you agree or disagree with Carter.”

The materials reviewed for Achievement First Mathematics Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 109 out of 127, which is approximately 86%.

• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 117 out of 132, which is approximately 89%. 

• The instructional minutes were calculated by taking the number of minutes devoted to the major work of the grade (10,380) and dividing it by the total number of instructional minutes (11,390), which is approximately 91%. 

A minute-level analysis is most representative of the 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 91% of the materials focus on major work of the grade.

The materials reviewed for Achievement First Mathematics Grade 3 meet expectations that supporting content 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:

• Unit 2, Lesson 5, Workshop, Problem 2, students analyze a pictograph where one picture represents 4 cars. The pictograph shows the following, Honda = 3 car pictures, Ford = 4 car pictures, Toyota = 6 car pictures, and Chevrolet = 4 car pictures. Students are asked, “a. Were there more Honda and Toyota cars or Ford and Chevrolet cars in the neighborhood? b. Eight of the Fords moved away, and 2 more families with Toyotas moved in. How many Ford and Toyotas are in the neighborhood now? c. Jiang is interpreting the pictograph and says there are 6 more Toyotas than Hondas in the neighborhood. Is he correct?” This problem connects the major work of 3.OA.1, interpret products of whole numbers, and 3.OA.5, apply properties of operations as strategies to multiple and divide, to the supporting work of 3.MD.3, solve “how many more” and “how many less” problems using information presented in the pictograph.

• Unit 5, Lesson 2, Independent Practice, Problem 2, “Build a model of the unit fraction below with your fraction strips. Then, record the shape you made on the rectangle and label one unit fraction \frac{1}{6}.” This problem connects the major work of 3.NF.1, understanding a fraction \frac{1}{b} as the quantity formed by one part when a whole is partitioned into b parts, to the supporting work of 3.G.2, partition shapes into parts with equal areas.

• Unit 6, Lesson 6, Exit Ticket, “Heather is measuring the length of glue sticks to the nearest \frac{1}{4} inch. The lengths she’s measured so far are in the table below. Measure the remaining glue sticks and add their lengths to the table. Use the data to draw a line plot below.” This problem connects the major work cluster of 3.NF.A to the supporting work standard of 3.MD.4, as students develop understanding of fractions as numbers by generating data and representing it on a line plot.

The materials reviewed for Achievement First Mathematics Grade 3 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 include: 

• Unit 2, Lesson 5 connects the supporting work of 3.MD.B to the supporting work of 3.NBT.A, as students interpret data and use the properties of operations to perform multi-digit arithmetic. Independent Practice, Problem 1a, using a bar graph students answer, “How many fewer visitors were there on the least busy day than on the busiest day?”

• Unit 3, Lesson 12 connects the major work of 3.MD.A, solve problems involving measurements and estimations of intervals of time, liquid volumes and masses of objects, to the major work of 3.OA.A, represent and solve problems involving multiplication and division. In Workshop, Problem 5, “Laila is practicing her new step routine. It takes her 8 seconds to do the routine once. How long will it take her to do the routine 5 times?”

• Unit 8, Lesson 8 connects the major work of 3.OA.D, solve problems involving the four operations, and identify and explain patterns in arithmetic, to the major work of 3.OA.A, as students represent and solve problems involving multiplication and division. In Workshop, Problem 4, “Joel needs highlighter and pencils for his classroom. He buys 6 packs of highlighters with 5 in each pack. He also buys 7 packs of pencils with 4 in each pack. How many more highlighters doesJoel buy than pencils?”

The materials reviewed for Achievement First Mathematics Grade 3 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. 

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:

• Unit 2, Unit Overview, Identify Desired Results: Identify the Standards lists 3.MD.3 as being addressed in this unit and identifies 2.MD.9, 2.NBT.2, 2.MD.10, and 3.OA.1 as Previous Grade Level Standards/Previously Taught & Related Standards. In the Linking Section, a brief description of the progression of the standards is given. “In grade 2, students draw a picture graph and a bar graph (with single-unit scale and including a title, axis labels, and category labels) to represent a data set with up to four categories. Using the information, students solve simple put-together, take-apart, and compare problems using information presented in a bar graph. Later in grade 3, students will return to generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch.”    

• Unit 8, Unit Overview, Identify Desired Results: Identify the Standards lists 3.OA.9 as being addressed in this unit and identifies 2.OA.1 as Previous Grade Level Standards/Previously Taught & Related Standards connected to it. In the Linking section, a brief description of the progression of the standards is given. “By the end of second grade they’ve mastered all of the addition/subtraction story problem types within 100 - and even tackled two step story problems. In third grade, they begin multiplication and solve equal groups/array story problem types within 100 and solve for two-step story problems with all four operations.” 

• Unit 9, Unit Overview, Identified Desired Results: Identify the Standards lists 3.G.1 as being addressed in this unit and identifies 2.G.A.1 under Previous Grade Level Standards/ Previously Taught and Related Standards. In the Linking section, a brief description of the progression of the standard is given. “In second grade, scholars learn to recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Specifically, they are taught to identify triangles, quadrilaterals, pentagons, hexagons, and cubes, many of which they have been able to recognize for years. In this unit, scholars use their same understanding of shape characteristics to classify different kinds of quadrilaterals. By the end of elementary school, scholars continue their work with classifying shapes based on their attributes. Specifically, scholars learn to classify shapes based on the presence or absence of parallel or perpendicular lines. They also learn to identify types of right triangles.”

The materials develop according to the grade-by-grade progressions in the Standards. Content from future grades are clearly identified and are related to grade-level work 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:

• Unit 4, Unit Overview, Linking (p.6), “Measurement as it pertains to estimating liquid volume and the masses of objects using standard units of grams, kilograms, liters, and milliliters is introduced in grade 3. Students will then have to apply this information to answer one- and two-step story problems about the measurements they collect. In grade 2, students followed a similar trajectory with length. They explored standard units of length and then related this to addition and subtraction. In fourth grade, students continue to solve word problems involving liquid volumes and masses of objects. However grade 4 scholars are also expected to be able to convert units within a single system (from a larger unit to a smaller unit) of units including km, m, cm; kg; g; lb., oz; l, ml; hr., min, sec.”

• Unit 9, Unit Overview, Linking (p.5), “In second grade, scholars learn to recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Specifically, they are taught to identify triangles, quadrilaterals, pentagon, hexagons, and cubes, many of which they have been able to recognize for years. In this unit, scholars use their same understanding of shape characteristics to classify different kinds of quadrilaterals. By the end of elementary school, scholars continue their work with classifying shapes based on their attributes. Specifically, scholars learn to classify shapes based on the presence or absence of parallel or perpendicular lines. They also learn to identify types of right triangles.”