3rd Grade - Gateway 3

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson.

There are seven instructional units in Grade 3. Lessons within the units include Anchor Tasks, Problem Sets, Homework, and Target Tasks. The Anchor Tasks serve either to connect prior learning or to engage students with a problem in which new math ideas are embedded. Students learn and practice new mathematics in the Anchor Tasks. For example:

• In Unit 6, Lesson 4, Anchor Task, Problem 2, students build and write non-unit fractions less than one whole (3.NF.1). The problem states, “Make a model in which the shaded part represents the corresponding unit fraction.” Students are given a circle to model, a rectangle to model, and a square to model.

In the Problem Set and Homework sections, students have opportunities to build on their understanding of each new concept. Each lesson ends with a Target Task which provides students the opportunity to apply what they have learned from the lesson, and can be used to formatively assess understanding of the content. For example:

• In Unit 2, Lesson 12, Problem Set, Problem 3, students solve one-step word problems involving multiplication and division using units of 3 and 4 (3.OA.1, 3.OA.2, 3.OA.3). The problem states, “Thirty third-graders go on a field trip. They are divided equally into 3 vans. How many students are in each van?”
• In Unit 4, Lesson 9, Homework, students compose and decompose rectangles, and learn that the sum of the areas of the decomposed rectangles is equal to the area of the composed rectangle (3.MD.7d). Problem 4 states, “Decompose the following area model into rectangles whose fact you can use to find the larger product.” Students are given a $$13 \times 7$$ rectangle on a grid to decompose.
• In Unit 5, Lesson 8, Target Task, students find rectangles with the same area and different perimeters (3.MD.8). The problem states, “Eddie wants to put a deck in his backyard. He has a few different options for sizes, one of which is shown below.” (A rectangle with the dimensions of 10 feet by 2 feet is shown.) a. What is the perimeter of Deck A above? b.  Deck B, another of Eddie’s options, has the same area as the one above by a different perimeter. Draw one possible shape for Deck B below. Explain how you found your answer.”

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for exercises within student assignments being intentionally sequenced.

Overall, Units, Lessons, Activities, and Target Tasks are intentionally sequenced, so students have the opportunity to develop understanding of the content. The structure of each lesson provides students the opportunity to activate prior knowledge. Anchor Tasks engage students in problems that are sequenced from the concrete to the abstract and increase in complexity. Each lesson closes with a Target Task which is typically two questions assessing the daily lesson objective. In the Problem Sets and Homework, students independently apply learning from the lesson. 

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for having variety in what students are asked to produce.

 The instructional materials prompt students to produce written answers and solutions in the Problem Sets, Homework, and Target Tasks. In the Anchor Tasks, whole group instruction provides students with the opportunity to produce oral arguments and explanations through discussion in whole group, small group, or partner settings. Written critiques of fictional students’ work are produced and include models, drawings, and calculations.

 Students are prompted through the materials to use appropriate mathematical vocabulary in all their oral and written work. The materials introduce a variety of mathematical representations through sequenced lessons. Students choose which representation to use in later lessons. Examples include, but are not limited to:

• In Unit 1, Lesson 7, students construct and critique reasoning for rounding two- and three-digit numbers to the nearest ten or hundred (3.NBT.A.1). For example, Anchor Task, Problem 1 states, “A pair of pants cost $52. Mrs. Ingall says the pants are about $50. Mr. Silver says they are about $100. Who is correct, Mr. Silver, Mr. Ingall, both of them, or neither of them? Explain your answer.”
• In Unit 3, Lesson 8, students use the associative property as a strategy to multiply by units of 6 (3.OA.5,7,9). For example, Problem Set, Problem 2 states, “Libby says the answer to the problem 5 x 2 x 3 = 25. Her work is shown. Step 1: $$5 \times 2 = 5 \times 2 = 10$$ Step 2: $$5 \times 3 = 15$$ Step 3: $$10 + 15 = 25$$ Which is true? A.  Libby’s answer is correct because $$10 + 15 = 25$$. B. Libby’s answer is correct because $$2 + 3 = 5$$ and $$5 \times 5 = 25$$. C. Libby’s answer is not correct because she multiplied $$5 \times 3$$ and $$5 \times 2$$. D. Libby’s answer is not correct because she should have multiplied $$10 \times 15$$.”
• In Unit 5, Lesson 8, students find rectangles with the same area and a different perimeter (3.MD.8). For example, Homework, Problem 7 states, “Imagine all of the rectangles you could build with an area of 25 square units. Which one do you think will have the least perimeter? Why?”

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

 The series integrates hands-on activities that include the use of physical manipulatives.

Manipulatives and other mathematical representations are aligned to the standards, and the majority of manipulatives used are commonly available in classrooms. Lessons include paper templates of many manipulatives, and examples include, but are not limited to:

• In Unit 2, Lesson 3, counters are used to create equal groups when exploring the concept of multiplication. 
• In Unit 4, Lesson 2, students use square tiles and centimeter cubes to understand the concept of area. Square centimeter grids and square inch grids cut into tiles are provided if tiles or cubes are not available.
• In Unit 6, Lesson 1, Anchor Task, Problem 1, students begin to investigate the concept of fractions using pattern blocks.

 Manipulatives used in Grade 3 include, but are not limited to: 

• Base ten blocks, number lines, place value charts, counters, tape diagrams, counters, grid paper, multiplication chart, square tiles, fraction strips, ruler, pattern blocks, analog scale, balance scale, beakers, containers of various capacities, digital scale, and snap cubes.
• Templates provided in place of three-dimensional manipulatives: tangrams, square inch grid, centimeter grid, and tetrominoes.

The instructional materials reviewed for Match Fishtank Grade 3 meet the expectations for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development. 

Most math lessons contain Anchor Tasks Guiding Questions, Anchor Task Notes, and/or Discussions of Problem Sets. Examples include:

• The materials state, “Each Anchor Task is followed by a set of Guiding Questions. The Guiding Questions can serve different purposes, including: scaffolding the problem, extending engagement of students in the content of the problem, and extending the problem. Not all Anchor Tasks include Guiding Questions that address all three purposes, and not all Guiding Questions are meant to be asked to the whole class as there is discretion for the teacher to determine how, when, and which questions should be used with which students.” For example, Unit 3, Lesson 1, Anchor Task, Problem 1, “Do you agree with Katia or Gerard? Why? What could you have drawn to support your argument? Write an equation that represents your argument. Can you generalize this to more numbers? If you know the value of 8 fours, do you know the value of 4 eights? Why?”
• Anchor Task Notes are often included after the Guiding Questions. These Notes include problem-specific information that may be helpful in understanding or executing the problem. 
• The Discussion of Problem Sets includes a list of “suggested questions for teachers to ask after students have worked on the Problem Set but before they attempt the Target Task. Similar to the Guiding Questions for Anchor Tasks, these questions can serve different purposes, including: connecting the content of the Problem Set to previous learnings (including major work and/or connections across clusters and domains, if applicable), more deeply engaging students in the content of the Problem Set, and extending on the Problem Set. Not all Discussions of Problem Sets include questions that cover all three purposes. Also, not all Discussion questions are meant to be asked to the whole class; rather, it should be at the discretion of the teacher to determine how, when, and which questions should be used with which students.” For example, Unit 3, Lesson 20 states, “In #1, how many more months will Lupe need to save so she has enough to buy the art supplies? How do you know? Explain the three unknowns you needed to find to solve #3. How did you solve #5? Which strategy did you use? Where did you draw your darts in the second part of #6? Is there more than one correct answer? How did you solve #7? Which strategy did you use? What made #8 challenging? What did you need to keep in mind in terms of finding the total number of rows on the airplane?”

The instructional materials reviewed for Match Fishtank Grade 3 meet the expectations for containing a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials also include teacher guidance on the use of embedded technology to support and enhance student learning. 

Tips for Teachers are present in most lessons, support teachers with resources, and include an overview of the lesson. The materials state, “Tips for Teachers serve to ensure teachers have the support and knowledge they need to successfully implement the content. This section includes helpful suggestions and notes to support understanding and implementation of the lesson.” Tips for Teachers includes, but is not limited to: guidance on pacing, connections to other lessons within the unit or in different units or grade-levels, prior skills or concepts students may need to access the lesson, standards for Mathematical Practice emphasized in the lesson, and potential misconceptions students may have with the content. For example: 

• In Unit 2, Lesson 7, Tips for Teachers states, “Students need not use formal terms for the properties of operations, including the terms ‘commutative’ or ‘commutative property.’ However, exposure to the term is helpful so that students can develop and use a common language and thus is introduced in this lesson.”

In Unit 7, Lesson 5, Tips for Teachers states, “According to 3.MD.1, students are expected to ‘solve word problems involving addition and subtraction of time intervals in minutes.’ Bill McCallum notes on his blog, ‘Time intervals in minutes doesn’t have to mean “less than an hour.” For example, there’s no reason why Grade 3 students can’t say how many minutes it is from 3:30 to 5:00’ (Elapsed Time (3.MD.1 vs. 4.MD.2), Mathematical Musings). Thus, the Problem Set and Homework include problems where students will work with elapsed time that is still given in minutes, as the standard requires, but exceeds an hour.”

The instructional materials for Match Fishtank Grade 3 meets the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum. For example:

• Each grade opens with a Course Summary, that identifies the “key advancements from previous years.” For example, the Grade 3 Course Summary states, “Grade 3 focuses on four key advancements from previous years: (1) developing understanding of and fluency with multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions; (3) developing understanding of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.” An explanation about how the units are sequenced is also provided.
• Each unit opens with a Unit Summary, which details the specific grade level content to be taught, as well as connections to previous and future grades.
• Each lesson provides current standards addressed in the lesson, as well as foundational standards taught in previous units or grades that are important background for the current lesson.

The instructional materials for Match Fishtank Grade 3 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions. Examples include: 

• In Unit 2, Lesson 1, Tips for Teachers states, “Students will learn to write factors in the conventional order, namely with the number of groups written as the first factor and the size of the groups as the second factor. But, since “some students bring th[e] interpretation of multiplication equations [where the meaning of the factors is switched] into the classroom, …it is useful to discuss the different interpretations and allow students to use whichever is used in their home” (OA Progression, p. 25), if it comes up. Thus, use the conventional way of writing factors when addressing the whole class, but allow individual students to write them in reverse order if they have experience doing so and they are able to explain the meaning of each factor. In Lesson 7, students will learn the commutative property, after which all students will be given much more free reign over the order in which they write their factors.”
• In Unit 5, Lesson 4, Tips for Teachers states, “‘Perimeter problems for rectangles and parallelograms often give only the lengths of two adjacent sides or only show numbers for these sides in a drawing of the shape. The common error is to add just these two numbers. Having students first label the lengths of the other two sides as a reminder is helpful,’ (MD Progression, p. 16).”

The instructional materials for Match Fishtank Grade 3 meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. 

Each lesson is designed with teacher-led Anchor Tasks, Problem Sets, and Target Tasks. The lessons contain multiple opportunities for practice with an assortment of problems. The Anchor Problems provided the teacher with guiding questions and notes in order to provide feedback for students’ learning. For example:

• In Unit 2, Lesson 4, Anchor Task, the Problem 2 Notes state, “You could introduce the use of skip-counting and/or repeated subtraction here to connect back to previous strategies used for multiplication. But since students are still either being given a model or asked to draw one for most problems, you can delay the discussion of those strategies.”
• In Unit 4, Lesson 5, Tips For Teachers states, “Today’s lesson is the first one where students will not be given concrete units in order to find the area of rectangles. Students may still want to draw individual units to find the area of rectangles, but hopefully most students are completing rows and columns instead. As the Progressions note, ‘less sophisticated activities of this sort were suggested for earlier grades so that Grade 3 students begin with some experience,’ so development towards this row and column understanding should be fairly straightforward (GM Progression, p. 17).”

The instructional materials for Match Fishtank Grade 3 meet the expectations for assessments clearly denoting which standards are being emphasized. 

Each unit provides an answer key for the Unit Assessment. The answer key identifies the targeted standard for each item number. For example: 

• In Unit 2, Multiplication and Division, Part 1, Assessment Item 2 correlates with 3.OA.1. 
• In Unit 5, Shapes and Their Perimeter, Assessment Item 5 correlates with 3.MD.8.
• In Unit 7, Measurement, Assessment Item 7 correlates with 3.MD.2.

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for embedding tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

 Anchor Tasks, Problem Sets, Homework, and Target Tasks provide students opportunities to apply their learning from multiple entry points. Though the materials may present a concept using a specific strategy, most practice problems allow students to choose from a variety of strategies they have learned. For example:

• In Unit 2, Lesson 3, students learn about multiplication involving unknown group size and finding group size in situations. The Anchor Task presents the concept using arrays or equal groups. However, in the Problem Set, students are asked to, “Create a visual model of the stacks of paper.” Students may choose which visual model they use.
• In Unit 4, Lessons 1-8, students have experienced a variety of strategies to find area. In Lesson 8, students are allowed to choose the strategy that works best for them to solve area word problems.
• In Unit 6, Lesson 16, students use area models to find equivalent fractions. However, in the Problem Set, Problem 7, students are given the opportunity to draw any model to explain their answer.

The instructional materials reviewed for Match Fishtank Grade 3 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. For example: 

• Unit 2, Lesson 16, Problem Set, Problem 7, “The cycle shop on Main Street sells bikes (two wheels) and trikes (three wheels). Yesterday, Sarah counted all of the cycles in the shop. There were seven bikes and four trikes in the shop. How many wheels were there on these eleven cycles?” “CHALLENGE: Today, Sarah counted all of the wheels of all the cycles in the shop. She counted that there were 30 wheels in all. There were the same number of bikes as there were trikes. How many bikes were there? How many trikes were there? Show how you figured it out.”

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for providing a balanced portrayal of various demographic and personal characteristics. The lessons contain students that have a variety of demographic and personal characteristics that do not illustrate gender bias, lack of racial or ethnic diversity, or racial or naming stereotyping. For example:  

• Different cultural names and situations are represented in the materials, for example: Spencer, Presley, Anthony, Karen, Heidi, Caesar, Lila, Mrs. Kozlow, and Marlene.
• In Unit 2, Lesson 1, Problem Set, Problem 4 states, “Caroline, Brian, and Marta share a box of chocolates. They each get the same amount. Circle the chocolates below to show 3 groups of 4. Then, write a repeated addition sentence and a multiplication sentence to represent the picture.” The problem does not have any student taking on a larger role than the other.