4th Grade - Gateway 3

The instructional materials reviewed for Match Fishtank Grade 4 meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson.

There are eight instructional units in Grade 4. 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 2, Lesson 3, Anchor Task, Problem 1, students solve multiplicative comparison problems with an unknown multiplier and interpret a multiplication equation as a comparison (4.OA.1,2).  The problem states, “Mrs. Ingall wants to place students’ pencil boxes on her bookshelf for the start of the school year. We know her bookshelf is 24 inches long. Each pencil box is 2 inches wide. a.How many pencil boxes can she line up along the bookshelf? b.How can you use your answer from Part (a) to determine how many times as long the bookshelf is than the pencil box?”

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 in which students have the opportunity to apply what they have learned from the activities in the lesson, and can be used to formatively assess understanding of the lesson content. For example:

• In Unit 4, Lesson 8, Problem Set, students measure angles that are greater than 180 (4.MD.5,6). Problem 2 states, “Maria says that this angle measures 153. Is she correct or incorrect? Why?” Students are given an angle to measure.
• In Unit 7, Lesson 12, Homework, students solve word problems involving the addition of decimals and decimal fractions (4.NF.5). Problem 2 states, “The snowfall in Year 1 was 2.03 meters. The snowfall in Year 2 was 1.6 meters. How many total meters of snow fell in Years 1 and 2?”
• In Unit 7, Lesson 5, Target Task, students express customary length measurements in terms of a smaller unit, and record measurement equivalents in a two-column table (4.MD.1). In Problem 2, students “Answer ‘true’ or ‘false’ for the following statements. If the statement is false, change the right side of the comparison to make it true. a.12 yards < 40 feet ______ b.  7 feet 1 inch > 70 inches ______ .”

The instructional materials reviewed for Match Fishtank Grade 4 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 4 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 9, students locate multi-digit numbers on a number line and explain their placement (4.NBT.2,3). For example, in Anchor Task, Problem 1, Part 1, a number line from 0 to 100 with a question mark about two-thirds of the way between the two marks is provided. The problem states, “Look at the line below. Based on where 0 and 100 are, what number do you think the question mark is on? Explain your choice.”
• In Unit 3, Lesson 6, students solve two-digit dividend division problems with a remainder in the tens and/or ones place with smaller divisors and quotients (4.NBT.6). For example, Problem Set states, “Cayman says that $$59\div4$$ is 10 with a remainder of 19. He reasons this is correct because $$(4\times10)+19=59$$. What mistake has Cayman made? Explain how he can correct his work.”
• In Unit 5, Lesson 6, students recognize and generate equivalent fractions with larger units using division (4.NBT.1). For example, Target Task, Problem 2 states, “Explain how you know  is equivalent to. Use a model to support your reasoning.”

The instructional materials reviewed for Match Fishtank Grade 4 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 6, square tiles are used to find all factors of a number. 
• In Unit 4, Lesson 15, Anchor Task, Problem 2, students use a protractor to draw an obtuse isosceles triangle.
• In Unit 5, Lesson 1, tape diagrams are used to generate equivalent fractions.

 Manipulatives used in Grade 4 include but are not limited to: 

• Base ten blocks, tape diagrams, number lines, grid paper, dice, square tiles, counters, pattern blocks, protractors, rulers, hundreds chart, millions place value chart, fraction strips, metric and customary weights, volume containers, meter stick, and yard stick.
• Templates provided in place of three-dimensional manipulatives: paper hundreds flat and square-sized paper.

The instructional materials reviewed for Match Fishtank Grade 4 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 2, Lesson 1, Anchor Task, Problem 1 states, “How can the length of The Twits help us to figure out the length of the bookshelf? How many copies of The Twits can fit on the bookshelf? We can express this relationship by saying the bookshelf is 6 times as long as the book. How can we represent this relationship with a tape diagram? With an equation?”
• 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 7, Lesson 8 states, “Look at #1f. 1.9 has 2 digits and 1.21 has three digits, and yet 1.9 is greater than 1.21. Why? How would #2 be different if given area models to use to represent the values? Which is easier to use to model the values? Which is easier to use to compare? Why? Would you rather have 2.7 pounds of strawberries or 2.34 pounds? Why? If you didn’t like strawberries, how might your answer change?”

The instructional materials reviewed for Match Fishtank Grade 4 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 3, Lesson 6, Tips for Teachers states, “As noted in Lesson 5 Anchor Task #2, because many of the computations in this lesson involve a remainder when computing the partial quotient in the ones place, the computation has been recorded using the partial quotients algorithm to avoid writing the ‘R’ notation after an equal sign. If you’d like to postpone the introduction of the partial quotient notation, you could either record the computation in a way that is similar to Lesson 5 Anchor Task #1 but in such a way to avoid confusion regarding the equality of a computation with its quotient and remainder. (See the Tips for Teachers section of Lesson 1 to read more.)”
• In Unit 8, Lesson 3, Tips for Teachers states, “This lesson is optional. It does, however, make a connection across domains between the work of metric measurement conversion (4.MD.1) and students’ place value understanding (4.NBT.A), since ‘expressing larger measurements in smaller units within the metric system is an opportunity to reinforce notions of place value’ (GM Progression, p. 20).”

The instructional materials for Match Fishtank Grade 4 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 4 Course Summary states, “Grade 4 focuses on three key advancements from previous years: (1) developing understanding with multi-digit multiplication and division; (2) developing an understanding of fraction equivalence, and certain cases of fraction addition, subtraction, and multiplication; and (3) understanding that geometric figures can be analyzed and classified based on their properties, including their angle measure and symmetry.” 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 4 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions. Examples include: 

• In Unit 3, Lesson 5, Anchor Task, the Problem 1 Notes state, "Students may need base ten blocks for this task (optional: see note below). For those students who are still developing their place value understanding, it may be beneficial for students to see the division with base ten blocks themselves, as shown in the diagram. Otherwise, you could draw the base ten block model or even just use an area model.”
• In Unit 4, Lesson 5, Tips for Teachers states, “John A. Van de Walle notes, ‘angle measurement can be a challenge for two reasons: the attribute of angle size is often misunderstood, and protractors are commonly introduced and used without understanding how they work’ (Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013. Page 335). Thus, this lesson serves to help students understand angle measure as the spread of an angle’s rays, which can be measured with smaller angles.”

The instructional materials for Match Fishtank Grade 4 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 Tasks provided the teacher with guiding questions and notes in order to provide feedback for students’ learning. For example:

• In Unit 1, Lesson 4, Anchor Tasks, the Problem 3 Notes state, “As students develop their fluency with reading number names, they can default to read numbers in unit form first and then practice reading them the usual way after hearing the teacher say it.”
• In Unit 7, Lesson 5, Anchor Tasks, the Problem 1 Notes state, “Students don’t need to use models here, but as in Lesson 3, they may help students reason abstractly and quantitatively (MP.2). An example of how to draw pictorial base ten blocks to hundredths is shown below:”

The instructional materials for Match Fishtank Grade 4 meet 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 1, Place Value, Rounding, Addition and Subtraction, Assessment Item 4a correlates with 4.OA.3 and 4.NBT.4. 
• In Unit 3, Multi-Digit Division, Assessment Item 5 correlates with 4.OA.5.
• In Unit 6, Fraction Operations, Assessment Item 3c correlates with 4.NF.3.a. 

The instructional materials reviewed for Match Fishtank Grade 4 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 lesson’s practice problems allow students to choose from a variety of strategies they have learned. For example:

• In Unit 2, Lesson 12, Anchor Task, Problems 1-3 students explore the use of area models when multiplying a two-digit number by a one-digit number. In the Target Task, Problem 2, students “Solve. Show or explain your work: $$35\times7$$.” Students may choose to use the area model strategy or choose another method to solve.
• In Unit 3, Lesson 4, the Anchor Tasks provide students opportunities to divide two-, three- and four-digit numbers by one-digit numbers using area models. In the Target Task, Problems 1-3, students “Solve. Show or explain your work.” Each student may independently choose a strategy that works for them.
• In Unit 5, Lesson 2, the Anchor Tasks provide students the opportunity to find equivalent fractions using number lines. In the Problem Set, Problem 3, students can choose any strategy to determine if two fractions are equivalent.

The instructional materials reviewed for Match Fishtank Grade 4 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. For example: 

• Unit 6, Lesson 17, Problem Set, Problem 9, “CHALLENGE: Make the smallest product by filling in the boxes using the whole numbers 1-9 no more than one each time.”

The instructional materials reviewed for Match Fishtank Grade 4 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: Ms. Roll, Ayana, Jada, Damon, Molly, Andre, Andrea, Yasmin, and Osvaldo.
• In Unit 3, Lesson 11, Anchor Task, Problem 2 states, “Now Edris wants to retile the rectangular patio in his backyard. He uses 128 tiles that are each one square foot. His patio is 8 feet wide. He wants to edge the patio with metal tape to make sure the tiles don’t move or shift at all. How many feet of metal tape should Edris buy?"