5th Grade - Gateway 1

​The instructional materials reviewed for Match Fishtank Mathematics Grade 5 meet the expectations for assessing grade-level content. The series is divided into units, and each unit contains a Unit Assessment available online to the teacher and can also be printed for students. 

Examples of assessment items aligned to grade-level standards include: 

• Unit 1 Assessment, Question 10 states, “Which is greater, 0.13 or 0.031? Explain. Which is greater, 0.203 or 0.21? Explain.” (5.NBT.3b)
• Unit 2 Assessment, Question 2 states, “A construction team uses 184 sheets of plywood for each house it builds.  The team will build 12 houses this year. What is the total number of sheets of plywood the team will use to build all 12 houses?” (5.NBT.5)
• Unit 3 Assessment, Question 5 states, “A cereal box has a height of 32 centimeters. It has a base with an area of 160 square centimeters. What is the volume, in cubic centimeters, of the cereal box?” (5.MD.5b)
• Unit 4 Assessment, Question 7 states, “Solve. 14.4 - 5.63.” (5.NBT.7)
• Unit 5 Assessment, Question 5 states, “Jim uses ribbon to make bookmarks. Jim has 9 feet of ribbon. He uses $$\frac{1}{3}$$ foot of ribbon to make each bookmark. What is the total number of bookmarks Jim makes with all 9 feet of ribbon?” (5.NF.7)
• Unit 6 Assessment, Question 6 states, “Tom has a water tank that holds 5 gallons of water. Tom uses water from a full tank to fill 6 bottles that each hold 16 ounces and a pitcher that holds $$\frac{1}{2}$$ gallon. How many ounces of water are left in the water tank?” (5.MD.1)
• Unit 7 Assessment, Question 3 states, “Dante and Helen each created a number pattern that started with the number 0. Dante used the rule “Add 3”. Helen used the rule “Add 6”. a. Complete the following table with both Dante’s and Helen’s pattern (table provided). b. Describe any patterns you see in the corresponding terms in Dante’s pattern and Helen’s pattern. Why do you think that pattern exists?” (5.OA.3)

The instructional materials reviewed for Match Fishtank Mathematics Grade 5 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 out of 7, which is approximately 86%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 100 out of 128, which is approximately 78%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 119 out of 140, which is approximately 85%. 

A lesson level analysis is most representative of the instructional materials because the units contain major work, supporting work, and assessments. As a result, approximately 78% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Match Fishtank Mathematics Grade 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major standards/clusters of the grade, for example:

• In Unit 2, Lesson 20, Anchor Tasks, students write and interpret numerical expressions (5.OA.A) to solve word problems involving multi-digit multiplication and division (5.NBT.5,6). Problem 4 states, “On Saturday, the owner of a department store gave away a $15 gift card to every 25th customer. A total of 8,879 customers came to the store on Saturday. What is the total value of the gift cards the owner gave away? How many additional customers would need to have come in for another gift card to be given away?”
• In Unit 5, Lesson 24, Problem Set, students use equivalent fractions as a strategy to add and subtract fractions (5.NF.A) to solve problems involving information presented in a line plot (5.MD.2). Problem 3 states, “The line plot below shows the lengths of all the pieces of string Emma used for an art project. She cut all these pieces from one original piece of string. Emma had 1 foot of string left over. How long, in feet, was the original piece of string?”
• In Unit 6, Lesson 24, Target Task, students add and subtract decimals (5.NBT.7) to solve real-world problems involving measurement conversions (5.MD.1). Problem 1 states, “Solve. Show or explain your work. Owen lives 1.2 kilometers from school. Lucia lives 0.86 kilometers from school. Ignacio lives 90 meters from school. If Ben, Alice, and Walter all walk to and from school, how far, in kilometers, did they all walk in total?”

The instructional materials reviewed for Match Fishtank Mathematics Grade 5 meet expectations that the amount of content designated for one grade-level is viable for one year. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. 

The Pacing Guide states, “We intentionally did not account for all 180 instructional days in order for teachers to fit in additional review or extension, teacher-created assessments, and school-based events.” As designed, the instructional materials can be completed in 140 instructional days (including lessons, flex days, and unit assessments). 

• There are 121 content-focused lessons designed for 50-60 minutes. Each lesson incorporates: Anchor Tasks (25-30 minutes), Problem Set (15-20 minutes), and a Target Task (5-10 minutes).
• There are seven unit assessments, one day each. 
• The pacing guide suggests 12 flex days be incorporated into the units throughout the year at the teacher’s discretion. It is recommended for units that include both major and supporting/additional work, that the flex days be spent on content that aligns with the major work of the grade.

The instructional materials for Match Fishtank Mathematics Grade 5 meet expectations for the materials being consistent with the progressions in the Standards. 

The instructional materials clearly identify content from prior and future grade-levels, relate grade-level concepts explicitly to prior knowledge from earlier grades, and use it to support the progressions of the grade-level standards, for example:

• The Unit 1 Summary states, “Unit 1 starts off with reinforcing some of this place-value understanding of multi-digit whole numbers to 1 million, building up to that number by multiplying 10 by itself repeatedly. After this repeated multiplication, students are introduced to exponents to denote powers of 10. Then, students review the relationship in a whole number between a place value and the place to its left (4.NBT.1) and learn about the reciprocal relationship of a place value and the place to its right (5.NBT.1). Students also extend their work from Grade 4 on multiplying whole numbers by 10 to multiplying and dividing them by powers of 10 (5.NBT.2). After extensive practice with whole numbers, students then divide by 10 repeatedly to extend their place-value system in the other direction, to decimals. They then apply these rules and perform these operations with powers of 10 to decimal numbers. Lastly, after deepening their understanding of the base-ten structure of our place-value system, students read, write, compare, and round numbers in various forms (5.NBT.3-4).” 
• The Unit 1 Summary also connects future grade level content: “This content represents the culmination of many years’ worth of work to deeply understand the structure of our place-value system, starting all the way back in Kindergarten with the understanding of teen numbers as ‘10 ones and some ones’ (K.NBT.1). Moving forward, students will rely on this knowledge later in the Grade 5 year to multiply and divide whole numbers (5.NBT.5—6) and perform all four operations with decimals (5.NBT.7). Students will also use their introduction to exponents to evaluate more complex expressions involving them (6.EE.1). Perhaps the most obvious future grade-level connection exists in Grade 8, when students will represent very large and very small numbers using scientific notation and perform operations on numbers written in scientific notation (8.EE.3-4).”
• The Unit 7 Summary states, “Students have coordinated numbers and distance before, namely with number lines. Students were introduced to number lines with whole-number intervals in Grade 2 and used them to solve addition and subtraction problems, helping to make the connection between quantity and distance (2.MD.5-6). Then in Grade 3, students made number lines with fractional intervals, using them to understand the idea of equivalence and comparison of fractions, again connecting this to the idea of distance (3.NF.2). For example, two fractions that were at the same point on a number line were equivalent, while a fraction that was further from 0 than another was greater. Then, in Grade 4, students learned to add, subtract, and multiply fractions in simple cases using the number line as a representation, and they extended it to all cases, including in simple cases involving fraction division, throughout Grade 5 (5.NF.1-7). Students’ preparation for this unit is also connected to their extensive pattern work, beginning in Kindergarten with patterns in counting sequences (K.CC.4.c) and extending through Grade 4 work with generating and analyzing a number or shape pattern given its rule (4.OA.3).“ 
• The Unit 7 Summary also connects future grade level content: “This work lays an important foundation for content that students will study deeply throughout middle school—proportional relationships and functions (6 - 7.RP, 6 - 8.EE, 8.F). This then deeply informs students’ work in all high school courses.”
• The CCSSM are listed for each unit at the very bottom of the main unit page. They categorize the list of standards by the content standards addressed in the grade level, foundational standards (standards from prior grades), future connections, and the MPs. 

The instructional materials for Match Fishtank Mathematics Grade 5 attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All lessons within the units include an “Anchor Task,” where students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Problem sets provide students the opportunity to solve a variety of problems and integrate and extend concepts and skills. Each problem set is wrapped up with a “Discussion of Problem Set,” where students are provided an opportunity to synthesize and clarify their understanding of the day’s concepts. The lesson concludes with a “Target Task” for students to independently demonstrate their learning for the day. Examples include:

• Unit 1, Lesson 8, Anchor Task, Problem 1 states, “1. Solve. a. $$0.05\times10=$$ ______, b. $$0.106\times10=$$ ______, c. $$34.8\times10=$$ ______ ; 2. What do you notice about #1? What do you wonder?” (5.NBT.1,2)
• Unit 2, Lesson 4, Problem Set, Problem 5 states, “For which of the following expressions would 200,000 be a reasonable estimate? Explain how you know.  $$2,146\times12$$ $$21,467\times121$$ $$2,146\times121$$ $$21,477\times1,217$$.” (5.NBT.2,5)
• Unit 3, Lesson 3, Target Task, Problem 1 states, “Use the figure to the right to answer the following questions. a. How many layers are in the figure to the right? b. How many cubes are in each layer? c. What is the volume of the figure? d. Explain how you could find the volume of the figure using a different number of layers.” (5.MD.5)
• Unit 4, Lesson 10, Anchor Task, Problem 2 states, “Joe is baking cookies. He needs a total of 2 cups of sugar for the recipe. Joe bought a $$4\frac{1}{2}$$ cup bag of sugar and has used $$2\frac{3}{4}$$ cups already. Without solving the problem, does Joe have enough sugar? Explain your thinking.” (5.NF.2)
• Unit 5, Lesson 2, Target Task, Problem 1 states, “Gordon has paper strips that are all equal in length. He lines them up end to end. When the line of paper strips is 3 feet long, Gordon says there are 12 paper strips. What is the length, in feet, of one paper strip if Gordon is correct?” (5.NF.3)
• Unit 6, Lesson 23, Problem Set, Problem 2 states, “Lincoln had 2 books in his backpack. One book has a mass of 3 pounds 7 ounces, and the other book has a mass of 2 pounds 10 ounces. What was the total mass, in ounces, of the books? a. 60  b. 77 c. 80 d. 97.” (5.MD.1)
• Unit 7, Lesson 1, Anchor Task, Problem 1 states, “Mr. Ingall, Mrs. Ingall’s husband, spotted a fly on the wall in their house. He wanted to catch it and let it free outside, but he hates bugs. How should he describe to Mrs. Ingall where the fly is on the wall so that she can catch it?” (5.G.1)
• Unit 7, Lesson 10, Discussion of Problem Set states, “What method would you choose in #1(d)? Can he expect to always get those results? What other things might affect the growth of the tomatoes? When did Howard likely get paid in #2(d)? Why do you think that? When did Howard likely buy a television? How do you know? How did you find the answer for #3(c)? Did you use subtraction or just look for the steepest line? How did you set up your work when solving for #3(e)? Would the graph of a different rainy day have the same shape as the graph in #3? How might it be the same? Different?” (5.G.2)
• Homework is provided for each lesson to extend students’ engagement with the content.

The materials identify Foundational Standards related to the content of the grade level lesson. Guidance related to the lesson’s content is also provided for teachers. For example:

• In Unit 1, Lesson 10, the Foundational Standards include Number and Operations in Base Ten, 4.NBT.2 (Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons). The materials state, “5th Grade Math - Unit 1: Place Value with Decimals. Students build upon their understanding of the place-value system by extending its patterns to decimals, and continue to read, write, compare and round numbers, including decimals, in various forms.” 
• In Unit 5, Lesson 4, the Foundational Standards include Numbers and Operations- Fractions, 4.NF.4 (Apply and extend previous understandings of multiplication to multiply a fraction by a whole number). The materials state, “5th Grade Math - Unit 5: Multiplication and Division of Fractions. Students deepen their understanding of fraction multiplication and begin to explore to fraction division (and fractions as division), as well as apply this new understanding to the context of line plots.”

The instructional materials reviewed for Match Fishtank 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 that are visibly shaped by CCSSM cluster headings, for example: 

• In Unit 1, Lesson 12, the lesson objective states, “Use place value understanding to round decimals to the nearest whole,” which is shaped by 5.NBT.A, “Understand the place value system.”
• In Unit 2, Lesson 2, the lesson objective states, “Write expressions that record calculations with numbers, and interpret expressions without evaluating them,” which is shaped by 5.OA.A, “Write and interpret numerical expressions.”
• In Unit 3, Lesson 1, the lesson objective states, “Understand volume as an attribute of solid figures that is measured in cubic units. Find the volume of concrete three-dimensional figures,” which is shaped by 5.MD.C, “Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.”
• In Unit 4, Lesson 11, the lesson objective states, “Add and subtract more than two fractions,” which is shaped by 5.NF.A, “Use equivalent fractions as a strategy to add and subtract fractions.”
• In Unit 5, Lesson 1, the lesson objective states, “Use area models to model fractions as division and solve word problems involving division of whole numbers with answers in the form of fractions or mixed numbers,” which is shaped by 5.NF.B, “Apply and extend previous understandings of multiplication and division to multiply and divide fractions.”
• In Unit 6, Lesson 6, the lesson objective states, “Multiply a decimal to tenths by a decimal to hundredths,” which is shaped by 5.NBT.B, “Perform operations with multi-digit whole number and with decimals to hundredths.”
• In Unit 7, Lesson 10, the lesson objective states, “Solve real-world problems by graphing information represented in a table in the coordinate plane and interpret coordinate values of points in the context of the situation,” which is shaped by 5.G.A, “Graph points on the coordinate plane to solve real-world and mathematical problems.”

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. For example:

• In Unit 3, Lessons 3 - 8, students connect 5.MD.C and 5.NBT.B by exploring volume of three dimensional shapes and connecting it to the operation of multiplication. For example, Unit 3, Lesson 3, Anchor Tasks, Problem 2 states, “Build a 2cm x 3cm x 4cm rectangular prism with your centimeter cubes. a. How many layers are there in the following figure? How many cubes are in each layer? What is the volume of the figure? b. Find another way to think of the layers in the figure.”
• In Unit 5, Lessons 3 and 4, students connect their understanding of the operation of multiplication (5.NBT.B) to their work multiplying fractions (5.NF.B). Students use previous multiplication models (set models, area models and tape diagrams) to model multiplying a fraction times a whole number. For example, Unit 5, Lesson 3, Target Task, Problem 2 states, “Out of 18 cookies, 23 are chocolate chip. How many of the cookies are chocolate chip?”
• In Unit 6, Lessons 1-16, students connect their procedural knowledge of multiplication and division with whole numbers (5.NBT.B) and their understanding of multiplication and division with fractions (5.NF.B) to multiply and divide with decimals (5.NBT.B) and reason about the placement of the decimal point (5.NBT.A). For example, Unit 6, Lesson 1, Anchor Tasks, Problem 1 states, “Solve. Show or explain your work. a. $$3\times2$$ tenths = _________ b. $$3\times3$$ tenths = _________ c. $$4\times3$$ tenths = _________.”