3rd Grade - Gateway 1

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 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 3, Part A states, “Round to the nearest ten the number of people who went to the school play on each of the three days. Show or explain how you got your answers.” (3.NBT.1)
• Unit 1 Assessment, Question 5 states, “There are 545 magazines and 620 books in the library. How many more books than magazines are in the library?” (3.NBT.2)
• Unit 2 Assessment, Question 5 states, “Dinah is selling pieces of bubble gum to her friends. She buys six packs of gum. Each pack has 5 pieces of gum. She sells 3 pieces of gum each day. How many days does it take Dinah to sell all of her gum?” (3.OA.8)
• Unit 4 Assessment, Question 2 states, “A patio is in the shape of a rectangle with a width of 8 feet and a length of 9 feet. What is the area in square feet, of the patio?” (3.MD.7b)
• Unit 5 Assessment, Question 5 states, “Sonia wants to put a fence around her backyard. Her backyard is 5 meters long and 6 meters wide. What is the total length of fence, in meters, Sonia needs to place around the play area?” (3.MD.8)
• Unit 7 Assessment, Question 5 states, “Freda buys horse food in 20-kilogram bags. Her horse eats 8 bags of horse food per month. How much horse food does Freda’s horse eat in one month?” (3.MD.2)

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 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 5 out of 7, which is approximately 71%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 103 out of 133, which is approximately 77%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 117 out of 145, which is approximately 81%. 

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 77% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 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 1, Lessons 10, 13 and 14, students solve word problems (3.OA.8) involving addition and subtraction (3.NBT.2), using rounding (3.NBT.1) to assess the reasonableness of the solution. For example, Lesson 10, Anchor Tasks, Problem 2 states, “Luke and Josh collect baseball cards. Luke has 347 baseball cards. Luke has 34 fewer baseball cards than Josh. How many baseball cards does Josh have? Solve. Then assess the reasonableness of your answer.”
• In Unit 3, Lessons 17 and 18, students determine the unknown whole number in a multiplication or division equation relating three whole numbers (3.OA.4) and apply the properties of operations as strategies to multiply and divide (3.OA.5), as well as multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations (3.NBT.3). For example, Lesson 17, Anchor Tasks, Problem 1 states, “There are 6 tables in Mrs. Potter's classroom. There are 4 students sitting at each table. Each student has a dime to use as a place marker on a board game. a. What is the value of the dimes at each table? b. What is the value of the dimes in Mrs. Potter’s classroom?”
• In Unit 3, Lesson 28, Problem Set, students solve one- and two-step word problems (3.OA.8) using information presented in scaled picture and bar graphs (3.MD.3). Problem 3 states, “The bar graph shows the number of visitors to a carnival from Monday through Friday. a. There were 500 more visitors on Wednesday and Friday combined than on Tuesday. How many visitors were there on Friday? Add that bar to the bar graph. b. How many fewer visitors were there on the least busy day than on the busiest day? c. How many more visitors attended the carnival on Monday and Tuesday combined than on Thursday and Friday combined?”
• In Unit 6, Lessons 1-3, students understand a fraction $$\frac{1}{b}$$ as the quantity formed by one part when a whole is partitioned into b equal parts and understand a fraction $$\frac{a}{b}$$ as the quantity formed by a parts of size $$\frac{1}{b}$$ (3.NF.1), as they partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole (3.G.2). For example, Unit 6, Lesson 1, Target Task, Problem 1 states, “Build the shaded shape below with your pattern blocks. Then, name the fraction that each triangle represents.”
• In Unit 6, Lesson 27, students understand a fraction as a number on the number line (3.NF.2) to measure lengths of multiple objects with fractional units, then use this data to create line plots (3.MD.4). The Target Task states, “Heather is measuring the length of strips of paper to the nearest quarter inch. The lengths she has measured so far are in the table below. Measure the remaining paper strips and add their lengths to the table. Then use the data to draw a line plot below.”

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 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 145 instructional days (including lessons, flex days, and unit assessments). 

• There are 126 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 3 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, “In the first module of Grade 3, students will build on their understanding of the structure of the place value system from Grade 2 (MP.7), start to use rounding as a way to estimate quantities (3.NBT.1), as well as develop fluency with the standard algorithm of addition and subtraction (3.NBT.2). Thus, Unit 1 starts off with reinforcing some of this place value understanding of thousands, hundreds, tens, and ones being made up of 10 of the unit to its right that students learned in Grade 2.” 
• The Unit 1 Summary connects to future grade level content, “Thus, while the majority of the content learned in this unit comes from an additional cluster, they are deeply important skills necessary to fully master the major work of the grade with 3.OA.8, as well as a foundation for rounding and the standard algorithms used to any place value learned in Grade 4 (4.NBT.1-4) and depended on for many grade levels after that.”
• The Unit 6 Summary states, “In Unit 6, students extend and deepen Grade 1 work with understanding halves and fourths/quarters (1.G.3) as well as Grade 2 practice with equal shares of halves, thirds, and fourths (2.G.3) to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number line. Throughout the module, students have multiple experiences working with the Grade 3 specified fractional units of halves, thirds, fourths, sixths, and eighths.” 
• The Unit 6 Summary also connects to future grade level content, “This unit places a strong emphasis on developing conceptual understanding of fractions, using the number line to represent fractions and to aid in students' understanding of fractions as numbers. With this strong foundation, students will operate on fractions in Grades 4 and 5 (4.NF.3-4, 5.NF.1-7) and apply this understanding in a variety of contexts, such as proportional reasoning in middle school and interpreting functions in high school, among many others.”
• 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 3 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. For example:

• Unit 1, Lesson 5, Target Task states, “Round each of the following numbers to the nearest hundred. Show or explain your thinking. a.  761_____ b.  135 _____ c. 84 _____” (3.NBT.1)
• Unit 2, Lesson 5, Anchor Task, Problem 1 states, “Presley has 10 markers. Her teacher gives her 2 boxes and asks her to put an equal number of markers in each box. Anthony has 10 markers. His teacher wants him to put 2 markers in each box until he is out of markers. a. Before you figure out what the students should do, write a multiplication sentence to correspond with each context above. b. Solve each problem for the missing factor.” (3.OA.3)
• Unit 3, Lesson 10, Problem Set, Problem 4 states, “Adriana wrote the expression shown below. $$(3 \times 1) + (3 \times 6)$$. Which of these shows another way to write Jody’s expression? a. $$3 \times 6$$   b. $$3 \times 7$$ c. $$6 \times 6$$ d. $$6 \times 7$$.” (3.OA.5)
• Unit 4, Lesson 6, Problem Set, Problem 4 states, “Mrs. Barnes draws a rectangular array. Mila skip-counts by fours and Jorge skip-counts by sixes to find the total number of square units in the array. When they give their answers, Mrs. Barnes says that they are both right. a. Use pictures, numbers, and words to explain how Mila and Jorge can both be right. b. How many square units might Mrs. Barnes’ array have had?” (3.MD.6, 3.MD.7a)
• Unit 5, Lesson 2, Anchor Task, Problem 1 states, “Use your ruler to find the perimeter, in inches, of the following shape.” (3.MD.8)
• Unit 6, Lesson 6, Discussion of Problem Set states, “Do you agree or disagree with the fraction in #2? What way was Marcos thinking about the model that resulted in the fraction $$\frac{17}{24}$$? Did students each eat $$\frac{10}{8}$$ or $$\frac{10}{16}$$ of a pan in #4? How do you know? What does $$\frac{10}{16}$$ represent? How many pizzas should Jeremy order in #6? How do you know? How can you tell just by looking at the numbers involved that it will be more than one pizza?” (3.NF.1)
• Unit 6, Lesson 1, Target Task, Problem 2 states, “Build the shaded shape below with your pattern blocks. Then, name the fraction that each triangle represents.” (3.G.2)
• Unit 7, Lesson 5, Discussion of Problem Set states, “How did you solve #1? Did you use the clock, draw a number line, or use some other strategy? Did you count forward or backward to solve #3? How did you decide which strategy to use? What made #6 and #8 slightly more difficult than the other problems? Did you solve them differently? How did we use counting as a strategy to problem solve today? How did you use hour benchmarks to problem solve today?” (3.MD.1)
• 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 4, the Foundational Standards include Number and Operations in Base Ten, 2.NBT.1 (Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:). The materials state, “3rd Grade Math- Unit 1: Place Value, Rounding, Addition and Subtraction. Students build on their understanding of the structure of the place value system, start to use rounding as a way to estimate quantities, and develop fluency with the standard algorithm of addition and subtraction. Students focus on the precision of their calculations, and use them to solve real-world problems.”
• In Unit 4, Lesson 4, the Foundational Standards include Measurement and Data, 2.MD.1. (Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.). The materials state, “3rd Grade Math - Unit 4: Area. Students develop an understanding of areas as how much two-dimensional space a figure takes up, and relate it to their work with multiplication from Units 2 and 3.” 

The instructional materials reviewed for Match Fishtank Grade 3 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 2, Lesson 3, the lesson objective states, “Identify and create situations involving unknown group size and find group size in situations,” which is shaped by 3.OA.A, “Represent and solve problems involving multiplication and division.”
• In Unit 3, Lesson 19, the lesson objective states, “Solve two-step word problems involving all four operations and assess the reasonableness of solutions,” which is shaped by 3.OA.D, “Solve problems involving the four operations, and identify and explain patterns in arithmetic.”
• In Unit 3, Lesson 23, the lesson objective states, “Identify arithmetic patterns and explain them using properties of operations,” which is shaped by 3.OA.D, “Solve problems involving the four operations, and identify and explain patterns in arithmetic.”
• In Unit 4, Lesson 7, the lesson objective states, “Find the area of a rectangle through multiplication of the side lengths,” which is shaped by 3.MD.C, “Geometric measurement: understand concepts of area and relate area to multiplication and addition.”  
• In Unit 4, Lesson 11, the lesson objective states, “Recognize area as additive. Find areas of composite figures when not all dimensions are given,” which is shaped by 3.MD.C, “Geometric measurement: understand concepts of area and relate area to multiplication and addition.” 
• In Unit 5, Lesson 3, the lesson objective states, “Find perimeter of shapes with all side lengths labeled,” which is shaped by 3.MD.D, “Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.”
• In Unit 6, Lesson 3, the lesson objective states, “Partition a whole into equal parts, identifying and counting unit fractions using pictorial area models and tape diagrams, identifying the unit fraction numerically,” which is shaped by 3.NF.A, “Develop understanding of fractions as numbers.”

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 2, Lesson 5 connects 3.OA.A to 3.OA.B when students relate multiplication and division and understand that division can represent situations of unknown group size or an unknown number of groups. For example, Unit 2, Lesson 5, Anchor Tasks, Problem 3 states, “Write a multiplication equation and a division equation to represent each of the following situations. a. Ross has 15 flowers that he wants to make into flower arrangements. Each flower arrangement will use 5 flowers. How many flower arrangements can he make? b. Heidi has 8 apps that she wants to place into rows of 4. How many apps will there be in each row?”
• In Unit 2, Lesson 10 connects 3.OA.A, 3.OA.B, and 3.OA.C by building fluency with multiplication and division facts using units of three. Students connect their conceptual understanding of multiplication and division to problems with an unknown value and demonstrate the commutative property. For example, Unit 2, Lesson 10, Problem Set, Problem 4 states, “a. Draw a model that shows 7 rows of 3. b. Write a multiplication sentence where the first factor represents the number of rows. ________ x ________ = ________.”
• In Unit 3, Lesson 1 connects 3.OA.B to 3.OA.D by having students study commutativity to find known facts of 6, 7, 8 and 9. Students also explore patterns on the multiplication chart to understand commutativity. For example, Unit 3, Lesson 1, Anchor Tasks, Problem 2 states, “Fill in the facts you know on the multiplication chart below. (A multiplication chart up to 10 is provided.)”