4th Grade - Gateway 1

The instructional materials reviewed for Match Fishtank Mathematics Grade 4 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 2 states, “The value of the digit 8 in the number 85,673 is ten times the value of the digit 8 in what number? A. 38,625 B. 286,379 C. 852,345 D. 516,800.” (4.NBT.1)
• Unit 2 Assessment, Question 5 states, “Which of these numbers are prime numbers? Select the three numbers that are prime. A. 15 B. 19 C. 27 D. 37 E. 43 F. 51.” (4.OA.4)
• Unit 3 Assessment, Question 6 states, “A truck delivers 9 cases of canned corn. Each case holds 36 cans of corn. When the cases are unpacked, 15 of the cans are missing. The store manager places 7 cans of corn on each shelf. What is the fewest number of shelves the manager will need for all of the cans of corn delivered by the truck.” (4.OA.3)
• Unit 4 Assessment, Question 3 states, “Draw an obtuse angle.” (4.G.1)
• Unit 5 Assessment, Question 2 states, “Fill in the blanks below with <, >, or = to make true number sentences. a. $$\frac{5}{12}$$__$$\frac{6}{10}$$  b. $$\frac{8}{6}$$__$$\frac{8}{7}$$.” (4.NF.2)
• Unit 5 Assessment, Question 4 states, “Of the students in one school, $$\frac{1}{12}$$ play soccer, $$\frac{3}{8}$$ play basketball, $$\frac{2}{5}$$ take music lessons, and $$\frac{2}{6}$$ take dance lessons. Which list orders the fractions from least to greatest? A. $$\frac{1}{12}$$,  $$\frac{2}{5}$$,  $$\frac{2}{6}$$,  $$\frac{3}{8}$$   B. $$\frac{2}{5}$$,  $$\frac{3}{8}$$,  $$\frac{2}{6}$$,  $$\frac{1}{12}$$   C. $$\frac{2}{5}$$,  $$\frac{3}{8}$$,  $$\frac{2}{6}$$,  $$\frac{1}{12}$$   D. $$\frac{1}{12}$$,  $$\frac{2}{6}$$,  $$\frac{3}{8}$$,  $$\frac{2}{5}$$.” (4.NF.2) 
• Unit 6 Assessment, Question 5 states, “Explain how to find $$2\times\frac{5}{12}$$ using the number line. Find the product.” Students are provided with a number line from 0 to 1 marked off in sixths. (4.NF.4b)
• Unit 7 Assessment, Question 7 states, “Plot the following points on the number line below: 7.11, 7.06, 7.6, 7.90, and 7.75. The first one has been done for you.” A number line is provided with 7.11 marked. (4.NF.7)
• Unit 8 Assessment, Question 6 states, “Ms. Ravelo bought a gallon of paint to paint her living room. She only used half of it. How much paint does she have left in cups? Show or explain your work.” (4.MD.2)

The instructional materials reviewed for Match Fishtank Mathematics Grade 4 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 7 out of 8, which is approximately 88%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 125 out of 145, which is approximately 86%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 144 out of 158, which is approximately 91%. 

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 86% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Match Fishtank Mathematics Grade 4 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 3, Lesson 11, Anchor Tasks, students apply the formulas for area and perimeter (4.MD.3) in real-world and mathematical problems involving all four operations (4.OA.3). Problem 1 states, “Edris wants to build a garden in his backyard to grow vegetables. He buys 60 yards of fencing to put around the garden to keep animals out. He wants the garden to be 12 feet long. What should the length of his garden be so that he uses all of the fencing he bought?”
• In Unit 3, Lesson 16, Problem Set, students explore number and shape patterns (4.OA.5) using the four operations to draw conclusions about them (4.NBT.B). Problem 1 states, “Here is part of a repeating pattern. a. Draw the next 4 shapes in this pattern. b. What will be the 75th shape in the pattern? Explain how you know.”
• In Unit 6, Lessons 22, Anchor Tasks, students extend their understanding of fraction equivalence and ordering (4.NF.A) to solve problems using information presented in line plots (4.MD.4). Problem 2 states, “Fourth-grade students interested in seeing how heights of students change for kids around their age measured the heights of a sample of eight-year-olds and a sample of ten-year-olds. Their data are plotted below. Describe the key differences between the heights of these two age groups.”
• In Unit 8, Lessons 1, Anchor Tasks, students use their understanding of place value (4.NBT.1) to express metric length measurements in terms of a smaller unit (4.MD.1). Problem 2 states, “Fill in the following conversion tables” and Guiding Questions include, “How many times larger is a kilometer than a meter? How many meters are equal to 1 kilometer? 2 kilometers? How did you convert from kilometers to meters in the last case? Write an equation to represent the computation. (Write ‘6 x (1 km) = 6 x (1,000 m) = 6,000 m.’)”

The instructional materials reviewed for Match Fishtank Mathematics Grade 4 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 158 instructional days (including lessons, flex days, and unit assessments). 

• There are 137 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 eight unit assessments, one day each. 
• The pacing guide suggests 13 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 4 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, “Because students did not focus heavily on place value in Grade 3, Unit 1 begins with where things left off in Grade 2 of understanding numbers within 1,000. Students get a sense of the magnitude of each place value by visually representing the place values they are already familiar with and building from there. Once students have a visual and conceptual sense of the “ten times greater” property, they are able to articulate why a digit in any place represents 10 times as much as it represents in the place to its right (4.NBT.1).” There are more examples that follow to illustrate the relation to grade-level concepts. 
• The Unit 1 Summary also connects future grade level content, for example, “In subsequent grade levels, students generalize their base ten understanding to decimals. While students do some work with tenths and hundredths later on in Grade 4 (4.NF.5-7), students in Grade 5 are able to extend the decimal system to many more place values, seeing that a digit represents 110 of what it represents in the place to its left (5.NBT.1-3). Students subsequently round, compare, and operate on decimals as they did with numbers greater than one in Grade 4. Thus, this unit sets a precedent for a deep understanding of the number system that supports much of their mathematical knowledge later this year and in years to come.”
• The Unit 8 Summary includes states, “In previous grades, students have worked with many of the metric and customary units (2.MD.1-6, 3.MD.1-2). They’ve noticed the relationship between some units to help them understand various measurement benchmarks but have not yet done any unit conversions. Not only does this unit build on measurement work from previous grades, but it also relies on myriad skills and understanding developed throughout Grade 4.” 
• The Unit 8 Summary also connects future grade level content, “The unit not only looks back on the year in review, it also prepares students for work in future grades, including the very direct link to converting from smaller units to larger ones in Grade 5 (5.MD.1) and also to ratios and proportions in the middle grades (6.RP.1) as well as many other areas to come.”
• 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 4 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 4, Anchor Task, Problem 1 states, “Look at your paper base ten blocks. The ones piece is the smallest square. Then tens piece is a $$10\times1$$ strip. The hundreds piece is the larger $$10\times10$$ square. a. Use the paper base ten blocks to construct 1,000. Use tape as needed. b. Use the paper base ten blocks to construct 10,000. Use tape as needed. c. What comes next? What shape will it be?” (4.NBT.1)
• Unit 2, Lesson 12, Problem Set, Problem 2 states, “Estimate. Then solve. Show or explain your work. a. $$5\times17$$ b. $$94\times2$$ c. $$9\times22$$ d. $$91\times7$$.” (4.NBT.5)
• Unit 3, Lesson 10, Target Task, Problem 1 states, “Solve. Show or explain your work. Then check your work. a. $$92\div 3$$  b. $$7,040\div 4$$.” (4.NBT.6)
• Unit 5, Lesson 4, Problem Set, Problem 5 states, “Explain how you know $$\frac{5}{8}$$ is equal to $$\frac{5\times6}{8\times6}$$. Use a model to explain your thinking.” (4.NF.1)
• Unit 6, Lesson 6, Anchor Task, Problem 1 states, “1. Estimate the following sums. a. $$\frac{3}{4}+\frac{2}{4}$$   b. $$\frac{5}{6}+\frac{3}{6}$$ Solve for the actual sums in #1 above.” (4.NF.3a)
• Unit 8, Lesson 3, Target Task, Problem 2 states, “________________ mL is equal to 342 L 645 mL.” (4.MD.1)
• Unit 8, Lesson 12, Problem Set, Problem 1 states, “A short string is 1.8 meters. It is 70 centimeters shorter than a longer string. How many centimeters long is the longer string?” The Discussion of Problem Set states, “How did you interpret the remainder in #2? In #7(a), how many different ways were 7 halves represented? (30 min 7, as $$\frac{7}{2}$$ and as $$\frac{6}{2}+\frac{1}{2}$$) What advantage is there to knowing all of these representations when it comes to solving a problem like this one? What shortcuts or efficiencies did you use today when solving your problems? How do you decide whether to start by converting to a smaller unit or to work with the mixed number or decimal measurements?” (4.MD.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 2, Lesson 6, the Foundational Standards include Operations and Algebraic Thinking, 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that $$8\times5=40$$, one knows $$40\div5=8$$) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers). The materials states, “4th Grade Math - Unit 2: Multi-Digit Multiplication. Students deepen their understanding of multiplication by exploring factors and multiples, multiplicative comparison, as well as multi-digit multiplication.” 
• In Unit 7, Lesson 9, the Foundational Standards include Numbers and Operations- Fractions, 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram). The materials state, “4th Grade Math - Unit 7: Decimal Fractions. Students expand their conception of what a ‘number’ is as they are introduced to an entirely new category of number, decimals, which they learn to convert, compare, and add in simple cases.” 

The instructional materials reviewed for Match Fishtank Grade 4 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 6, the lesson objective states, “Find factor pairs for numbers to 100 and recognize that a whole number is a multiple of each of its factors,” which is shaped by 4.OA.B, “Gain familiarity with factors and multiples.”
• In Unit 4, Lesson 1, the lesson objective states, “Identify and draw points, lines, line segments, rays and angles,” which is shaped by 4.G.A, “Draw and identify angles, and classify shapes by properties of their lines and angles.”
• In Unit 4, Lesson 10, the lesson objective states, “Identify and measure angles as turns and recognize them in various contexts,” which is shaped by 4.MD.C, “Geometric Measurement: understand concepts of angle and measure angles.”
• In Unit 5, Lesson 4, the lesson objective states, “Recognize and generate equivalent fractions with smaller units using multiplication,” which is shaped by 4.NF.A, “Extend understanding of fraction equivalence and ordering.”
• In Unit 6, Lesson 8, the lesson objective states, “Decompose and compose non-unit fractions greater than two as a sum of unit fractions and as a whole number times a unit fraction,” which is shaped by 4.NF.B, “Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.”
• In Unit 7, Lesson 10, the lesson objective states, “Compare two or more decimals written in various forms,” which is shaped by 4.NF.C, “Understand decimal notation for fractions, and compare decimal fractions.”
• In Unit 8, Lesson 8, the lesson objective states, “Express time measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require time unit conversion,” which is shaped by 4.MD.A, “Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.”

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 1, Lesson 15 connects 4.OA.A with 4.NBT.A,B as students solve multi-step word problems involving addition, and assess the reasonableness of answers using rounding. For example, Unit 1, Lesson 15, Target Task states, “In January, Scott earned $8,999. In February, he earned $2,387 more than in January. In March, Scott earned the same amount as in February. 1. Choose a place value to round to, then use those rounded values to estimate the amount Scott earned altogether during those three months. 2. Exactly how much did Scott earn in those three months? 3. Assess the reasonableness of your answer in (b). Use your estimate from (a) to explain.”
• In Unit 3, Lesson 12, students connect 4.OA.A to 4.NBT.B by solving two-step word problems, including those involving interpreting the remainder. For example, Unit 3, Lesson 12, Problem Set, Problem 2 states, “The first grade went on a field trip to the museum. There are 26 students in each class and four classes in total. Each van can hold 7 students. How many vans were needed to get all the students to the museum?”
• In Unit 5, Lesson 3 connects 4.NF.A to 4.OA.A as students generate equivalent fractions with smaller units using the area model. For example, Unit 5, Lesson 3, Anchor Tasks, Problem 1 states, “a. A garden is divided into rows of various vegetables. Three out of four rows are tomatoes. Partition and shade the square below to show how much of the garden is tomatoes. b. The garden is going to be shared with family and friends so that each person’s share of the harvest is three-fourths tomatoes. How would you partition the garden if it’s shared by two people? Show on the model above. c. What fraction of the newly divided garden is corn when it is shared by two people? Write an equation to show this relationship. d. Go through the same process for the garden but now splitting it evenly for three and five people on the models below.”