5th Grade - Gateway 1

The materials reviewed for Achievement First Mathematics Grade 5 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. Each unit contains a Post-Assessment which is a summative assessment based on the standards designated in that unit. 

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

• Unit 1, Common Core, Item 23, “What is 43.98 rounded to the nearest tenths place?” (5.NBT.4)

• Unit 4, Unit Assessment, Item 3, “A rectangular garden has an area of 400 square meters. If the garden has a width of 5 meters, how long is the garden?” (5.NBT.2)

• Unit 5, Unit Assessment, Item 1, “At a Sand Castle building contest, the tallest tower was 2 yards tall and the shortest tower was 1 foot and 4 inches tall. How much taller was the tallest tower than the shortest tower?” (5.MD.2)

• Unit 8, Post-Assessment, Item 4, “Anthony has 12 marbles if \frac{3}{4} of the marbles are clear, how many clear marbles does Anthony have. Draw a model to show your answer.” (5.NF.4) 

Achievement First Mathematics Grade 5 has assessments linked to external resources in some Unit Overviews; however there is no clear delineation as to whether the assessment is used for formative, interim, cumulative or summative purposes.

The materials reviewed for Achievement First Mathematics Grade 5 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each lesson provides State Test Alignment practice, Exit Tickets, Think About It, Test the Conjecture or Exercise Based problems, Error Analysis, Partner Practice, and Independent Practice, which all include grade-level practice for all students. The Partner and Independent Practice provide practice at different levels: Bachelor, Masters and PhD. Each unit also provides Mixed Practice, Problem of the Day, and Skill Fluency practice. By the end of the year, the materials address the full intent of the grade-level standards. Examples include:

• Unit 1, Lesson 6, Day 2 Independent Practice Question 2 (Master Level), students explain the pattern in the placement of the decimal point when a decimal is divided by a power of ten. “How many powers of ten would you need to divide 4,700 by to get a result of forty-seven thousandths? Prove your thinking in the space below.” (5.NBT.2)

• Unit 3, Lesson 2, Mixed Practice, Problem 5, students multiply multi-digit whole numbers. “A petroleum company has 14 large barrels full of oil that they sell to local gas stations. All 14 barrels hold approximately 315 gallons of oil, and a gas station will typically buy 500 gallons of oil each time they order. The owner of the company estimates that they have around 4500 gallons of oil, so they allow 9 gas stations to buy oil. a. Explain how the owner likely found the estimate of 4500. b. Does the petroleum company have enough oil to allow 9 gas stations to buy oil? If not, how many more barrels of oil would they need to produce?” (5.NBT.5)

• Unit 7, Lesson 4, Exit Ticket, students estimate sums and differences of fractions with unlike denominators. “Kendra made the following statements while estimating. Determine whether you agree with each, and mark yes or no. 0.33 + \frac{9}{10} is about 1\frac{1}{2}; 1\frac{4}{5} - \frac{3}{7} is approximately 2 - \frac{1}{2}” (5.NF.1, 5.NF.2).

• Unit 8, Lesson 4, Mixed Practice, Day 3, Problem 2, students divide decimals using place value strategies (5.NBT.7). “Alyssa had $0.70. She put $$\frac{1}{10}$$ of it in her penny jar to save. How much money did she save? a) .07 cents b) 7 cents c) 70 cents d) 7 dollars.”

The materials reviewed for Achievement First Mathematics Grade 5 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 88 out of 132, which is approximately 67%.

• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 113 out of 143, which is approximately 79%. 

• The instructional minutes were calculated by taking the number of minutes devoted to the major work of the grade (11,365) and dividing it by the total number of instructional minutes (12,870), which is approximately 88%. 

A minute-level analysis is most representative of the materials because the units and lessons do not include all of the components included in the math instructional time. The instructional block includes a math lesson, math stories, and math practice components. As a result, approximately 88% of the materials focus on major work of the grade.

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

There are opportunities in which supporting standards/clusters are used to support major work of the grade and are connected to the major standards/clusters of the grade. Examples include:

• Unit 3, Lesson 2, Independent Practice, Ph.D Level Problem 1, “Carol sells bracelets and pairs of earrings at a craft fair. Each item sells for $8. Write an expression to show how much money Carol makes if she sells 23 bracelets and 17 pairs of earrings, but pays $25 to rent her booth.” This problem connects the major work of 5.NBT.5, fluently multiply multi-digit whole numbers, to the supporting work of 5.OA.A, writing and interpreting numerical expressions, as students write an expression and solve the problem. 

• Unit 5, Lesson 5, Exit Ticket, Problem 2, “Valerie uses 12 fluid oz of detergent each week for her laundry. If there are 5 cups of detergent in the bottle, in how many weeks will she need to buy a new bottle of detergent. Explain how you know.” This problem connects the major work of 5.NBT.B, perform operations with multi-digit whole numbers and with decimals to the hundreths, to the supporting standard 5.MD.1, convert among different sized standard measurement units within a given measurement system, as students perform a conversion and utilize at least one of the four operations to solve the problem. 

• Unit 10, Cumulative Review 10.1, Problem of the Day, Day 3, “This year, the managers of the farm will change the fraction of the budget for housing to \frac{1}{8} but will leave the fraction of the budget for food and medical care the same. Again, the remaining portion of the budget will be for maintenance expenses. What is the difference between the fraction of the budget for maintenance this year and last year?” This problem connects the major work of 5.NF.1 to the supporting cluster 5.MD.B, as students represent and interpret data while solving a multi-step problem involving adding and subtracting fractions with unlike denominators

The materials reviewed for Achievement First Mathematics Grade 5 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Examples include:

• Unit 6, Lesson 5, students connect 5.MD.C, understand concepts of volume and relate volume to multiplication and addition, to 5.NBT.B, perform operations with multi-digit whole numbers and decimals, as they determine unknown values for measurements based on a given volume. In Exit Ticket, Problem 2, “Bernard is packing a box with a volume of 96 cubic inches. Enter a possible base area and height for his box below.” 

• Unit 8, Cumulative Review 8.3, Problem of the Day, Day 3 connects 5.NBT.A, 5.NBT.B, and 5.OA.A, as students use their understanding of the place value system to evaluate a multi-step problems involving decimals, giving the answer in various forms. The materials state, “A.) Evaluate and express your answer in the three given forms: [(15×2)+(2×4)]+[12.06-(3×4)]; Standard Form, Expanded Form, Word Form.”

• Unit 9, Cumulative Review 9.3, Problem of the Day, Day 2 connects 5.NBT.B with 5.NF.B, as students perform operations with multi-digit whole numbers and fractions. “A chocolate factory produced 5,301 pounds of chocolate every day for 31 days in the month of January and 4,592 pounds of chocolate every day for 28 days in the month of February. Of their total chocolate produced, \frac{5}{8}  was milk chocolate. How many ounces of non-milk chocolate did the factory produce?”

• Unit 11, Lesson 5, students connect 5.MD.B, represent and interpret data to 5.G.A, graph points on the coordinate plane to solve real-world and mathematical problems, as they generate data and develop a coordinate graph. Independent Practice, Bachelors Level, “There is a $25 annual fee for membership at the gym. It also costs 5 per visit to use the gym. Fill in the table to show the total cost of \frac{5}{8} visits to the gym. A. Write the ordered pairs, and graph the data on the coordinate graph. B. Write the ordered pair that represents 6 visits to the gym. Explain what the ordered pair means. C. If Amaya can only spend up to $50 in one month, how many times can she visit the gym? Explain.”

The materials reviewed for Achievement First Mathematics Grade 5 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 

Each unit has a Unit Overview and a section labeled “Identify Desired Results” where the standards for the unit are provided as well as a correlating section “Previous Grade Level Standards/Previously Taught & Related Standards” where prior grade-level standards are identified. Examples include:

• Unit 2, Unit Overview, Identify Desired Results: Identify the Standards lists 5.NF as being addressed in this unit and 4.NF.1, 4.NF.2, and 4.NF.3 as Previous Grade Level Standards/ Previously Taught & Related Standards connections. “Starting in 3rd grade, students learn to recognize fractions as numbers (3.NF.A). They learn to represent fractions concretely and pictorially using unit fractions, on a number line and with equivalent fractions. They also learn to reason about relative sizes of fractions that have the same numerator or denominator. In 4th grade, students extend their understanding of fractions to compare and order fractions using equivalent fractions (4.NF.A), add and subtract fractions with like denominators, and multiply fractions and whole numbers (4.NF.B).” 

• Unit 6, Unit Overview, Identify the Narrative connects the work of this unit to prior work in 3rd and 4th grades. “Unit 6 draws heavily from Geometry and Numbers in Base Ten content learned in grades 3 and 4. In grade 3, students develop an understanding of area and relate the concept to both multiplication and addition. They also apply the concept to explore number properties (commutative and distributive) (3.MD.C). In fourth grade, students solidify their understanding of area and learn to apply the area formula fluently when measuring the area of rectangles (4.MD.3). These understandings and skills are useful moving into 5th grade as the concept of volume is developed concretely, pictorially and abstractly by making connections between volume and base-area using unit cubes, pictures and formulas as well as addition and multiplication to calculate the volume of a right rectangular prism. (5.MD.3,4,5).”

The materials develop according to the grade-by-grade progressions in the Standards. However, content is not consistently connected to future grades within each Unit Overview. Each Unit Overview contains a narrative that includes a “Linking” section that describes in detail the progression of the standards within the unit. Examples include:

• Unit 2, Overview, Identify the Narrative, “Following this unit, students study multi-digit whole number computation to develop fluency with standard algorithms for whole number in multiplication and division, before moving into fraction and decimal operations. In later grades students continue to leverage this work when forms of rational numbers (grade 6), operating with all forms of rational numbers (grades 6 and 7), understanding ratios and rates of changes (grade 6-8), creating probability models (grade 7), working on coordinate grids (grades 5-8), and creating graphs to represent data (grades 5-8).” 

• Unit 4, Unit Overview, Identify the Narrative, “Throughout elementary school students are also writing simple expressions or equations to represent and solve word problems (2.OA.1, 3.OA.3, 4.OA.2). They use bar models to make sense of, think about, and solve simple real-world applications of multiplication. In fifth grade, students will leverage early work in Operations and Algebraic thinking to represent and solve real-world problems, and to write and evaluate mathematical expressions using the order of operations (5.OA.1, 5.OA.2).” 

• Unit 7, Unit Overview, Identify the Narrative, “In 5th grade, students will progress to adding fractions and mixed numbers with unlike denominators. In 4th grade and Unit 1 in 5th grade, scholars learned to find equivalent fractions using models and the identity property. This skill will be a crucial prerequisite to this unit. Additionally, scholars also learned how to add and subtract fractions and mixed numbers with like denominators by using fraction tiles, drawing models, and using the standard algorithm. In fourth grade, this included some regrouping, which is typically where scholars struggle the most. It is recommended to assess prior knowledge/skill for adding and subtracting mixed numbers (with like denominators) where regrouping is required to determine how to best target pre-existing gaps while progressing in this unit.”