In This Unit of Study…

Students apply place value knowledge and reasoning to read and write decimals to the thousandths by using standard, expanded, and word form. They compose and decompose the values of multi-digit numbers with decimals in multiple ways by using objects, drawings, and expressions or equations. Concrete models, place value charts, and number lines will support student understanding.

B.E.S.T. Benchmarks:

• MA.5.NSO.1.2 Read and write multidigit numbers with decimals to the thousandths using standard form, word form and expanded form.
• MA.5.NSO.1.3 Compose and decompose multidigit numbers with decimals to the thousandths in multiple ways using the values of the digits in each place. Demonstrate the compositions or decompositions using objects, drawings and expressions or equations.

Overarching Key Concepts:

• Read and write decimals in standard and word form
• Read and write decimals in expanded form

In This Unit of Study…

StuStudents build upon their prior knowledge and understanding of place value, comparing, and ordering numbers, and decimals as fractions to compare decimals up to the thousandths place. They use comparative language (greater than, less than, or equal to) and symbols (>,<, or =) to make comparisons. Students will also order decimals within this range from greatest to least and from least to greatest.

B.E.S.T. Benchmarks:

• MA.5.NSO.1.4 Plot, order and compare multidigit numbers with decimals up to the thousandths.
• MA.5.DP.1.1 Collect and represent numerical data, including fractional and decimal values, using tables, line graphs or line plots.  

Overarching Key Concepts:

• Compare and order decimals to the thousandths place

In This Unit of Study…

Students extend their understanding and application of place value concepts in the base 10 system. Students extend their understanding and application of place value concepts in the base-10 system as they encounter multi-digit numbers with decimals to the thousandths place. Students reason about the magnitude of numbers by recognizing that a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Students use concrete and representational manipulatives, such as decimal squares, base-ten blocks, place-value charts, drawings, and interactive digital tools to investigate place value relationships.

B.E.S.T. Benchmarks:

• MA.5.NSO.1.1 Express how the value of a digit in a multidigit number with decimals to the thousandths changes if the digit moves one or more places to the left or right.
• MA.5.DP.1.1 Collect and represent numerical data, including fractional and decimal values, using tables, line graphs or line plots.  

Overarching Key Concepts:

• Compare and describe place value relationships

In This Unit of Study…

Fifth-grade students extend their understanding of place value by working with decimals to the thousandths place. Students at this grade have a deep understanding of place value and number sense, so they can explain and reason about rounded answers. Fifth-grade students round decimals to the nearest whole, tenth, and hundredths place. Students are expected to apply rounding while estimating an approximation and to determine the reasonableness of an answer.

B.E.S.T. Benchmarks:

• MA.5.NSO.1.5 Round multi-digit numbers with decimals to the thousandths to the nearest hundredth, tenth or whole number.

Overarching Key Concepts:

• Round decimals to the nearest whole number, tenth, or hundredth.

In This Unit of Study…

Students add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.

B.E.S.T. Benchmarks:

• MA.5.NSO.2.3 Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.
• MA.5.M.2.1 Solve multi-step real-world problems involving money using decimal notation.  

Overarching Key Concepts:

• Add and subtract decimals with procedural fluency

In This Unit of Study…

Students describe and reason about why volume formulas work, and they apply these formulas as an efficient and accurate means of determining volume. When presented with a problem where one of the side lengths is unknown, students use the formula that includes a variable to represent the unknown value. To solve, students use the mathematical concept that division is the inverse operation of multiplication to reason that the cubic volume of a right rectangular prism can be divided by the product of the known values to arrive at the unknown value. Once students have a strong conceptual understanding of how to represent multiplication, they gain efficiency with the calculations and are ready to become fluent with the standard algorithm.

B.E.S.T. Benchmarks:

• MA.5.GR.3.2  Find the volume of a right rectangular prism with whole-number side lengths using a visual model and a formula. 
• MA.5.GR.3.3 Solve real-world problems involving the volume of right rectangular prisms, including problems with an unknown edge length, with whole-number edge lengths using a visual model or a formula. Write an equation with a variable for the unknown to represent the problem. 
• MA.5.NSO.2.1 Multiply multidigit whole numbers including using a standard algorithm with procedural fluency.
• MA.5.AR.1.1 Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpreted within the context.  

Overarching Key Concepts:

• Explore and apply Volume formula
• Multiply multi-digit whole numbers with procedural fluency 

In This Unit of Study…

Building on previous knowledge of both multiplying whole numbers and adding and subtracting decimals, students will apply their knowledge to explore multiplication problems with multi-digit numbers with decimals to the hundredths place. To multiply decimals, students may begin with repeated addition and then move to more efficient strategies like place value, area models, arrays, and partial products to support their thinking. Students will also focus on place value to multiply a multi-digit number with decimals to the tenths by one-tenth and one-hundredth. Estimation by using rounding is another component of multiplying decimals. Number lines may be used to support rounding.

B.E.S.T. Benchmarks:

• MA.5.NSO.2.4 Explore the multiplication and division of multi-digit numbers with decimals to the hundredths using estimation, rounding and place value.
• MA.5.NSO.2.5 Multiply and divide a multi-digit number with decimals to the tenths by one-tenth and one-hundredth with procedural reliability.
• MA.5.M.2.1 Solve multi-step real-world problems involving money using decimal notation.  
• MA.5.GR.2.1 Find the perimeter and area of a rectangle with fractional OR DECIMAL side lengths using visual models and formulas.  

Key Concepts:

• Apply place value patterns to multiply by 0.1 and 0.01.
• Multiply multi-digit numbers with decimals to the hundredths place. 

In This Unit of Study…

Students make the connection between fractions and division by understanding that fractions can also represent division of a numerator by a denominator. Students will have many opportunities to explore the relationship between the numerator and denominator within real-world contexts. Students work with fractions greater than one; however, it is not the expectation for students to simplify fractions to lowest terms.

B.E.S.T. Benchmarks:

• MA.5.FR.1.1 Given a mathematical or real-world problem, represent the division of two whole numbers as a fraction

Overarching Key Concepts:

• Represent the division of whole numbers as a fraction

In This Unit of Study…

Once students have a strong conceptual understanding of how to represent division, they gain efficiency with the calculations and are ready to become fluent with the standard algorithm. Students will solve multi-step problems involving any of the 4 operations.

B.E.S.T. Benchmarks:

• MA.5.NSO.2.2 Divide multidigit whole numbers, up to five digits by two digits, including using a standard algorithm with procedural fluency. Represent remainders as fractions.  
• MA.5.AR.1.1 Solve multi-step real-world problems involving any combination of the four operations with whole numbers, including problems in which remainders must be interpreted within the context. 

Overarching Key Concepts:

• Divide multi-digit whole numbers with procedural fluency
• Problem solve with all four operations

In This Unit of Study…

Building on previous knowledge of both multiplying whole numbers and adding and subtracting decimals, students will apply their knowledge to explore multiplication problems with multi-digit numbers with decimals to the hundredths place. To multiply decimals, students may begin with repeated addition and then move to more efficient strategies like place value, area models, arrays, and partial products to support their thinking. Students will also focus on place value to multiply a multi-digit number with decimals to the tenths by one-tenth and one-hundredth. Estimation by using rounding is another component of multiplying decimals. Number lines may be used to support rounding.

B.E.S.T. Benchmarks:

• MA.5.NSO.2.4 Explore the multiplication and division of multidigit numbers with decimals to the hundredths using estimation, rounding and place value.
• MA.5.NSO.2.5 Multiply and divide a multi-digit number with decimals to the tenths by one-tenth and one-hundredth with procedural reliability
• MA.5.M.2.1 Solve multi-step real-world problems involving money using decimal notation. 

Overarching Key Concepts:

• Apply place value patterns to divide by 0.1 and 0.01
• Divide multi-digit numbers with decimals to the hundredths place

In This Unit of Study…

Students add and subtract fractions with unlike denominators, including mixed numbers and fractions greater than one, and they apply these operations to solve real-world problems. Instruction includes the use of estimation, manipulatives, visual models, and the properties of operations. When finding common denominators, students apply their understanding of factors up to 12 and their multiples.

B.E.S.T. Benchmarks:

• MA.5.FR.2.1 Add and subtract fractions with unlike denominators, including mixed numbers and fractions greater than 1, with procedural reliability.
• MA.5.AR.1.2 Solve real-world problems involving the addition, subtraction, or multiplication of fractions, including mixed numbers and fractions greater than 1.

Overarching Key Concepts:

• Explore the need for common denominators. 
• Add and subtract fractions less than 1. 
• Add and subtract mixed numbers. 

In This Unit of Study…

Students first become acquainted with the coordinate plane in fifth grade. They identify the origin and axes in the coordinate system, and they plot, and label ordered pairs in the first quadrant. Students connect their understanding of the number line to the x- and y-axes. Once they learn to navigate along the coordinate plane, they apply this knowledge by representing mathematical and real-world problems involving plotted points, and they interpret their values within the context of the situation. Instruction includes the connection between two-column tables and coordinates on a coordinate plane. In fifth grade, coordinate planes and corresponding ordered pairs should only include whole numbers.

B.E.S.T. Benchmarks:

• MA.5.GR.4.1 Identify the origin and axes in the coordinate system. Plot and label ordered pairs in the first quadrant of the coordinate plane.
• MA.5.GR.4.2 Represent mathematical and real-world problems by plotting points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.

Overarching Key Concepts:

• Solve problems involving the coordinate plane. 

In This Unit of Study…

Students multiply a fraction by a fraction, including mixed numbers and fractions greater than 1. When multiplying a given number by a fraction less than 1 or a fraction greater than 1, students predict and explain the relative size of the product to the given number without calculating. They accomplish this by connecting their knowledge of the relationship between fractions and decimals and by using estimation strategies to assess the reasonableness of an answer. They apply their understanding of multiplying fractions to solve real-world problems involving the multiplication of fractions. Problem solving includes using visual models and formulas to determine the perimeter and area of a rectangle with fractional side lengths. Instruction includes the use of manipulatives, drawings, and the properties of operations. Denominators are limited to whole numbers up to 20.

B.E.S.T. Benchmarks:

• MA.5.FR.2.2 Extend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability.
• MA.5.FR.2.3 When multiplying a given number by a fraction less than 1 or a fraction greater than 1, predict and explain the relative size of the product to the given number without calculating.
• MA.5.AR.1.2 Solve real-world problems involving the addition, subtraction or multiplication of fractions, including mixed numbers and fractions greater than 1.
• MA.5.GR.2.1 Find the perimeter and area of a rectangle with fractional or decimal side lengths using visual models and formulas.  

Overarching Key Concepts:

• Use models to explore multiplication of a fraction by a fraction 
• Use models to explore multiplication of mixed numbers 
• Predict and explain the relative size of the product 

In This Unit of Study…

Students make the connection between fractions and division by understanding that fractions can also represent division of a numerator by a denominator. Students will have many opportunities to explore the relationship between the numerator and denominator within real-world contexts. Students work with fractions greater than one; however, it is not the expectation for students to simplify fractions to lowest terms.

B.E.S.T. Benchmarks:

• MA.5.FR.2.4 Extend previous understanding of division to explore the division of a unit fraction by a whole number and a whole number by a unit fraction.
• MA.5.AR.1.3 Solve real-world problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.

Overarching Key Concepts:

• Explore division of whole numbers and unit fractions

In This Unit of Study…

Fifth-grade students use the geometric properties of sides, angles, and symmetry to classify quadrilaterals and triangles in hierarchies. For example, they conclude that squares are parallelograms because they are quadrilaterals with opposite sets of parallel and congruent sides. Students use deductive reasoning to justify their thinking about the categories into which shapes are sorted while gaining a deeper understanding of “if . . . , then . . . ” relationships. For example, if a shape is a parallelogram, then it must also be a quadrilateral.

B.E.S.T. Benchmarks:

• MA.5.GR.1.1 Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not belong to a category.
• MA.5.GR.4.1 Identify the origin and axes in the coordinate system. Plot and label ordered pairs in the first quadrant of the coordinate plane. 
• MA.5.GR.4.2 Represent mathematical and real-world problems by plotting points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation. 

Overarching Key Concepts:

• Classify triangles and quadrilaterals

In This Unit of Study…

Students will build on their prior knowledge of three-dimensional figures to identify and classify three-dimensional figures. In addition, students will learn about and understand attributes of right pyramids, right prisms, right circular cylinders, right circular cones, and spheres.

B.E.S.T. Benchmarks:

• MA.5.GR.1.2 Identify and classify three-dimensional figures into categories based on their defining attributes. Figures are limited to right pyramids, right prisms, right circular cylinders, right circular cones and spheres.

Overarching Key Concepts:

• Identify and classify three-dimensional figures

In This Unit of Study…

Students solve multistep real-world problems that involve converting measurement units to equivalent measurements within a single system of measurement. Students are not expected to memorize the conversions. Conversions include length, time, volume, and capacity represented as whole numbers, fractions, and decimals.

B.E.S.T. Benchmarks:

• MA.5.M.1.1 Solve multistep real-world problems that involve converting measurement units to equivalent measurements within a single system of measurement.

Overarching Key Concepts:

• Convert length measurement units
• Convert volume, capacity, and weight measurement units
• Convert time measurement units

In This Unit of Study…

Students collect, represent, and interpret numerical data with fractional and decimal values by using tables, line graphs, and line plots. They solve real-world problems in relation to the data collected, and they consider the distribution data by determining and analyzing measures of mode, median, mean, and range.

This unit of study also includes two Explores from Grade 4 focused on Data and Probability concepts that were not taught in MAFS, these Explores should be taught to address gaps in learning as we transition from MAFS to BEST Benchmarks.

B.E.S.T. Benchmarks:

• MA.5.DP.1.2 Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode, median or range.

Overarching Key Concepts:

• Interpret numerical data

In This Unit of Study…

Students identify and write a rule to represent the relationship between values in a numerical pattern.  They will use input-output tables to represent, generate, and extend numerical patterns.

B.E.S.T. Benchmarks:

• MA.5.AR.3.1 Given a numerical pattern, identify and write a rule that can describe the pattern as an expression.
• MA.5.AR.3.2 Given a rule for a numerical pattern, use a two-column table to record the inputs and outputs.

Overarching Key Concepts:

• Write rules for numerical patterns
• Complete input and output tables