In This Unit of Study…

Students extend their understanding and application of place value concepts in the base 10 system. Students will read and write numbers up to 1,000,000 by using standard, expanded, and word form. They will solidify the concept that in the base-10 system, the value of each place is ten times the value of the place to the immediate right.

B.E.S.T. Benchmarks:

• MA.4.NSO.1.1 Express how the value of a digit in a multi-digit whole number changes if the digit moves one place to the left or right.
• MA.4.NSO.1.2 Read and write multi-digit whole numbers from 0 to 1,000,000 using standard form, expanded form and word form.
• MA.4.NSO.2.1 Recall multiplication facts with factors up to 12 and related division facts with automaticity.  

Overarching Key Concepts:

• Fluency: Multiply by 10
• Read and Write Multi-Digit Whole Numbers 
• Explore Place Value Relationships 

In This Unit of Study…

Students build upon their prior knowledge of comparing and ordering whole numbers to compare whole numbers up to 1,000,000. Students use place value and scaled number lines to make comparisons. They use comparative language (greater than, less than, or equal to) and symbols (>, <, or =) to make comparisons.  Students will also order numbers within this range from greatest to least and from least to greatest.

B.E.S.T. Benchmarks:

• MA.4.NSO.1.3 Plot, order and compare multi-digit whole numbers up to 1,000,000.
• MA.4.NSO.2.1 Recall multiplication facts with factors up to 12 and related division facts with automaticity. 
• MA.4.AR.3.2 Generate, describe, and extend a numerical pattern that follows a given rule.

Overarching Key Concepts:

• Fluency: Multiply by 5
• Compare and Order Numbers up to 1,000,000

In This Unit of Study…

Fourth-grade students continue to use number lines to round, but experience with place value and number sense allows them to generalize the process of rounding numbers. This leads to being able to round much larger numbers and to round to digits other than the leading digit. For example, to round 5,397 to the nearest 10, the tens place changes from 90 to 100, and this affects the resulting digits in the ones, tens, and hundreds places. Students begin to develop efficiency rules for rounding numbers by thinking about the proximity of a benchmark number in relation to a midpoint set between two compatible numbers. Students recognize that rounding is a tool for estimation while solving problems. Fourth-grade students round multi-digit numbers up to 10,000 efficiently and appropriately, both in and out of the context of a word problem.

B.E.S.T. Benchmarks:

• MA.4.NSO.1.4 Round whole numbers from 0 to 10,000 to the nearest 10, 100 or 1,000.
• MA.4.NSO.2.1 Recall multiplication facts with factors up to 12 and related division facts with automaticity. 
• MA.4.AR.3.2 Generate, describe, and extend a numerical pattern that follows a given rule.

Overarching Key Concepts:

• Fluency: Use doubles to multiply by 2, 4, and 8
• Round whole numbers 0 to 10,000

In This Unit of Study…

Students will model and represent various multiplicative comparison scenarios with the unknown in any position. Students will use concrete manipulatives, representations, and equations to model multiplicative comparison scenarios.

B.E.S.T. Benchmarks:

• MA.4.AR.1.1 Solve real-world problems involving multiplication and division of whole numbers including problems in which remainders must be interpreted within the context. 
• MA.4.AR.2.2 Given a mathematical or real-world context, write an equation involving multiplication or division to determine the unknown whole number with the unknown in any position. (limited to factors within 12 and related division facts) 
• MA.4.NSO.2.1 Recall multiplication facts with factors up to 12 and related division facts with automaticity. 
• MA.4.AR.3.1 Determine factor pairs for a whole number from 0 to 144. Determine whether a whole number from 0 to 144 is prime, composite or neither.  

Overarching Key Concepts:

• Fluency: Multiply by 3 and 6
• Represent and solve multiplicative comparison problems

In This Unit of Study…

Students will learn to multiply two whole numbers up to three digits by numbers up to two digits with procedural reliability.  Students will explore various multiplication strategies including base ten model, area model, and partial product. In addition, students will use the standard algorithm to solve two-digit by two-digit multiplication problems.

B.E.S.T. Benchmarks:

• MA.4.NSO.2.2 Multiply two whole numbers, up to three digits by up to two digits, with procedural reliability.
• MA.4.NSO.2.3 Multiply two whole numbers, each up to two digits, including using a standard algorithm with procedural fluency.
• MA.4.NSO.2.5 Explore the multiplication and division of multi-digit whole numbers using estimation, rounding and place value 
• MA.4.AR.1.1 Solve real-world problems involving multiplication and division of whole numbers including problems in which remainders must be interpreted within the context. 
• MA.4.NSO.2.1 Recall multiplication facts with factors up to 12 and related division facts with automaticity. 

Overarching Key Concepts:

• Fluency:  Multiply by 11 and 12 
• Apply Patterns of Multiplication to Estimate Products 
• Use Area Models to Represent Multiplication 
• Use Partial Products and a Standard Algorithm to Multiply  

In This Unit of Study…

Students will extend division to include quotients with up to four-digit dividends and one-digit divisors. They are expected to find and write remainders as fractional parts of the divisor. A variety of strategies are explored based on place value, properties of operations, and the relationship between multiplication and division. Students will focus on choosing a method they can use reliably.

B.E.S.T. Benchmarks:

• MA.4.NSO.2.4 Divide a whole number up to four digits by a one-digit whole number with procedural reliability. Represent remainders as fractional parts of the divisor.   
• MA.4.NSO.2.5 Explore the multiplication and division of multi-digit whole numbers using estimation, rounding and place value.   
• MA.4.AR.1.1 Solve real-world problems involving multiplication and division of whole numbers including problems in which remainders must be interpreted within the context.   
• MA.4.NSO.2.1 Recall multiplication facts with factors up to 12 and related division facts with automaticity.   
• MA.4.AR.3.2 Generate, describe, and extend a numerical pattern that follows a given rule.

Overarching Key Concepts:

• Fluency: Multiply by 7
• Use Equal Groups Models and Place Value to Divide 
• Use Area Models to Represent Division 
• Use Partial Products to Divide
• Determine and Interpret Remainders

In this Unit of Study...

Students will use models, drawings, and tables to convert customary and metric units of length, weight/mass, and liquid volume. They will convert within a single system of measurement, and will apply what they know about measurement  to solve two-step real-world problems involving distance, weight/mass, and volume. 

B.E.S.T. Benchmarks

• MA.4.M.1.2 Convert within a single system of measurement using the units: yards, feet, inches; kilometers, meters, centimeters, millimeters; pounds, ounces; kilograms, grams; gallons, quarts, pints, cups; liter, milliliter; and hours, minutes, seconds. 
• MA.4.M.2.1 Solve two-step real-world problems involving distances and intervals of time using any combination of the four operations.  

Overarching Key Concepts

• Convert Customary and Metric Units of Length
• Convert Customary and Metric Units of Weight/Mass, and Liquid Volume

In This Unit of Study…

Students solve perimeter and area mathematical and real-world problems, including problems with unknown sides, for rectangles with whole-number side lengths. They also investigate problems involving rectangles with the same-size perimeter and different-size areas or with the same-size area and different-size perimeters. Problems involving multiplication are limited to products of up to 3 digits by 2 digits, and problems involving division are limited to up to 4 digits divided by 1 digit. When calculating area and perimeter, it is the expectation that students express the appropriate units in word form.

B.E.S.T. Benchmarks:

• MA.4.GR.2.1 Solve perimeter and area mathematical and real-world problems, including problems with unknown sides, for rectangles with whole-number side lengths.
• MA.4.GR.2.2 Solve problems involving rectangles with the same perimeter and different areas or with the same area and different perimeters.
• MA.4.NSO.2.1 Recall multiplication facts with factors up to 12 and related division facts with automaticity.  
• 4.MA.DP.1.1 Solve real-world problems involving numerical data.  

Overarching Key Concepts:

• Fluency: Multiply by 9
• Determine Perimeter and Area of a Rectangles 
• Solve Problems involving Perimeter and Area Relationships 

In This Unit of Study…

Students will explore equalities and determine if equations are true or false. Students will explain how they determined an equation was true or false using comparative relational thinking. When given a real-world or mathematical context, students will write an equation involving multiplication or division using a variable for the unknown. Students will also solve for the unknown.

B.E.S.T. Benchmarks:

• MA.4.AR.2.1 Determine and explain whether an equation involving any of the four operations with whole numbers is true or false. (12×12)  
• MA.4.AR.2.2 Given a mathematical or real-world context, write an equation involving multiplication or division to determine the unknown whole number with the unknown in any position. (12×12)  
• MA.4.NSO.2.1 Recall multiplication facts with factors up to 12 and related division facts with automaticity.   

Overarching Key Concepts:

• Fluency: Multiply by 0 and 1
• Determine and Explain whether Equations are True or False
• Determine an Unknown value that will Make an Equation True

In This Unit of Study…

Students will explore angles as an attribute of two-dimensional figures. They will identify and classify angles as acute, right, obtuse, straight, or reflex. Students will understand that the vertex of an angle is located at the center of a circle; it is from this point that two rays can create angle measurements. They are introduced to a new type of measurement when learning to measure angles. Students will learn that angles are measured by the “turning distance” between two rays, which use increments of 1/360 of a circle, or a 1° (degree) angle. In addition, students will estimate angle measures and practice measuring angles by using a protractor. This includes aligning the vertex, the zero edge, and the ray properly to tell the degrees of an angle. Fourth-grade students will learn to read, document, and draw angles in the proper mathematical format. This scope helps students discern that angle measure is additive. Through decomposing angles into nonoverlapping parts, students will see that the angle measure of the whole is the sum of the angle measures of the parts. In conclusion, students will solve real-world and mathematical problems to find unknown angles, and they will write an equation to represent the unknown.

B.E.S.T. Benchmarks:

• MA.4.GR.1.1 Informally explore angles as an attribute of two-dimensional figures. Identify and classify angles as acute, right, obtuse, straight or reflex.
• MA.4.GR.1.2 Estimate angle measures. Using a protractor, measure angles in whole-number degrees and draw angles of specified measure in whole-number degrees. Demonstrate that angle measure is additive.
• MA.4.GR.1.3 Solve real-world and mathematical problems involving unknown whole-number angle measures. Write an equation to represent the unknown.

Overarching Key Concepts:

• Identify and Classify Angles
• Estimate and Measure Angles
• Determine Unknown Angle Measures

In This Unit of Study…

Students will decompose a fraction, including mixed numbers and fractions greater than one, into a sum of fractions with the same denominator in multiple ways. They will demonstrate each decomposition with objects, drawings, and equations.

B.E.S.T. Benchmarks:

• MA.4.FR.2.1 Decompose a fraction, including mixed numbers and fractions greater than one, into a sum of fractions with the same denominator in multiple ways. Demonstrate each decomposition with objects, drawings, and equations.

Overarching Key Concepts:

• Decompose Fractions and Mixed Numbers in Multiple Ways

In This Unit of Study…

Students add and subtract fractions with like denominators, including mixed numbers and fractions greater than one. They apply these operations to solve real-world problems. Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16, and 100. Problems include creating real-world situations based on an equation or by representing a real-world problem with a visual model or equation. Fractions within problems must reference the same whole. Students are expected to use word form, manipulatives, drawings, and number lines when adding and subtracting fractions. It is not necessary for students to simplify fractions.

B.E.S.T. Benchmarks:

• MA.4.FR.2.2 Add and subtract fractions with like denominators, including mixed numbers and fractions greater than one, with procedural reliability.  
• MA.4.AR.1.2 Solve real-world problems involving addition and subtraction of fractions with like denominators, including mixed numbers and fractions greater than one.  

Overarching Key Concepts:

• Add and Subtract Fractions Less than One 
• Add and Subtract Mixed Numbers 

In This Unit of Study…

Students use visual models, such as area models and number lines, as they generate and describe how the numerator and denominator are affected when the equivalent fraction is created. Students explore the addition of a fraction with a denominator of 10 to a fraction with a denominator of 100 by using equivalent fractions. It is not the expectation that students write their fractional answers in lowest terms.

B.E.S.T. Benchmarks:

• MA.4.FR.1.1 Model and express a fraction, including mixed numbers and fractions greater than one, with the denominator 10 as an equivalent fraction with the denominator 100.
• MA.4.FR.1.3 Identify and generate equivalent fractions, including fractions greater than one. Describe how the numerator and denominator are affected when the equivalent fraction is created.
• MA.4.FR.2.3 Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100 using equivalent fractions.  

Overarching Key Concepts:

• Identify and generate equivalent fractions (including fractions greater than one)

In This Unit of Study…

Students plot, order, and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators. Instruction includes utilizing an appropriately scaled number line and reasoning about relative sizes of fractions. Students reason about distances of each fraction from benchmark fractions.  Comparisons will be made by using the symbols >, <, or =, accompanied with a justification of the comparison, and denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16, and 100.

B.E.S.T. Benchmarks:

• MA.4.FR.1.4 Plot, order and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators.

Overarching Key Concepts:

• Compare and Order Fractions and Mixed Numbers

In This Unit of Study…

Students explore the multiplication of a fraction by a whole number or a whole number by a fraction. Instruction includes the use of visual models or number lines and the connection to the commutative property of multiplication. Students apply their understanding of multiplying fractions to solve real-world problems involving multiplication of a fraction by a whole number or a whole number by a fraction. Problems include creating real-world situations based on an equation or representing a real-world problem with a visual model or equation. Fractions are less than 1, and denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16, and 100.

B.E.S.T. Benchmarks:

• MA.4.FR.2.4 Extend previous understanding of multiplication to explore the multiplication of a fraction by a whole number or a whole number by a fraction.
• MA.4.AR.1.3 Solve real-world problems involving multiplication of a fraction by a whole number or a whole number by a fraction.

Overarching Key Concepts:

• Multiply Fractions and Whole Numbers

In This Unit of Study…

Fourth-grade students use their understanding of place value to use decimal notation to represent fractions and mixed numbers with denominators of 10 or 100 and to use fractional notation with denominators of 10 or 100 to represent decimals. They build upon their prior knowledge and understanding of place value, comparing, and ordering numbers, and decimals as fractions to compare decimals up to the hundredths place. Fourth-grade students also apply their knowledge of decimals and place value to identify the number that is one-tenth more, one-tenth less, one-hundredth more, and one-hundredth less than a given number.

B.E.S.T. Benchmarks:

• MA.4.FR.1.2 Use decimal notation to represent fractions with denominators of 10 or 100, including mixed numbers and fractions greater than 1, and use fractional notation with denominators of 10 or 100 to represent decimals.
• MA.4.NSO.1.5 Plot, order and compare decimals up to the hundredths.

Overarching Key Concepts:

• Represent Decimals to the Hundredths Place
• Compare and Order Decimals to the Hundredths Place

In This Unit of Study…

Students explore the addition and subtraction of multi-digit numbers with decimals to the hundredths, and they solve one- and two-step addition and subtraction real-world problems involving money by using decimal notation.

B.E.S.T. Benchmarks:

• MA.4.NSO.2.6 Identify the number that is one-tenth more, one-tenth less, one-hundredth more and one-hundredth less than a given number. 
• MA.4.NSO.2.7 Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths.
• MA.4.M.2.2 Solve one- and two-step addition and subtraction real-world problems involving money using decimal notation.
• MA.4.M.1.1 Select and use appropriate tools to measure attributes of objects.   

Overarching Key Concepts:

• Explore Addition and Subtraction of Decimals

In This Unit of Study…

Students collect, represent, and interpret numerical data with fractional values by using tables, stem-and-leaf plots, 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, and range. (Fraction Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100)

B.E.S.T. Benchmarks:

• MA.4.DP.1.1 Collect and represent numerical data, including fractional values, using tables, stem-and-leaf plots or line plots.
• MA.4.DP.1.2 Determine the mode, median or range to interpret numerical data including fractional values, represented with tables, stem-and-leaf plots or line plots.
• MA.4.DP.1.3 Solve real-world problems involving numerical data.
• MA.4.M.1.1 Select and use appropriate tools to measure attributes of objects.   

Overarching Key Concepts:

• Collect and Represent Numerical Data
• Interpret Numerical Data

In This Unit of Study…

Students will use models, drawings, and tables to convert units of time. They will apply what they know about time to solve two-step real-world problems to solve for the missing start time, elapsed time, and end time.  

B.E.S.T. Benchmarks:

• MA.4.M.1.2 Convert within a single system of measurement using the units: yards, feet, inches; kilometers, meters, centimeters, millimeters; pounds, ounces; kilograms, grams; gallons, quarts, pints, cups; liter, milliliter; and hours, minutes, seconds. 
• MA.4.M.2.1 Solve two-step real-world problems involving distances and intervals of time using any combination of the four operations.  

Overarching Key Concepts:

• Convert Time
• Solve Problems Involving Intervals of Time