Category: Grade 4 Math

Decimals

Unit description: Students will extend their understanding of the base-ten number system to place values smaller than one.  Students will consider tenths and hundredths and how they are represented as fractions and in decimal form. Students will compare decimals using strategies based on place value.  

Essential Outcomes of the Unit

Number and Operations—Fractions- Understand decimal notation for fractions, and compare decimal fractions.

Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

NY-4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.

NY-4.NF.6 Use decimal notation for fractions with denominators 10 or 100.

NY-4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

Essential Questions and Big Ideas

How are decimals related to fractions?

Decimals represent fractions with denominators that are powers of ten. 

Where do decimals fit in the base ten system?

Decimal places are to the right of whole number places. 

Decimal places represent quantities that are smaller than whole numbers.  

How do I compare decimals? 

Decimals can be compared by comparing greater place values first.  

Download the complete Grade 4 Math Unit 6 framework to customize for your own planning.

Conversions, Area, and Perimeter

Unit description: Students will learn how to complete metric conversions, as well as customary conversions for length and time.  Students will extend their knowledge of area and perimeter from third grade to complete multi-step real world and mathematical problems involving area, perimeter, and different types of rectangles. 

Essential Outcomes of the Unit

Measurement and Data- Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit

• NY-4.MD.1 Know relative sizes of measurement units: ft., in.; km, m, cm. Know the conversion factor and use it to convert measurements in a larger unit in terms of a smaller unit: ft., in.; km, m, cm; hr., min., sec. Given the conversion factor, convert all other measurements within a single system of measurement from a larger unit to a smaller unit. Record measurement equivalents in a two-column table.
• NY-4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. e.g., Find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Other Standards Addressed in the Unit

Measurement and Data- Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit

• NY-4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money. 
• NY-4.MD.2a Solve problems involving fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. 
• NY-4.MD.2b Represent measurement quantities using diagrams that feature a measurement scale, such as number lines. Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Measurement and Data- Represent and interpret data

NY-4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit 1/2 , 1/4 , 1/8. Solve problems involving addition and subtraction of fractions by using information presented in line plots.

Essential Questions and Big Ideas

• How do I convert different sized units?
  • The metric system is based on powers of 10. 
  • There are 12 inches in 1 foot. 
  • There are 60 minutes in an hour.
  • There are 60 seconds in a minute. 
  • Conversions can be recorded in tables.  `
• How do I solve area and perimeter word problems involving rectangles? 
  • Area represents the total amount of space a flat shape takes up. 
  • Perimeter represents the distance around a shape. 
• How do I solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money?
  • Distances can be added or compared.
  • Times can be added or subtracted using understandings of minutes and hours. 
  • Volumes can be added or compared based on measurements in beakers or other tools. 
  • Masses can be added or compared based on measurements on scales or other tools. 
  • Money can be added or compared using understandings of cents and dollars. 
• How do I represent data using a line plot?
  • Line plots represent numerical data. 
  • Xs represent data points of a numerical value. 
  • The scale on a line plot must have equal sized units.

Download the complete Grade 4 Math Unit 5 framework to customize for your own planning.

Classifying 2-D Shapes

Unit description: Students will build on their work in third grade classifying triangles, quadrilaterals, pentagons, and hexagons. Students will differentiate between acute, obtuse, and right angles, as well as parallel, perpendicular, and intersecting lines. Students will be able to classify triangles as acute, obtuse, or right, and quadrilaterals as parallelograms, trapezoids, rectangles, rhombi, or squares. Students will also consider symmetry.

Essential Outcomes of the Unit

Geometry- Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

• 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
• 4.G.2a. Identify and name triangles based on angle size (right, obtuse, acute).
• 4.G.2b Identify and name all quadrilaterals with 2 pairs of parallel sides as parallelograms.
• 4.G.2c Identify and name all quadrilaterals with four right angles as rectangles.
• 4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Essential Questions and Big Ideas

How can I describe lines and angles?

• Lines can be described using the terms parallel, perpendicular, and intersecting.
• Angles can be described using the terms acute, obtuse, and right.

How can I classify triangles?

• Triangles can be classified as acute, obtuse, or right.

How can I classify quadrilaterals?

• Quadrilaterals can be classified based on their lines (parallelograms, trapezoids).
• Quadrilaterals can be classified based on their angles (rectangle)
• Quadrilaterals can be classified based on the length of their sides (rhombi, squares)

What is symmetry?

• Symmetric objects can be folded in half and match up.

Download the complete Classifying 2-D Shapes framework to customize for your own planning.

Fractions

Unit description: Students will extend their knowledge of fractions from third grade by looking at fractions with denominators of 10 and 12.  They will also extend their understanding of fractions equal to 1 whole to multiply and divide fractions by 1 whole to create equivalent fractions.  Students will begin to interpret and solve word problems that require combining or separating fractions within the same whole and with the same denominator.  Students will also interpret word problems that involve equal groups of a fraction.  Students will understand fractions larger than one and how to convert them into mixed numbers.  

Essential Outcomes of the Unit

• NY-4.NF.1 Explain why a fraction abis equivalent to a fraction a x nb x nby using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
• NY-4.NF.2 Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 12. Record the results of comparisons with symbols >, =, or <, and justify the conclusions. e.g., using a visual fraction model.
  • Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
• NY-4.NF.3 Understand a fraction abwith a > 1 as a sum of fractions 1b Note: 1brefers to the unit fraction for ab
• NY-4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
• NY-4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions. e.g., by using a visual fraction model such as, but not limited to:
  • 3/8 = 1/8 + 1/8 + ⅛
  • 3/8 = 1/8 + 2/8
  • 218= 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
• NY-4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
• NY-4.NF.4 Apply and extend previous understandings of multiplication to multiply a whole number by a fraction.
• NY-4.NF.4a Understand a fraction abas a multiple of 1b e.g., Use a visual fraction model to represent 54 as the product 5 × 14, recording the conclusion with the equation 54= 5 × 14.
• NY-4.NF.4b Understand a multiple of abas a multiple of 1b, and use this understanding to multiply a whole number by a fraction. e.g., Use a visual fraction model to express 3 x 25as 6 x 15, recognizing this product as 65, in general, n × ab= (n x a)b.
• NY-4.NF.4c . Solve word problems involving multiplication of a whole number by a fraction.

Essential Questions and Big Ideas

How can I find equivalent fractions and compare fractions? 

• Equivalent fractions can be found by drawing models or by multiplying or dividing by a whole.  
• Fractions can be compared by drawing models or by giving the fractions the same denominator and comparing their number of pieces.  

How can I use addition to represent non-unit fractions? 

• Non-unit fractions can be written as the sum of unit fractions.  

How can I use addition and subtraction to relate fractions?

• Fractions with the same denominator or referring to the same whole can be added or subtracted by focusing on the number of parts.   

How can I show equal groups relationships with fractions?

• Fractions can exist in equal groups.  
• If you have a whole number of equal groups of a fraction, you can multiply the whole number by the numerator to figure out how many total parts you will have.  The denominator would remain the same.    

Download the complete Fractions framework to customize for your own planning.

Multiplication and Division

Students will grow in their abilities to multiply and divide by working with multi-digit numbers. Students will also work with multi-step story problems with all four operations.

Note: Lessons will vary in length, depending on the amount of time you have with students, the resources that you choose to accompany the unit, the level of rigor within each learning target, and any other factors that may contribute to the pacing of your learning progressions. It is recommended that you adjust the pace and length of each learning progression(s) accordingly in response to these factors.

These learning progressions were developed using Next Generation Learning Standards and were cross-walked with the Common Core Standards.

Download the complete Grade 4 Math Unit 2 framework to customize for your own planning.

Essential Outcomes

Operations and Algebraic Thinking

• NY-4.OA.2: Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Use drawings and equations with a symbol for the unknown number to represent the problem.
• NY-4.OA.3: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.
• NY-4.OA.3a: Represent these problems using equations or expressions with a letter standing for the unknown quantity.
• NY-4.OA.3b: Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
• NY-4.OA.4: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Number and Operations in Base Ten

• NY-4.NBT.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
• NY-4.NBT.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Other Standards Addressed in this Unit

Operations and Algebraic Thinking

• NY-4.OA.1: Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. e.g.,
  • Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 or 7 times as many as 5.
  • Represent “Four times as many as eight is thirty-two” as an equation, 4 x 8 = 32.
    
• NY-4.OA.5: Generate a number or shape pattern that follows a given rule. Identify and informally explain apparent features of the pattern that were not explicit in the rule itself. e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Measurement and Data

• NY-4.MD.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. e.g., Find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Essential Questions and Big Ideas

• What are factors and multiples? What are patterns?
  • Factors are numbers that can multiply to make another number.
  • Multiples are numbers that are made when skip counting by a number.
  • A whole number is a multiple of each of its factors.
  • Prime numbers only have two factors, 1 and itself.
  • Composite numbers have more than two factors.
  • Patterns show relationships between things. 
  • In a pattern each term changes in a constant way.
• What are efficient strategies to multiply multi-digit numbers?
  • Partial products can be used to multiply multi-digit numbers.
  • The area model is a way to organize partial products to multiply multi-digit numbers.
  • The multiplication algorithm is an organized method of partial products.
  • Multiplication is completed by multiplying by each place value. 
• What are efficient strategies to divide multi-digit numbers by single digit numbers?
• • Partial quotients can be used to divide multi-digit numbers.
  • The area model is a way to organize partial quotients.
  • The division algorithm is an organized method of partial quotients.
  • Division is completed by dividing up each place value and then dividing the remainder.
  • In division the dividend is broken into multiples of the divisor. 
• What is multiplicative comparison?
• • Multiplicative comparison represents comparisons based on multiplication.
  • Multiplicative comparison is phrased as “times as many”.
  • To solve multiplicative comparison you may need to multiply or divide, depending on if you are solving for a larger or smaller amount. 

• How do I solve multi-step word problems?
  • Multi-step word problems have more than one unknown.
  • Sometimes an unknown is reliant on another unknown.
  • Multi-step word problems have more than one action or relationship.

Download the complete Grade 4 Math Unit 2 framework to customize for your own planning.

Place Value, Addition and Subtraction

Students will deepen their understandings of place value by investigating numbers up to 1,000,000. Students will explore the values of digits and the relationships between digits. Students will also compare, round, add, and subtract numbers using strategies based on place value.

Essential Outcomes

Number and Operations in Base Ten

• NY-4.NBT.4: Fluently add and subtract multi-digit whole numbers using a standard algorithm. Note: Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.

Other Standards Addressed in this Unit

Number and Operations in Base Ten

• NY-4.NBT.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. e.g., Recognize that 70 × 10 = 700 (and, therefore, 700 ÷ 10 = 70) by applying concepts of place value, multiplication, and division. Note: Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.
• NY-4.NBT.2a: Read and write multi-digit whole numbers using base- ten numerals, number names, and expanded form. e.g., 50,327 = 50,000 + 300 + 20 + 7
• NY-4.NBT.2b: Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Note: Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.
• NY-4.NBT.3: Use place value understanding to round multi-digit whole numbers to any place. Note: Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.

Essential Questions and Big Ideas

• How does understanding place value help you to understand numbers, compare numbers, and recognize their relationships to powers of ten?
  • A number is made of digits which are in different place values which dictate their value.
  • When comparing numbers, the larger place values carry more weight.
  • When rounding numbers you’re considering “about how many” of a certain place value the number is.
  • To round a number, consider how many of that place value a number has and then look above for the next largest.
• How does the value of the digit in a number change when it moves places?
  • A digit in one place represents ten times what it represents in the place to its right.
• What are efficient strategies to add multi-digit whole numbers?
  • When you make more than 9 of a place value, you regroup to the largest place value.
  • You can use the standard algorithm to add multi-digit numbers.
• What are efficient strategies to subtract multi-digit whole numbers?
  • If you do not have enough of a place value to subtract, you can regroup a larger place value.
  • You can use the standard algorithm to subtract multi-digit numbers.

Download the complete Grade 4 Math Unit 1 framework to customize for your own planning.