Fourth Grade Overview
Overview
In fourth grade your children will focus in 3 critical areas:
Critical Area 1
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Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends. Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.
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Critical Area 2
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Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers. Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.
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Critical Area 3
understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.
Unit 1
Fourth Grade Mathematics
Unit 1
Addition and Subtractions of Whole Numbers
Printable Parent Letter
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During Unit 1, your children will develop and practice efficient addition and subtraction of multi-digit whole numbers, while extending their understanding of place value concepts. Fourth grade is the initial grade level in which students are expected to be proficient at using the standard algorithm for addition and subtraction. As well, your children may continue to use previously learned strategies, based on place value concepts and the properties of operations. They will reason about the magnitude of the digits in a whole number. Your children will demonstrate flexibility with the different forms that numbers can be written. They will apply their understanding of place value and number sense to reason and explain about rounded answers. |
Students Need To
- Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
- Use place value understanding to round multi-digit whole numbers to any place.
- Add and subtract multi-digit whole numbers using the standard algorithm.
Ways Parents Can Help
- Encourage your child to practice their basic addition and subtraction math facts.
- Challenge your child to use their knowledge of subtraction to create problems for each of the following conditions:
- a. You don't have to use regrouping.
- b. You would naturally use regrouping from the tens to the ones place.
- c. You would naturally use regrouping from the hundreds place to the tens place.
- d. You would naturally use regrouping in all places.
- Challenge your child to use their knowledge of addition and subtraction to create problems for each of the following conditions:
- a. The answer rounded to the nearest ten is 90 (or any two-digit multiple of 10).
- b. The answer rounded to the nearest hundred is 500 (or any three-digit multiple of 100).
- c. The answer rounded to the nearest thousand is 3,000 (or any four-digit multiple of 1,000).
Key Vocabulary
Unit 2
Fourth Grade Mathematics
Unit 2
Multiplication and Division
Printable Parent Letter
| In this unit, the students will build on their work with multiplication and division from grade 3. In the first part of the unit, they will extend their understanding of the base-ten system by recognizing that the value of each place is ten times the value of the place to the immediate right. Students will develop understanding of multiples and factors, applying their understanding of multiplication from grade 3. This understanding lays a strong foundation for generalizing strategies learned in previous grades to develop, discuss, and use efficient, accurate, and generalizable computational strategies involving multi-digit numbers. These concepts and the terms “prime” and “composite” are new to grade 4, so they are introduced early in the year to give students ample time to develop and apply this understanding. Students will focus on building conceptual understanding of multiplication of larger numbers and division with remainders. Area of rectangles provides a context for further developing this understanding. |
Students Need To
- 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. For example, recognize that 700 ÷70 = 10 by applying concepts of place value and division.
- 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 prime or composite.
- Generate a number pattern that follows a given rule.
- Solve word problems posed with whole numbers, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- 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.
- 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.
- Apply the area formula for rectangles in real-world and mathematical problems.
Ways Parents Can Help
- Encourage your child to regularly practice basic multiplication and division facts. The Internet has many free fact practice sites available.
- Extend multiplication fact practice to include multiples of 10 and 100. Have your child try to solve them mentally!
Examples: 20 x4 = 80; 7 x 300 = 2,100
- Look for opportunities for your child to apply multiplication and division to solve real-life problems. Discuss how to interpret the "leftover," or remaining, amount in a division situation.
For example: If party plates come in packages of 8, and you are having 75 people for a party, how many packages of plates would you need to buy?
Would there be any plates leftover?
Key Vocabulary
Unit 3
Fourth Grade Mathematics
Unit 3
Decomposing and Composing Fractions
Printable Parent Letter
| During Unit 3, your children will extend their understanding of fraction equivalence and ordering. They will use visual fraction models to explore how the number and size of the parts differ between two fractions even though they are equivalent. Your children will recognize and generate equivalent fractions. They will compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing them to a benchmark fraction such as ½ or 1 whole. Your children will use the symbols >, =, and < to record their comparison and use visual fraction models to justify their conclusions. They will extend their understanding of addition as putting together when they see the way fractions are built from unit fractions. Your children will decompose and compose fractions with the same denominator, and add and subtract fractions with the same denominator. They will convert an improper fraction to a mixed number by decomposing the fraction into a sum of a whole number and a number less than 1. |
Students Need To
- Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
- Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
- 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. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
- Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by 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.
- Compare two fractions with different numerators and different denominators, e.g. by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or < and justify the conclusions, e.g. by using a visual fraction model.
Ways Parents Can Help
- Fold a piece of paper into halves, and then into halves again with your child. Open it up to show the division of fourths. Fold the paper again into fourths then make another fold to show eighths. Shade in portions of the paper and talk about the different (equivalent) fractions that can be named by the shaded and not shaded portions of the paper. For example, you shade 4/8, which is also 2/4 and ½. This can also be done by folding fractions other than eighths.
- Involve your child in cooking activities. Have them select the appropriate measuring spoons and cups for the recipe. If ingredients need to be doubled or halved, ask them to figure out what the new quantity would be for the recipe.
- Also experiment with decomposing a measurement fraction by using the unit fraction multiple times to get the needed amount. For example, if ¾ of a cup is needed measure ¼ of a cup three times and talk with your child about the equation that would match the decomposition ¾ = ¼ + ¼ + ¼.
Key Vocabulary
Unit 4
Fourth Grade Mathematics
Unit 4
Addition and Subtraction of Fractions
Printable Parent Letter
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During Unit 4, your child will build upon his knowledge of fractions and the base-ten system to develop an understanding of decimals to the hundredths place. The relationship between fractions and decimals is formed using visuals including area models, grids, and number lines and is used to develop students’ understanding that decimals (like fractions) can be used to name values less than 1 or values between whole numbers. Additionally, your child will utilize whole number patterns in the base-ten system and extend them to the right of the ones place with decimals. Fourth graders will apply their understanding of equivalent fractions and decimals in order to understand relative size and to compare/order and add/subtract decimals. They will make connections between adding/subtracting fractions as they apply these concepts to word problems and line plots involving measurement data. They will add and subtract fractions with the same denominator and convert an improper fraction to a mixed number by decomposing the fraction into a sum of a whole number and a number less than 1. Throughout this unit, students will build a deep number sense of fraction and decimal numbers. |
Students Need To
- Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
- Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
- 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.
- 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. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100
- Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
- Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model
Ways Parents Can Help
- Involve your child in cooking activities. Have them select the appropriate measuring spoons and cups for the recipe. If ingredients need to be doubled or halved, ask them to figure out what the new quantity would be for the recipe.
- Dollars and cents provide a real-world example of decimal numbers. Have your child count a handful of coins. Relate the number of 10- cent equivalents to tenths of a dollar and the number of cents to hundredths of a dollar. Ask your child what the fraction equivalent of the coins would be …$0.64 can be expressed as 6 dimes and 4 pennies or 64/100 of a dollar.
- Statistics in baseball, basketball, swimming, and football provide a great opportunity to discuss decimal numbers and how they relate to sports’ players’ performance. Have your child get active and do math, too, by taking ten basketball shots or baseball swings and counting how many baskets or hits are made. Express the results as a fraction and a decimal. Ex. Six shots made out of ten …6/10 or 0.6.
Key Vocabulary
Unit 5
Fourth Grade Mathematics
Unit 5
Geometry and Patterns
Printable Parent Letter
| During Unit 5, your child will build their understanding of geometry by making constructions, identifying attributes within geometric figures such as perpendicular and parallel lines, obtuse, right, and acute angles, and classifying figures based on those attributes. Students will also understand angles as the space between intersecting rays or line segments. They will see angles as parts of a circle and will be able to measure angles in degrees using a protractor or information about the angle in relation to a circle. Students will recognize patterns within a group of shapes and be able to make a conjecture based on the pattern. Patterns will also be found when studying symmetry of shapes. |
Students Need To
- Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
- Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
- 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 symmetrical figures and draw lines of symmetry.
- Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- Understand that an angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
- Recognize that an angle that turns through n one-degree angles is said to have an angle measure of n degrees.
- Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
- Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
- Generate a shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.
Ways Parents Can Help
Key Vocabulary
| Key Vocabulary to Know | |
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acute angle/triangle angle circle decompose degree endpoint figure geometric shape intersect line line segment parallel perpendicular |
point protractor obtuse angle/triangle one-degree angle ray right angle/triangle straight unknown vertex equilateral triangle isosceles triangle scalene triangle line of symmetry |
Unit 6
Fourth Grade Mathematics
Unit 6
Multiplicative Comparisons and Measurement
Printable Parent Letter
| During Unit 6, your children will apply their understanding of measurement conversions and multiplicative comparison to solve multiplication and division situation problems. Multiplicative comparison problems involve a comparison of two quantities in which one is described as a multiple of the other. The relationship between the amounts is described in terms of how many times larger one is than the other. “Larger” can also be interpreted as “longer,” “wider,” or “heavier” with problems involving measurement. In 4th grade, whole number values are utilized in multiplicative comparison problems. This will provide a foundation for fraction problems in 5th grade when students use language such as “one fourth as much.” |
Students Need To
- Interpret a multiplication equation as a comparison, e.g. interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations
- Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
- Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- Know relative sizes of measurement units within one system of units including km, m, cm, kg, g, lb., oz., l, mL, hr., min, and sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
- Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
Key Vocabulary
| Key Vocabulary to Know | |
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Additive Comparison Convert/Conversion Dividend Divisor Equation Factor Multiple Product Quotient Multiplicative Comparison Customary Foot (ft.) Inch (in.) Yard (yd.) Ounce (oz.) |
Pound (lb.) Metric Meter (m) Centimeter (cm) Kilometer (km) Gram (g) Kilogram (kg) Liter (l) Milliliter (mL) Hour (hr.) Second (sec) Minute (min) |
Unit 7
Fourth Grade Mathematics
Unit 7
Multiplying Fractions by Whole Numbers
Printable Parent Letter
| During Unit 7, your child will apply their understanding of composing and decomposing fractions to develop a conceptual understanding of multiplying a fraction by a whole number. Students also use and extend their previous understandings of multiplication with whole numbers and relate that understanding to fractions. |
Students Need To
- Interpret a multiplication equation as a comparison, e.g. interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. (This standard is addressed in this unit to include multiplication of fractions and apply the understanding of “times as much” to multiplying a fraction by a whole number.)
- Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
- Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. (For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. In general, n x (a/b) = (n x a/b))
- Solve word problems involving multiplication of a fraction by a whole number, e.g. by using visual fraction models and equations to represent the problem. (For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?)
Ways Parents Can Help
- Help your child to make real world connections to the multiplication of whole numbers and fractions when you can. For example, when following a recipe that calls for ¾ a cup of something, have your child help you measure by using a ¼ measuring cup. Have them figure out that they will need to use the ¼ measuring cup 3 times in order to have ¾. In other words, 3 “groups of” ¼ cup equals ¾ cup, 3 x ¼ = ¾.
Key Vocabulary
Unit 8
Fourth Grade Mathematics
Unit 8
Measurement Problem Solving
Printable Parent Letter
| During Unit 8, your child will solve real world problems that require him to use his knowledge of measurement units and conversions. Problems may have multiple steps and require the use of one or more of the four operations. In addition to problems involving whole numbers, problems may involve the use of simple fractions and decimal numbers. Your child may use a diagram, number line, or equation to model the solution to a problem. He will also need to understand the concepts of perimeter and area and apply the formulas to real world and mathematical problem situations. Your child will also focus on problem solving in order to demonstrate fluency with addition and subtraction to 1000 and demonstrate fluency for multiplication and division within 100. He will solve problems involving measurement and estimation of liquid volumes, and masses of objects. |
Students Need To
- Know relative sizes of measurement units within one system of units including km, m, cm, kg, g, lb, oz, l, mL, hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft. is 12 times as long as 1 in. Express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
- Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
- Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. For example, 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.