Kindergarten

## Fourth Grade Math Common Core State Standards and Curriculum

in 4th grade, math standards begin incorporating higher math concepts into the curriculum. Students were introduced to some of these concepts in the third grade. In the fourth, these concepts will be deepened and expanded upon. Rather than the introduction of new math concepts, 4th grade Common Core math standards aim to perfect and refine ideas already established. Like a spiral, these mathematical concepts move downward, clarifying more and more. Fourth grade has a reputation for being difficult, but this doesn’t have to be the case. By understanding what Common Core math standards for fourth grade require, students are more likely to have a successful academic year.

Levels of competency in previous grades impact the success of future grades in the design of Common Core math standards. Grade 4 success in math is directly affected by that achieved in the third grade. This is because most of what students learn in the fourth grade is dedicated to creating deeper and more flexible understanding of what third graders learned. By the beginning of fourth grade, children should be able to:

#### Add and subtract digits up to the thousands place with ease.

Addition equations involving only tens and ones should not require pencil and paper. Mental strategies should be used for these types of equations. This means that third grade students should be able to multiply 3x9 in their minds without having to draw arrays or use other grouping strategies. Students should be familiar with solving addition and subtraction problems with up to three digits using vertical equation strategies.

#### Understand the base ten system (to the thousands place.)

Place value and what each refers to should be fluent up to 4 digits of a number. The base ten system should be familiar to students and incorporated into mental math strategies. Students should have the ability to break down numbers into groups based on place value, both mentally and on paper. For example, students should be able to see 749 as 7 groups of 100, 4 groups of 10, and 9 groups of one.

#### Multiply fluently (products up to 100.)

Students should understand the meaning of multiplication and the definition of a product. Multiplying fluently within 100 should be familiar and systematic before working on fourth grade Common Core math standards. Students should have multiplication tables of equations using two numerals with one digit each memorized by the end of third grade. These include 1x1 all the way up to 9x9. Students should also understand the commutative property of multiplication. This property refers to the fact that changing the order of numbers in a multiplication problem does not change the outcome. For example, if 9x4=36, then 4x9 is also known as 36.

#### Divide numbers within 100.

By the end of third grade, students should understand the meaning of division and the definition of a quotient. Students should apply mental and written strategies to divide within 100. Students should also understand the connection between the practice of both division and multiplication. They should use this relationship as a strategy in solving division problems. For example, if 5x3=15, then it is known that 15/5=3. It is also known that 15/3=5.

#### Be familiar with unit fractions and comparing fractions.

Unit fractions, which are those that represent one part of a total number of parts (ex. 1⁄4), should be familiar to students. Students should also have experience comparing fractions based on their denominators. For example, a student should understand that 1⁄4 is larger than 1⁄5 because a piece of pie cut into 4 pieces is larger than a piece of pie that has been cut into 5 pieces. In the same vein, 1⁄4 is smaller than 1⁄2 because a piece of pie cut into 4 pieces is smaller than a piece of pie cut into 2 pieces. Identify shapes, their common properties, and find area of rectangular arrays. Students should be able to name shapes, how they are similar, and how to describe them (properties) by the end of 3rd grade. They should also be able to find the area of shapes that are square or rectangular.

#### CCSS Math: 4th Grade Curriculum’s 3 Focus Areas

Your student will not spend study time learning new concepts during 4th grade math. Common Core standards instead focus on three areas that expand on those instated during 3rd grade. Focus areas for 4th grade math standards fall into one of three general focus areas. As aforementioned, third grade created the basics for these concepts to be built upon. To further these concepts, fourth graders should have a competent understanding of the framework. If you feel that your student is facing detriment in any of these subjects, make a summer plan to strengthen their math weaknesses. ArgoPrep provides an extensive educational online platform with a wide selection of math materials at the ready.

### Math Standards: 4th Grade Focus Area Breakdowns and Study Suggestions

#### Area 1: Develop multi-digit multiplication and division skills.

Understanding of place value will extend to 1,000,000. In multiplication, students will apply understanding of properties (distributive) to solve equations involving whole numbers with more than 1 digit. Students will also become familiar with factors of numbers from 1 to 100 and understand definitions of prime and composite numbers. For example, students will know that 37 is prime because it has two factors: 1 and 37. Students will also understand that 42 is composite because it has more than two factors, which are 1, 2, 3, 6, 7, 14, 21, and 42. In division, students will create fluency with strategies to solve division problems of multi-digit numbers. Students will also become familiar with remainders in division and estimation strategies.

#### Area 1 Study Suggestion

With memorization of facts, repetition is key. Timed multiplication worksheets are a fun challenge for students. With multi-digit multiplication, systematic practice of the process is important. ArgoPrep provides extensive workbooks and correlating tutorials explaining each step for a thorough and comprehensive approach. There are other things teachers and parents can do to help with memorization. Online games, flashcards, and using dice and other manipulatives are a good place to start.

#### Area 2: Operations and comparing of fractions.

Students will learn the concept of fraction equivalence and explain why two fractions are the same. For example, students will understand 2/4 and 1/4 are the same. This is because they are similar expressions of the same part of a whole; by dividing 2 and 4 by their shared factor, 2, 2/4 can be written as 1/2. Students will also practice addition and subtraction of fractions with like denominators. They will also practice multiplication of fractions by whole numbers. Students will also practice decimal notation for fractions involving 1, 10, and 100 as a denominator.

#### Area 2 Study Suggestion

Fractions create frustration in many students. This is because the numbers (1⁄4, 1⁄5, etc.) can seem like such a foreign concept. One way to combat this problem is to use pictures and manipulatives such as fraction bars and pieces of chocolate. Using real-world examples and situations can help this 4th grade Common Core math standard feel real. Use visuals, such as illustrations or physical examples, chocolate to help them understand what fractions mean. Online videos can help as well. For more help, browse ArgoPrep’s colorful tutorials involving operations with fractions.

#### Area 3: Analysis and classification of geometric figures based on their properties.

In geometry, students will become familiar with angles and different lines. In the fourth grade they will practice drawing lines and points. They will also identify and sketch line segments and rays. Fourth grade Common Core math standards also require students to learn about the three types of angles (acute, right, obtuse.) They will also recognize parallel and perpendicular lines and use these to analyze various shapes. Students will identify and categorize right triangles while focusing on the symmetry of shapes.

#### Area 3 Study Suggestion

Practice drawing or tracing shapes with your students. As you go along, ask them to describe the shape: How many sides does it have? Is it symmetrical? Where is the line of symmetry? Using a protractor, ask them to measure angles within shapes. Be sure to identify right angles within shapes. Compare different angles and ask which is the most obtuse or the most acute. It is important that students be able to estimate angle degrees as well as add angles together to make certain degree numbers (i.e. 180.)

## Operations & Algebraic Thinking

### Use the four operations with whole numbers to solve problems.

#### CCSS.MATH.CONTENT.4.OA.A.1

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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.

#### CCSS.MATH.CONTENT.4.OA.A.2

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.1

#### CCSS.MATH.CONTENT.4.OA.A.3

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.

### Gain familiarity with factors and multiples.

#### CCSS.MATH.CONTENT.4.OA.B.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.

### Generate and analyze patterns.

#### CCSS.MATH.CONTENT.4.OA.C.5

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, 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.

## Number & Operations in Base Ten

### Generalize place value understanding for multi-digit whole numbers.

#### CCSS.MATH.CONTENT.4.NBT.A.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. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

#### CCSS.MATH.CONTENT.4.NBT.A.2

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.

#### CCSS.MATH.CONTENT.4.NBT.A.3

Use place value understanding to round multi-digit whole numbers to any place.

### Use place value understanding and properties of operations to perform multi-digit arithmetic.

#### CCSS.MATH.CONTENT.4.NBT.B.4

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

#### CCSS.MATH.CONTENT.4.NBT.B.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.

#### CCSS.MATH.CONTENT.4.NBT.B.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.

## Number & Operations—Fractions

### Extend understanding of fraction equivalence and ordering.

#### CCSS.MATH.CONTENT.4.NF.A.1

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.

#### CCSS.MATH.CONTENT.4.NF.A.2

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 1/2. 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.

### Build fractions from unit fractions.

#### CCSS.MATH.CONTENT.4.NF.B.3

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
##### CCSS.MATH.CONTENT.4.NF.B.3.A
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
##### CCSS.MATH.CONTENT.4.NF.B.3.B
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.
##### CCSS.MATH.CONTENT.4.NF.B.3.C
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.
##### CCSS.MATH.CONTENT.4.NF.B.3.D
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.

#### CCSS.MATH.CONTENT.4.NF.B.4

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
##### CCSS.MATH.CONTENT.4.NF.B.4.A
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 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
##### CCSS.MATH.CONTENT.4.NF.B.4.B
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 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
##### CCSS.MATH.CONTENT.4.NF.B.4.C
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?

### Understand decimal notation for fractions, and compare decimal fractions.

#### CCSS.MATH.CONTENT.4.NF.C.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 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

#### CCSS.MATH.CONTENT.4.NF.C.6

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.

#### CCSS.MATH.CONTENT.4.NF.C.7

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.

## Measurement & Data

### Solve problems involving measurement and conversion of measurements.

#### CCSS.MATH.CONTENT.4.MD.A.1

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), ...

#### CCSS.MATH.CONTENT.4.MD.A.2

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.

#### CCSS.MATH.CONTENT.4.MD.A.3

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.

### Represent and interpret data.

#### CCSS.MATH.CONTENT.4.MD.B.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. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

### Geometric measurement: understand concepts of angle and measure angles.

#### CCSS.MATH.CONTENT.4.MD.C.5

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
##### CCSS.MATH.CONTENT.4.MD.C.5.A
An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.
##### CCSS.MATH.CONTENT.4.MD.C.5.B
An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

#### CCSS.MATH.CONTENT.4.MD.C.6

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

#### CCSS.MATH.CONTENT.4.MD.C.7

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.

## Geometry

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

#### CCSS.MATH.CONTENT.4.G.A.1

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

#### CCSS.MATH.CONTENT.4.G.A.2

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.

#### CCSS.MATH.CONTENT.4.G.A.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.

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