Grade 4 Math South Dakota Standards

Use visual models and reasoning to explain why a fraction 𝑎𝑎/𝑏𝑏 is equivalent to another fraction when both the numerator and denominator are multiplied by the same number.

Solve word problems involving multiplication of fractions by whole numbers.

Add two fractions with denominator of 10 and 100 by expressing the denominator of 10 as an equivalent fraction with a denominator of 100.

Understand a decimal number to be a number with a whole part and a fractional part separated by a decimal point.

Apply decimal notation for fractions with denominators 10 or 100; locate these decimals on a number line.

Read, write, and describe the value of decimal numbers to the hundredths place.

Compare decimals to the hundredths place on a number line and by using the symbols <, > , =.

Compare fractions with different numerators and denominators, by creating common denominators or numerators, using the symbols <, >, =.

Add and subtract fractions with like denominators.

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

Break apart fractions into sums of fractions with the same denominator and smaller numerators.

Add and subtract mixed numbers with like denominators using various strategies.

Multiply a fraction by a whole number and a whole number by a fraction.

Understand a fraction 𝑎𝑎/𝑏𝑏 is a multiple of 1/𝑏𝑏.

Understand a multiple of 𝑎𝑎/𝑏𝑏 is also a multiple of 1/𝑏𝑏.

Recognize angles as geometric shapes that are formed where two rays share a common endpoint.

Identify and draw lines of symmetry for two-dimensional figures.

Measure angles in degrees using a protractor and understand a degree as 1/360 of a circle; draw angles of specific measure.

Classify angles as right, acute, obtuse, or straight. Draw right, acute, obtuse, and straight angles.

Recognize and apply the concept of additive angles: when angles are broken apart the sum of the parts is equal to the angle measure of the whole.

Identify, describe, and draw points, lines, segments, rays, and angles.

Identify, describe, and draw intersecting, parallel, and perpendicular lines.

Understand a trapezoid to be a two-dimensional shape with four sides, where exactly one pair of sides is parallel.

Identify and describe various quadrilaterals by their properties of parallel and perpendicular lines including square, rectangle, trapezoid, and rhombus.

Identify, describe, and draw equilateral, scalene, right, acute, and obtuse angles and triangles.

Measure length, weight, mass, and capacity using U.S. Customary and metric systems of measurement (including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.).

Express larger units in terms of smaller units through conversions within a single system of measurement.

Solve word problems using addition, subtraction, multiplication, and division involving distance, intervals of time, capacity, masses, and money, using fractional and decimal values.

Use visual models and reasoning to explain how area and perimeter formulas for rectangles relate to their side lengths and solve real-world problems.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8) and solve problems using the line plot.

Recall from memory multiplication facts (0-12).

Recall from memory division facts (0-12).

Fluently add and subtract multi-digit whole numbers using an algorithm including, but not limited to, the standard algorithm.

Recognize that a digit in a given place represents ten times what it represents in the place to its right.

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

Compose and decompose five-digit numbers into ten thousands, thousands, hundreds, tens, and ones.

Read and write whole numbers up to 1,000,000 using standard form, word form, and expanded form.

Compare two multi-digit numbers based on values of the digits in each place value using the symbols <, >, =.

Represent and explain multiplicative comparisons using equations, drawings, and verbal reasoning.

Determine whether a whole number from 1 to 100 is prime or composite.

Generate a number or shape pattern that follows a given rule, identifying apparent features of the pattern that are not explicit in the rule itself.

Demonstrate understanding of addition and multiplication problems using properties (commutative, associative, distributive, and identity).

Evaluate a numerical expression including addition, subtraction, multiplication, and division using the order of operations of whole numbers without parenthesis and exponents.

Solve real-world problems involving multiplicative comparison, using drawings and/or equations with a symbol for the unknown number, and distinguish between multiplicative comparison and additive comparison.

Multiply four-digit whole numbers by one-digit whole numbers, and multiply two two-digit whole numbers.

Divide four digit whole numbers by one-digit divisors; quotients should be with and without whole number remainders.

Interpret a remainder of a one-step division problem.

Solve multistep word problems using addition, subtraction, multiplication, and division, with whole numbers and having whole number answers, including problems in which remainders must be interpreted; assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Find factor pairs for whole numbers up to 100.

Recognize that a whole number (within 100) is a multiple of each of its factors.

Find multiples of single-digit whole numbers.

Fractions

Geometry

Measurement

Mathematical Fluency

Numbers

Place Value

Operations and Properties

Measurement Concepts

Number Operations

Geometric Measurement

Shapes

Data

Operations and Algebraic Thinking

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, and identify categories of right, acute, and obtuse triangles.

Recognize and draw lines of symmetry for two-dimensional figures.

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 1ft 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 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.

Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

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.

An angle that turns through in 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.

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 the 7 in 700 is 10 times greater than the 7 in 70 because 700 ÷ 70 =10 and 70 x 10=700.

Read and write multi-digit whole numbers.

Read and write multi-digit whole numbers using base-ten numerals (standard form), number names (word form), and expanded form.

Compare two multi-digit numbers based on values 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.

Fluently add and subtract multi-digit whole numbers using an algorithm including, but not limited to, the standard algorithm.

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.

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.

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, 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 <, >, =, and justify the conclusions.

Understand a fraction a/b with a > 1 as a sum of fractions 1/b. For example, 4/5 = 1/5 + 1/5 + 1/5 + 1/5

Add and subtract of fractions e.g., joining and separating parts referring to the same whole.

Decompose a fraction into a sum of fractions with like denominators in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

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.

Apply and extend previous understandings of multiplication to multiply 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 (¼), recording the conclusion by the equation 5/4 = 5 x (¼).

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 = (n x a) x 1/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?

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.

Read and write decimal notation for fractions with denominators 10 or 100. Locate these decimals on a number line.

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.

Use and interpret multiplicative equations.

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 or written statements of multiplicative comparisons as multiplication equations. Example: Tom has 7 toy cars; Joe has 5 times as many. How many toy cars does Joe have? Answer: 35, because 7 x 5 = 35 or 5 x 7 = 35.

Know from memory (quick effortless recall of facts) all products of two one-digit numbers.

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), and distinguish 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.

Using whole number in the range 1–100.

Find all factor pairs for a given whole number.

Recognize that a whole number is a multiple of each of its factors.

Determine whether a given whole number is a multiple of each of a given one-digit number.

Determine whether a given whole number is prime or composite.

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 is 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.

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Generate and analyze patterns.

Geometry

Use the four operations with whole numbers to solve problems.

Operations and Algebraic Thinking

Number and Operation in Base Ten

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

Number and Operations — Fractions

Represent and interpret data.

Measurement and Data

Extend understanding of fraction equivalence and ordering.

Standards for Mathematical Practice

Generalize place value understanding for multi-digit whole numbers.

Solving problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Geometric measurement: understand concepts of angle and measure angles.

Gain familiarity with factors and multiples.

Understand decimal notation for fractions, and compare decimal fractions.

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