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Sibley-Ocheyedan Grade 4 Math Benchmarks

Operations and Algebraic Thinking (OA)

Use the four operations with whole numbers to solve problems.

4.OA.1-Interpret a multiplication equation as a comparison

Ex-5 x 7 = 7 x 5

4.OA.2-Multiply or divide to solve world problems involving comparative multiplication.

4.OA.3-Solve multistep word problems using whole numbers and having whole number answers using all four operations.  This will include problems where remainders must be interpreted. Equations with a letter standing for the unknown quality will be used.  Solutions will be assessed for reasonableness using mental computation and estimation strategies including rounding.

Gain familiarity with factors and multiples.

4.OA.4-Find all factors for a whole number 1-100.  Understand that a whole number is a multiple of its factors.  Understand divisibility rules and be able to apply them to whole numbers 1-100  to determine if a number is a multiple of  a given one-digit number.  Determine prime or composite.  Ex- 24, factors 1,2,3,4,6,8,12,24, is composite

Generate and analyze patterns.

4.OA.5-Generate a number or shape pattern that follows a given rule.  Identify secondary patterns.  Ex-1,2,4,7,11,16… primary pattern-1,2,3,4,5 secondary pattern-add 1

Number & Operations in Base Ten (NBT)

Generalize place value understanding for multi-digit whole numbers.

4.NBT.1-Recognize the base ten system and understand that a number in the 10s place is ten times it’s value in the ones place and 1/10th its value in the hundreds place.

4.NBT.2-Read and write multi-digit whole numbers in standard, expanded, and word form. Compare multi-digit whole numbers based on the value of their places utilizing >, <, =.

4.NBT.3-Round multi-digit whole numbers.  Ex  4,857 à 4,900

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

4.NBT.4-Using the standard algorithm, fluently add and subtract multi-digit whole numbers.

4.NBT.5-Using strategies based on properties, such as the commutative property, multiply a four-digit whole number by a one-digit whole number and multiply two two-digit whole numbers.  Demonstrate multiplication with equations and area models.  Ex à 3,562 x 4 = 3,000 x 4 + 500 x 4 + 60 x 4 + 2 x 4

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4.NBT.6- Using strategies based on operations and the relationship between multiplication and division, find whole number quotients and remainders using up to four-digit dividends and one-digit divisors, . Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.  Ex  4,507 ÷ 34

Number & Operations—Fractions (NF)

1 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.

2 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.

Extend understanding of fraction equivalence and ordering.

4.NF.1-Explain how two fractions can be equivalent even though their numerators and denominators are not equal. Recognize that the numerator and denominator of fraction a/b are multiplied by the same whole number to generate fraction (n x a)/(n x b) Use this principle to recognize and generate equivalent fractions.  Ex à  ¾  =  ¾ x  4/4  =  12/16

4.NF.2. Compare two fractions with different numerators and denominators by creating common numerators or denominators.; or comparing to a benchmark e.g., 1/2.   Record the comparison using >, <, =.  Use a visual model of the fractions to justify the comparison.

Ex à  3/8  ¢ 4/5        3/8 = 15/40 and  4/5 = 32/40,

so 3/8 < 4/5  or  3/8 < ½  and 4/5 > 1/2

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

4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

4.NF.3a-Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Ex- 4/7 + 1/7 = 5/7

4.NF.3b-In more than one way, show the decomposition of a fraction more than one way.  Use equations to record the decompositions.  Ex à 3/7 = 1/7 + 1/7 + 1/7

4.NF.3c-Add and subtract mixed numbers with like denominators.

Ex- 2 3/9 + 4 2/9 = 6 5/9

4.NF.3d-Use fraction models and equations to solve addition and subtraction word problems involving fractions with like denominators.

4.NF.4. Multiply a fraction by a whole number utilizing understandings of multiplication.

4.NF.4a-Understand a fraction a/b as a multiple of 1/b.

Ex à 4 x 1/7 = 4/7

4.NF.4b-Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Ex à 5 x 2/9 = 10/9

4.NF.4c-Solve word problems involving multiplication of a fraction by a whole number.

Understand decimal notation for fractions, and compare decimal fractions.

4.NF.5-Express a fraction with a denominator of 10 as being equivalent to a fraction with a denominator of 100 and then add them.

Ex à 3/10 + 51/100 = 30/100 + 51/100 = 81/100

4.NF.6-Convert fractions with denominators of 10 or 100 into fractions.

Exà 3/10 = .3 or 45/100 = .45 or 7/10 meters = .7 meters

4.NF.7-Compare two decimals to the hundredths place using >, <, =.

Ex à .46 > .35  because .4 > .3

Measurement & Data (MD)

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

4.MD.1-Know relative sizes of measurement units within one system of units including metric and standard/customary systems. 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.

Ex à  12 in. = 1 ft, 1,000 mm = 1 m

4.MD.2-Use the four operations to solve word problems involving measurement. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

4.MD.3-Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Represent and interpret data.

4.MD.4-Display data in fractions on a line plot and use this data to solve addition and subtraction problems.

Ex à Find the difference between the greatest and least points in the data set.

Geometric measurement: understand concepts of angle and measure angles.

4.MD.5-Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

4.MD.5a-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.

4.MD.5b-An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.6-Use a protractor to measure angles and sketch angles with a specific degree.

4.MD.7-Recognize angles as being a sum of different angles.  Use addition and subtraction to find the measure of unknown angles on a diagram in real world and mathematical problems.

Ex- 36° + 117° = 153°; 232° + x = 270°

Geometry (G)

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.2- Classify two-dimensional shapes 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.

Exà parallelograms have two sets of parallel sides.  A square has the same with 4 right angles, or perpendicular intersections.

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.