GRADE 4 MATH COMPETENCY STATEMENTS / PERFORMANCE INDICATORS

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1 Common Core State Standards Alignment Codes Everyday Math Strands & Goals Alignment Codes OA; Operations and Algebraic Thinking NBT; Number and Operations in Base Ten NOF; Number and Operations - Fractions MD; Measurement and Data G; Geometry OC; Operations and Computation PFA; Patterns, Functions, and Algebra NN; Number and Numeration MRF; Measurement and Reference Frames DC; Data and Chance G; Geometry Underlined Items have been created for E level expectations and do not necessarily align with EDM or CCSS. Items in Bold are items directly from the CCSS In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (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. 1. 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. 2. 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. 3. 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. Revised June 14, 2014 Page 1

2 Competency 1: Operations and Algebraic Thinking - Students will demonstrate the ability to compute accurately, make reasonable estimates, understand meanings of operations and use algebraic notation to represent and analyze patterns and relationships. Beyond C1PI1a. Students will use the four operations with whole numbers to solve problems. 4.OA.1 C1PI1b. 4.OA.2 C1PI1c. 4.OA.3 I can accurately write a multiplicative equation using a symbol for an unknown and solve. I can accurately translate a word problem using both a multiplicative and additive comparison into an equation with an unknown and solve. A big penguin will eat 420 grams of fish. How much more fish does a big penguin eat than a small penguin? 420/3 = s; s = 140; = m; m = 280 more grams of fish. I can write different word problems involving a specific equation where the solutions are best represented with differing answers. Use 44/6 = p to write word problems with an answer of 7; answer of 8; answer can be 7 or 8; answer of 7 2/6; answer of 7 r. 2 Mary had 44 pencils. Six pencils fit into each of her pencil pouches. How many pouches did she fill? In a word problem involving division, what needs to happen with the remainder? Report as decimal or fraction? Round up? Ignore? I can identify which quantity in a multiplicative equation is being multiplied and which number tells how many times. I can accurately describe and give written examples of the differences between a multiplicative comparison and an additive comparison. I can accurately identify and explain in writing which estimation strategy is most appropriate to use given the particular word problem. I can verify my solutions by determining the reasonableness of my answer. I can interpret a multiplicative equation as a comparison. interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. I can accurately multiply or divide to solve word problems involving multiplication or division with an unknown. By using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. I can accurately solve multistep word problems posed with whole numbers using the four operations, including problems in which remainders must be interpreted. I can accurately represent these problems using equations with a letter standing for the unknown quantity and assess the reasonableness of my answers using mental computation and estimation strategies including rounding. Inaccurate and/or inconsistent demonstration of the C-level expectation Revised June 14, 2014 Page 2

3 Beyond C1PI2. Students will gain familiarity with factors and multiples. 4.OA.4 I can accurately determine factors of whole numbers greater than 100 using rules of divisibility for 4, 6, 8, and 9. I can accurately determine factor pairs of whole numbers greater than 100 using rules of divisibility for 2, 3, 5, and 10. I can accurately: find all factor pairs for a whole number in the range I can recognize that a whole number is a multiple of each of its factors. I can determine whether a given whole number in the range is a multiple of a given one-digit number. I can determine whether a given whole number in the range is prime or composite. C1PI3. Students will generate and analyze patterns. 4.OA.5 I can identify and extend a pattern or number sequence without tools. I can accurately use a t-chart, table, and/or diagram to identify and describe features of a number or shape pattern by identifying the rule and other features explicit in the rule. There are four beans in the jar. Each day 3 beans are added. How many beans are in the jar for each of the first five days? I can accurately generate a number or shape pattern that follows a given rule and identify apparent features of the pattern that were not explicit in the rule itself. 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. C1PI4. Students will be able to use parentheses to make a number sentence true. I can accurately use two sets of parentheses in a number sentence to make it true. I can accurately use a set of parentheses in a number sentence to make it true. I can accurately solve number sentences containing parentheses. Revised June 14, 2014 Page 3

4 Competency 2: Number and Numeration in Base Ten/Fractions - Students will demonstrate the ability to understand the meanings, uses, and representations of numbers as well as equivalent names of numbers. Beyond Number & Operations in Base Ten: G4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. C2PI1a. Students will be able to generalize place value understanding for multi-digit whole numbers. 4.NBT.1 C2PI1b. 4.NBT.2 C2PI1c. 4.NBT.3 C2PI2a. Students will be able to use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.4 I accurately convert between place values through millions. 90,000 =? ones;? tens,? hundreds,? thousands,? ten thousands. I can accurately compare inequalities using mixed operations ? I can accurately use place value to estimate products and quotients of whole numbers to any place. I can accurately find missing digits in any portion of a subtraction equation using the standard algorithm of subtraction ? 372 I can accurately use mathematical language, (i.e. place value, greater than, less than, equal to, multiplication, division) to describe how a digit is similar or different from the same digit in another number. How is the 2 in 1,582 similar or different from 2 in 258? I can accurately read and write multi-digit numbers in a variety of different forms. 285 = 28 tens + 5 ones; 1 hundred + 18 tens + 5 ones. I can accurately use place value to estimate sums and differences of whole numbers to any place. I can accurately find missing digits in a sum or addend while using the standard algorithm of addition ? 66 I accurately 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. Recognize that = 10 by applying concepts of place value and division. I can accurately read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form and compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. I can accurately use place value understanding to round multi-digit whole numbers to any place. I can accurately and fluently add and subtract multidigit whole numbers using the standard algorithm. Inaccurate and/or inconsistent demonstration of the C-level expectation Revised June 14, 2014 Page 4

5 Beyond C2PI2b. 4.NBT.5 I can accurately multiply a whole number of up to four digits by a onedigit whole number, and multiply two two-digit numbers using the partial products algorithm and the standard algorithm. I can accurately multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using the partial products algorithm. I can accurately multiply a whole number of up to four digits by a one-digit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. I can illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. C2PI2c. 4.NBT.6 I can accurately check whole number division problems without remainders with up to four digit dividends and two digit divisors by finding the related multiplication equation. I can accurately find whole number quotients with three or four digit dividends and two digit divisors. I can accurately 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. I can illustrate and explain the calculation by using equations, rectangular arrays, and/or models. C2PI3. Students will be able to solve addition and subtraction problems using decimal notation. I can create and solve addition and subtraction problems using three or more three digit whole numbers and decimal numbers up to the hundredths place in a real world context. I can accurately solve addition and subtraction problems using three or more three digit whole numbers and decimal numbers up to the hundredths place. I can accurately solve addition and subtraction problems using two three-digit whole numbers and decimal numbers up to the hundredths place. Revised June 14, 2014 Page 5

6 Number & Operations-Fractions: G4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. 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 G4. C2PI4a. Students will extend an understanding of fraction equivalence and ordering. 4.NF. 1 I can accurately complete a pattern using equivalent fractions. 1/5 = 2/10 = 3/n = 4/20 I can accurately calculate equivalent fractions by multiplying a given fraction by another fraction equivalent to 1/1. 1/3 x 2/2 = 2/6 I can accurately explain why a fraction a/b is equivalent to another fraction (nxa)/(nxb) 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. I can use this principle to recognize and generate equivalent fractions. C2PI4b. 4.NF.2 I can accurately explain in writing how four or more fractions with unlike denominators are placed in decreasing or increasing order. I can accurately compare and record three fractions with like and unlike denominators using <, =, or >. 2/8 < 5/6 < 7/8 I can accurately 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. I can recognize that comparisons are valid only when the two fractions refer to the same size whole. I can record results with symbols <, =, and >. ½ or 1/8 of a medium pizza is different from ½ or 1/8 of a large pizza. I can record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. C2PI5a. Students will be able to build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.3 and 4.NF.3a I can accurately demonstrate an understanding of how to add and subtract fractions with like denominators which may result in an improper fraction renamed to a whole or mixed number. I can accurately demonstrate an understanding of how to add and subtract two or more fractions with like denominators. I can accurately demonstrate an understanding of addition and subtraction of fractions as joining and separating parts referring to the same whole, with like denominators. C2PI5b. 4.NF.3b I can accurately record multiple ways to decompose (break apart) a mixed number into the sum of proper fractions with same denominator. I can accurately record multiple ways to decompose (break apart) an improper fraction into the sum of fractions with the same denominator and create a visual model. I can accurately decompose (break apart) a fraction into a sum of fractions with the same denominator in more than one way, by recording each one with an equation. I can support my reasoning by using a visual fraction model or other means. 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = /8; or 8/8 + 8/8 + 1/8 Revised June 14, 2014 Page 6

7 Beyond C2PI5c. 4.NF.3c I can accurately add and subtract mixed numbers with unlike denominators using real world problems, and express my answer in simplified form. I can accurately add and subtract mixed numbers with unlike denominators using real world problems. I can accurately add and subtract mixed numbers with like denominators. C2PI5d. 4.NF.3d I can solve and explain word problems involving addition and subtraction of fractions with like and unlike denominators. I can accurately solve word problems involving addition and subtraction of fractions with unlike benchmark denominators (2, 3, 4, 5, 6, 8, 10, 12, and 100). ¼ + ½ + 2/8 = 1 I can accurately 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. A cake recipe calls for ¾ cup of milk, ¼ cup oil, and 2/4 cup of water. How much liquid was needed to make the cake? C2PI6a. Students will be able to apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 4.NF.4 and 4a I can accurately write an equation that represents a fraction a/b as a multiple of 1/b and explain in writing my reasoning for how the equation works. I can accurately explain how addition of unit fractions relates to multiplying fractions. i.e. 3/5 = 1/5 +1/5 + 1/5; 3/5 = 3 (1/5). I can accurately demonstrate an understanding that fraction a/b s is a multiple of 1/b. 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); 5/4 = 1/4+1/4+1/4+1/4+1/4 C2PI6b. 4.NF.4b I can accurately explain in writing how multiplying a whole number by a fraction results in the general rule of multiplying n x (a/b) = (n x a)/b I can accurately multiply a whole number by a fraction without visual model. I can accurately demonstrate understanding and extend my prior knowledge of multiplication to multiply a fraction by a whole number. use a visual fraction model to express 3 (2/5) as 6 (1/5) = 1/5+1/5+1/5+1/5+1/5+1/5 and recognizing this product as 6/5. (In general, n (a/b) = (n a)/b) C2PI6c. 4.NF.4c I can accurately solve and explain word problems involving multiplication of a fraction by a whole number. I can accurately solve word problems involving multiplication of a fraction by a whole number with and without visual models. I can accurately 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. 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? Revised June 14, 2014 Page 7

8 Beyond C2PI7a. Students will understand decimal notation for fractions, and compare decimal fractions. 4.NF.5 I can accurately explain in writing how to express a fraction with denominator 10 as an equivalent fraction with denominator 100 and how to use this technique to add two fractions with respective denominators 10 and 100. I can accurately add and subtract using equivalent fractions with denominators of 10 and /10 5/100 = 60/100 5/100 = 55/100 I can accurately express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100, and use this technique to add two fractions with respective denominators of 10 and 100. express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100 C2PI7b. 4.NF.6 I can use decimal notation for fractions with denominators 10 or 100 in a word problem. I can accurately explain multiple ways to decompose (break apart) a decimal using addition..56 = ; or.56 = ; or.56 = ; or I can use decimal notation for fractions with denominators 10 or 100. rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. C2PI7c. 4.NF.7 I can accurately compare a set of more than three decimals to hundredths and explain my reasoning. I can accurately compare two decimals using at least two different models and explain how I know my comparisons are valid. I can accurately compare two decimals to hundredths by reasoning about their size in relation to the same size whole. I recognize that comparisons are valid only when the two decimals refer to the same whole and I can record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. Revised June 14, 2014 Page 8

9 Competency 3: Measurement - Students will demonstrate the ability to understand the systems and processes of measurement; use appropriate techniques, tools, units and formulas in making measurements. Beyond C3PI1a. Students will be able to solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 4.MD.1 I can accurately convert given measurements to various unit measures i.e. 5 cups = x pints and y cups. I can accurately represent measurement diagrams and explain how they help me solve word problems. I can accurately demonstrate understanding of relative sizes of measurement units within one system and convert larger units to smaller units by recording them in a t-chart or graphic organizer. Units include: km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. C3PI1b. 4.MD.2 C3PI1c. 4.MD.3 C3PI2a. Students will understand concepts of angle and measure angles. 4.MD.5 4.MD.5a 4.MD.5b 4.MD.6 I can accurately solve word problems resulting in fractional units. I can explain how fractional increases/decreases in area affect the dimensions of a shape. I can accurately measure an angle within 1 degree. I can accurately represent and explain how measurement diagrams help me solve word problems. I can accurately apply the area and perimeter formulas for parallelograms and triangles in real world and mathematical problems. I can accurately estimate angle measurements and support my estimate in writing with relevant math vocabulary. I can estimate the measure of an angle in writing before checking its measure with a protractor. I can accurately 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. I can accurately represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. I can accurately apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example: Find the width of a rectangular room given its area and length. I can accurately demonstrate understanding of the relationship between angle measurement and a circle. I can define angles as geometric shapes that are formed wherever two rays share a common endpoint. An angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure angles. I can accurately demonstrate understanding that an angle that turns through n one-degree angles is said to have an angle measure of n degrees. I can accurately measure angles in whole-number degrees using a protractor within 3 degrees and sketch angles of specified measure. Inaccurate and/or inconsistent demonstration of the C-level expectation Revised June 14, 2014 Page 9

10 C3PI2b. 4.MD.7 I can compare and contrast the relationship between adjacent and supplemental angles. I can determine missing angle measurements using the relationship between supplemental angles. I can accurately recognize angle measure as additive by using addition and subtraction to determine the sums and differences of two adjacent angle measures. Competency 4: Data - Students will demonstrate the ability to represent and analyze data. Beyond C4PI1a. Students will be able to represent and interpret data. 4.MD.4 C4PI1b. I can accurately use a line plot to find landmark data points. maximum, minimum, range, median, and mean. I can accurately design a set of real life data based on a given set of data landmarks. Unit 2 Open Response I can accurately interpret a line plot and communicate generalizations or create questions from it. I can compare and contrast two sets of data. I can accurately 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 involving addition and subtraction of fractions by using information presented in line plots. I can accurately identify data landmarks including maximum, minimum, mode, and range when given a set of data. Inaccurate and/or inconsistent Revised June 14, 2014 Page 10

11 Competency 5: Geometry - Students will demonstrate the ability to investigate characteristics and properties of two and/or three- dimensional geometric shapes and apply transformations and symmetry in geometric situations. C5PI1a. Students will be able to draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.1 C5PI1b. 4.G.2 C5PI1c. 4.G.3 I can accurately analyze a set of attributes to construct a polygon. I can accurately classify quadrilaterals and triangles based on their properties and explain my classifications. I can accurately classify polygons with more than two lines of symmetry and explain patterns of symmetry in regular polygons. Beyond I can accurately use relevant math vocabulary to describe various two-dimensional figures and/or shapes. I can accurately classify quadrilaterals based on their properties using a Venn diagram or other graphic organizer. I can accurately classify polygons that have more than one line of symmetry. I can accurately draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. I can identify these in 2D figures. I can accurately classify two-dimensional figures based on the properties of parallel or non-parallel lines, perpendicular or non-perpendicular lines, and angle size. I can recognize right triangles as a category and identify right triangles. I can accurately identify line-symmetric figures and draw lines of symmetry for two-dimensional figures. Inaccurate and/or inconsistent demonstration of the Competency 6: Fact Fluency - Students will demonstrate the ability to quickly and accurately verbalize and compute fact fluency. C6PI1. Students will be able to demonstrate memorization of products and related quotients up to 12 x 12. I can demonstrate memorization of products and related quotients up to 12 x 12. Not Yet I inconsistently demonstrate memorization of products and related quotients up to 12 x 12. Revised June 14, 2014 Page 11

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