# Progressing toward the standard

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1 Report Card Language: add, subtract, multiply, and/or divide to solve multi-step word problems. CCSS: 4.OA.3 Solve multistep work 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. Meets consistently choose the correct operation to solve a single-step word problem. choose the correct operation and use and equation needed to solve a single-step word problem. In multiple step problems, the student sometimes misses critical steps or information needed to solve the problem. The student makes some errors when using mental math or estimation strategies. choose the correct operation to perform at each step of a multi-step word problem. use mental math or estimation strategies to check for reasonableness (e.g.,rounding up when needed with a remainder as in a problem asking how many busses are needed to carry students) use an equation with a letter standing for an unknown quantity. The student fluently chooses the correct operation to perform at each step of a more complex multi-step word problem and solves accurately. use multiple mental math or estimations strategies to check for reasonableness. write expressions that record their calculations with numbers, parentheses, and a letter standing for the unknown quantity.

2 Report Card Language: find all factors and multiples for whole numbers within 100. CCSS: 4.OA.4 Find all factor pairs for a whole number in the range of Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. Meets Terms to know: multiplication/multiply division/divide factor pairs facto multiple prime composite find few factors and multiples within 100 without assistance. Lists of factors are extremely limited. The student does not show an understanding of prime and composite. find factors and multiples of many numbers within 100, but lists may be incomplete. The student may rely on manipulatives and visuals such as rectangular arrays to determine if a number is prime or composite. use strategies such as division, divisibility rules, and skip counting to identify all factors and multiples of whole numbers within 100. then identify whether any given number with 100 is prime or composite. identify all factors and multiples of any give number and whether the number is prime or composite, including numbers greater than 100.

3 Report Card Language: generate and analyze number patterns. CCSS: 4.OA.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. Meets The does not require students to infer or guess the underlying rule, but rather asks them to generate a pattern from a given rule and identify features of the pattern. extend a pattern when given a rule and the beginning sequence of a numerical or shape pattern. Given a rule and the beginning sequence of a numerical or shape pattern, the student can extend the pattern but is unable to make observations about how the pattern changes and grows. Given a rule, the student can generate a numerical or shape pattern. make observations about how the pattern changes and grows. For example, given the rule Add 3 and the starting number 1, generate the next several numbers in the pattern, and observe that the terms appear to alternate between even and odd numbers. generate two numerical patterns following two given rules. The student can make observations and give explanations identifying relationships between corresponding terms.

4 Report Card Language: fluently add and subtract multi-digit numbers using algorithm. CCSS: 4.NBT.4 Fluently add and subtract multi-digit whole numbers using algorithm. Meets Grade level expectations for this are limited to whole numbers less than or equal to 1,000,000. The student struggles to set up the problem according to base ten. The student may be working from left to right, rather than starting in the ones place and working to the left. set up a problem according to base ten, but makes frequent errors in problems that require regrouping. set up numbers according to base ten (ones with ones, tens with tens, etc.) with automaticity and can fluently add and subtract multi-digit numbers using the algorithm, including problems that require regrouping. set up whole numbers according to base ten (ones with ones, tens with tens, etc.) with automaticity and can multiply multi-digit numbers using the algorithm.

5 Report Card Language: compare* and round multi-digit numbers to any place value up to 1,000,000 CCSS: 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. Meets Grade level expectations in this domain are limited to whole numbers less than or equal to 1,000,000 *NOTE: Comparing numbers is actually part of 4.NBT.2. This will be changed on the report card for the school year. not use place value understanding to accurately round numbers. accurately compare multi-digit numbers up to 100 using place value and record the comparison using symbols <, >, or =. use place value understanding to round whole numbers to the nearest 10 or 100. accurately compare multi-digit numbers up to 1,000 using place value and record the comparison using symbols <, >, or =. use place value to round multi-digit whole numbers up to 1,000,000 to any place. accurately compare multi-digit numbers up to 1,000,000 using place value and record the comparison using symbols <, >, or =. apply the concept of rounding and comparing numbers up to the 1,000,000 place in real world problems. understand place value and what digits to look at to round decimals to any place.

6 Report Card Language: read and write multi-digit whole numbers and use expanded form up to 1,000,000. (Note: COMPARE will be added to this report card item for the school year.) CCSS: 4.NBT.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 >,=,< symbols to record the results of comparisons. Meets Grade level expectations in the domain are limited to numbers less than or equal to 1,000,000 The student makes frequent errors when reading multi-digit whole numbers. The student makes frequent errors when writing multi-digit whole numbers. The student makes frequent errors when using expanded form on multi-digit whole numbers. accurately read multidigit whole numbers up to 1,000. accurately write multidigit whole numbers up to 1,000. accurately use expanded form up to 1,000. accurately read multidigit whole numbers up to 1,000,000. accurately write multidigit whole numbers up to 1,000,000. accurately use expanded form up to 1,000,000. accurately read, write, and use expanded form for numbers with decimals up to the thousandths. explain that a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 or what it represents in the place to its left.

7 Report Card Language: multiply two 2-digit numbers using algorithms and models (e.g., 24 X 36) CCSS: 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit number, 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. Meets The student is not able to multiply two digit numbers without significant teacher support. multiply one-digit numbers by multiples of ten. show multiplication of two twodigit numbers using rectangular arrays, place value, and the area model. multiply a three digit by two digit whole number numbers using the algorithm. solve multiplication of two twodigit numbers using algorithms and properties of operations.

8 Report Card Language: use models to explain equivalent fractions, compare and order fractions. CCSS: 4.NF.1 and 4.NF.2 under the cluster: Extend understanding of fraction equivalence and ordering. See flipbook for detailed explanation. Meets The student is unable use visual models to show fractional amounts without significant teacher support. model fractional amounts using an area number and number line. explain why two fractions are equivalent by using visual fraction models. compare two fractions using visual fraction models. order three or more fractions using visual fraction models. use equations and models to show equivalent fractions. use multiplication to find common denominators to compare two or more fractions.

9 Report Card Language: add and subtract fractions and mixed numbers with like denominators by using models and algorithms. CCSS: 4.NF.3 Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. See flipbook for parts a-d. Meets Terms for students: operations fraction unit fraction equivalent denominator numerator mixed number decomposing add fractions with like denominators without significant teacher support. solve word problems involving addition and subtraction of fractions with like denominators without significant teacher support. The student relies on visual models to add and subtract fractions with like denominators. The student requires teacher support to solve word problems involving addition and subtraction of fractions with like denominators. use models and algorithms to add and subtract fractions with like denominators. solve word problems involving addition and subtraction of fractions with like denominators by using visual models and equations to represent the problem. use equivalent fractions to add and subtract fractions with unlike denominators.

10 Report Card Language: convert fractions to decimals. CCSS: 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. Meets write fractions with denominators of 10 and 100 as a decimal without significant teacher support. write fractions with denominators of 10 and 100 as a decimal, but is unable to explain the relationship between a fraction and a decimal without teacher support. explain the relationship between a fraction and a decimal. write fractions with denominators of 10 and 100 as a decimal. convert any fraction to a decimal, not limited to fractions with a denominator of 10 and 100. identify the tenths and hundredths place of a decimal.

11 Report Card Language: compare and order decimals to the hundredths place. CCSS: 4.NF.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 >,=,<, and justify conclusions, e.g., by using a visual model. Meets use visual models to show decimal amounts to the hundredths place without significant teacher support. use visual models to show decimal amounts to the hundredths place. compare two decimals to the hundredths place by using a visual model. compare two decimals to the hundredths place and record the comparison using symbols <, >, or =. compare two decimals that extend beyond the hundredths place and explain the comparison using their knowledge of place value.

12 Report Card Language: identify relative sizes of measurement units such as kilometer, meter, and centimeter. CCSS: 4.MD.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 measurements in a two-column table. Meets Students have been introduced to units of measurements in prior grades. New to this grade is converting measurements and expressing measurements in a larger unit in terms of a smaller unit. Examples: a 4-foot snake is 48 inches. describe the relative size of measurement units without significant teacher support. represent a larger unit as a multiple of smaller units within the same system of measurement and record the equivalent measurements in a twocolumn table without significant teacher support. describe the relative size of SOME measurement units but has an incomplete understanding of common measurement units. (e.g., Can describe inch and cm, but not meter or foot.) represent a larger unit as a multiple of smaller units within the same system of measurement and record the equivalent measurements in a twocolumn table with teacher support. describe the relative size of measurement units such as meter (e.g., about the height of a tall chair), kilometer (about the length of ten football fields), etc. represent a larger unit as a multiple of smaller units within the same system of measurement and record the equivalent measurements in a twocolumn table. convert measurement units within the same system of measurement. solve multi-step word problems using measurement conversions.

13 Report Card Language: solve word problems involving money. CCSS: 4.MD.2 Use the 4 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. Meets The reported references money only, so the proficiency rubric is written this way. However, references problems involving distances, intervals of time, volumes, masses, and problems with fractions and decimals. Students should have exposure to all types of problems. consistently choose the correct operation to solve a single-step word problem involving money. choose the correct operation is needed to solve a single-step word problem involving money. choose the correct operation to perform at each step of a multi-step word problem involving money. use mental math or estimation strategies to check for reasonableness. choose the correct operation to perform at each step of a multi-step word problem involving money. use mental math or estimations strategies to check for reasonableness. write expressions that record their calculations with numbers, parentheses, and a letter standing for the unknown quantity.

14 Report Card Language: find area and perimeter of rectangles. CCSS: 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Meets determine area and/or perimeter without significant teacher support. measure area by counting square units. calculate perimeter. determine when to find the area and when to find the perimeter to solve real world problems with teacher support. use and explain the formulas for area and perimeter. determine when to find the area and when to find the perimeter to solve real world problems. apply the formula for area to irregular shapes with right angles to solve real world problems.

15 Report Card Language: draw and identify lines and angles and classify shapes by properties of their lines and angles. CCSS: 4.G.1, 4.G.2. 4.G.3 Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. See flipbook for detailed explanation of the cluster. Evidence/ Assessments Meets Terms in this strand point line line segment ray angle vertex right, obtuse, acute perpendicular parallel isosceles, equilateral, scalene triangle line of symmetry identify basic shapes learned in previous grades. identify parts of shapes such as angles, points, lines, rays, with support from a teacher. sort two dimensional shapes based on simple attributes such as number of sides, types of angles, numbers of points, etc. draw and identify an example of a point, line, line segment, ray, right angle, obtuse angle, perpendicular lines, and parallel lines. sort two dimensional shapes into categories based on properties of their lines and angles (such as, right triangles, parallel lines group together two dimensional shapes that share a single property, and then among these shapes, group together those that share a second property, and then among these, group together those that share a third property. Students can identify shapes corresponding with terms for the strand

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