Progressing toward the standard

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1 Report Card Language: form ordered pairs and graph the coordinates. CCSS: 5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. toward numerical pattern corresponding terms ordered pair coordinate plane x-axis y-axis x coordinates y coordinates Example: Plot the points on a coordinate plane, make a line graph, and then interpret the graph. generate one numerical pattern from one rule, with significant support. The student confuses x- axis and y-axis. The student confuses x coordinates and y coordinates. graph ordered pairs on a plane. label x- axis and y-axis generate one numerical pattern from one rule. generate two numerical patterns with the same starting number for two given rules. identify relationships between independent and dependent variables. use knowledge of number patterns and operations to identify and extend a pattern. generate two numerical patterns with different starting numbers for two given rules. compare given rules and determine patterns to justify the line sequence.

2 Report Card Language: read, write, compare, and round decimals to the thousandths place. CCSS: 5.NBT.3 Read, write, and compare decimals to the thousandths...using base-ten numerals, number names, and expanded form...compare two decimals using >,=,< symbols to record results. toward * Students should use concrete models and number lines to extend understanding of decimals to the thousandths place value. decimal decimal place tenths hundredths thousandths Example: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). read and write decimals to the tenths in word form, base-ten numerals, and expanded form. read and write decimals to the hundredths place value in word form, base-ten numerals, and expanded form, with significant help and/or only able to match the different forms when all are presented. read and write decimals to the hundredths place value in word form, base-ten numerals, and expanded form. read and write decimals to the thousandths place value in word form, base-ten numerals, and expanded form, with help and/or only able to match the different forms when all are presented. read and write decimals to the thousandths place value in word form, base-ten numerals, and expanded form. compare two decimals to the thousandths using place value and record the comparison using symbols <, >, or =. The student understands the size of decimal numbers and relates them to common benchmarks such as 0.5 and 0.50 and 0.500, using models. read, write and compare decimals to the tenthousandths and or hundred thousandths place value.

3 Report Card Language: multiply and divide numbers using an algorithm and models. CCSS: 5.NBT.5 Fluently multiply multi-digit whole numbers using algorithm. 5.NBT.6 Find whole number quotients of whole numbers with up to four digit dividends and two-digit divisors...illustrate and explain by using equations, rectangular arrays, and/or area models. toward * Size of numbers should NOT exceed a three-digit factor by a two-digit factor for proficient. * Fluently refers to accuracy (correct answer), efficiency (a reasonable amount of steps), and flexibility (using strategies such as the distributive property or breaking numbers apart) algorithm models multiply and divide within 100, using strategies such as the relationship between multiplication and division. multiply a whole number of up to four digits by a onedigit whole number with support. fluently multiply a whole number of up to four digits by a one-digit whole number. fluently multiply two two-digit numbers, using strategies based on place value and the properties of operations. fluently divide whole numbers with up to four-digit dividends and one-digit divisors. fluently multiply a three digit by a two digit whole number using an algorithm and a model. fluently divide a whole number with four-digit dividends and two digit divisors using the algorithm and models. explain, orally or in writing, the algorithm for multiplication and division of multi-digit numbers. Students can apply their understanding of multiple multi-digit whole numbers to multiplication and division of decimals.

4 Report Card Language: add and subtract decimals to the hundredths place using models. CCSS: 5.NBT.7 Add, subtract, multiply, and divide decimals to the hundredths place, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. toward *This work should focus on concrete models and pictorial representation, rather than relying solely on the algorithm. decimal tenths hundredths model algorithm add and subtract decimals to the tenths place, using manipulative or models with significant support. Even with significant support the student is unable to add and subtract decimals to the hundredths place. add and subtract decimals to the hundredths place, using models with support. add and subtract decimals to hundredths place, using models. *multiplying and dividing will be added to for the school year. **students will multiply tenths with tenths and tenths with hundredths, but they do not need to multiply hundredths with hundredths. add, subtract, multiply, and divide decimals to hundredths, using models, algorithms, and can justify their thinking orally and/or by writing.

5 Report Card Language: use equivalent fractions as a strategy to add and subtract fractions and unlike denominators. CCSS: 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. toward *It is not necessary to find a least common denominator to calculate sums of fractions, and in fact the effort of finding a least common denominator is a distraction from understanding adding equivalent fractions. (Progression for the CCSSM, Number and Operation-Fractions, CCSS Writing Team August 2011, page 10) Even with significant support the student cannot find common denominators. add and subtract fractions with common denominators. find equivalent fractions with common denominators, with support. find equivalent fractions with common denominators. add and subtract fractions with like denominators. determine common multiples of unlike denominators. create equivalent fractions using common multiples. add and subtract fractions with unlike denominators (including mixed numbers) using equivalent fractions. rename, reduce, and or simplify the answer when adding and subtracting fractions. mixed numbers equivalent fractions

6 Report Card Language: use models to multiply and divide fractions. CCSS: 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Evidence/ Assessments toward * Division of a fraction by a fraction is not a requirement at this grade. unit fraction *A unit fraction is a fraction that has a one in the numerator. The student is at the beginning stages of drawing a model but needs significant support to understand how to multiply and divide fractions. The student is unable to multiply and divide fractions using a model or an algorithm. The student understands that multiplication of a fraction by a whole number could be represented as repeated addition of a unit fraction, with support and guidance. The students can divide unit fractions by whole numbers only using the algorithm. divide whole numbers by unit fractions only using the algorithm. The student understands that multiplication of a fraction by a whole number could be represented as repeated addition of a unit fraction. e.g., 2 x (1/4) =1/4 + 1/4 divide unit fractions by whole numbers using models. divide whole numbers by unit fractions using models. multiply fractions. The student is able to use multiple models and algorithms to multiply and divide fractions by fractions.

7 Report Card Language: use a line plot to display data and solve problems. CCSS: 5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for the grade to solve problems involving information presented in line plots. toward line plot unit fraction Resource with video tutorials: grade5commoncoremat h.wikispaces.hcpss.org/ 5.MD.2 Example Line Plot The student is able to label some of the fractional units (1/2, 1/4) with significant support. use information in a line plot to solve single-step problems, with significant support. The student is able to label 1/2 and 1/4 of the fractional units. use information in a line plot to solve single-step problems. make a line plot with 1/2, 1/4 and 1/8 to display given data. use information in a line plot to solve multi-step problems. use fractions to solve problems involving information in line plots. The student is able to interpret, organize, and construct line plots with 1/2, 1/4, 1/8 and more to create line graphs

8 Report Card Language: find the volume of three-dimensional figures. CCSS: 5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. toward * Students should have ample experiences with concrete models before moving to pictorial representations. volume unit cube cubic unit find the volume of a 3-D figure, with significant support. find the area of 2-D with significant support. find the volume of a 3-D figure, inconsistently or sometimes with assistance. find the area of a 2-D shape but struggles to relate them to 3-D shapes. find the volume of a 3-D figure, using algorithms and/or models. explain what volume is, when to use it, and the use of cubic units. Students can apply concepts to find the volume of other 3D shapes. (Hexagonal base, etc.) Student can apply the concepts of volume to more complex (i.e. irregular shapes)

9 Report Card Language: graph points on a coordinate plane. CCSS: 5.G.1, 5.G.2 See flip-book under cluster: Graph points on the coordinate plane to solve real-world and mathematical problems. toward coordinate graph coordinates location ordered pair point x-axis x-coordinate y-axis y-coordinate quadrant The student confuses the x-axis and the y- axis. The student confuses x coordinates and y coordinates. use a coordinate grid to plot pairs, but tends to confuse the x- coordinates and y- coordinates, even with significant help. identify the origin, with or without help. use a coordinate grid to plot pairs, but tends to confuse the x- coordinates and y- coordinates. locate ordered pairs in the first quadrant of a coordinate plane but is not able to plot coordinates yet. determine when a mathematical problem has a set of ordered pairs. represent real-world and mathematical problems by locating and plotting ordered pairs in the first quadrant of a coordinate plane. * Example: Using the coordinate grid, which ordered pair represents the location of the school? Explain a possible path from the school to the library. explain the relationship between the ordered pair and the location on the coordinate plane. relate the coordinate value of any graphed point to the context of the problem.

10 Report Card Language: classify two-dimensional figures into categories based on their characteristics. CCSS: 5.G.4 Classify two-dimensional figures in a hierarchy based on properties. toward sphere cube square pyramid cylinder three-dimensional edge triangular prism face radius vertex (vertices) rectangular prism Additional Resources: m/article.aspx? storycode= * This website states s and aligned resources. group shapes based on their properties when provided significant support. identify geometric attributes (length of sides, parallel sides, angles). sometimes sort shapes by only 1-2 properties. classify two-dimensional figures in a hierarchy based on properties. * Possible student solution: *** The term property in these s is reserved for those attributes that indicate a relationship between components of shapes. The student understands that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. Example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

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