Progressing toward the standard


 Geoffrey Lester
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1 Report Card Language: The student can fluently multiply and divide within 100. CCSS: 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of grade 3, know from memory all of the products of two onedigit numbers. toward Meets Fluently means accuracy, efficiency, and flexibility. Know from memory should not focus only on timed tests and repetitive practice, but ample experiences working with manipulatives, pictures, arrays,word problems, and numbers to internalize the basic facts. The student needs significant teacher support to multiply and divide within 50 and to recall multiplication facts 0 s, 1 s, 2 s, and 5 s. The student can multiply and divide within 50 and knows from memory multiplication facts 0 s, 1 s, 2 s, and 5 s. The student can fluently multiply and divide within 100 and knows from memory multiplication facts 09. The student can multiply and divide beyond 100 and/or knows from memory multiplication facts 10 s, 11 s and 12 s. Terms for students: operation, multiply, divide, factor, product, quotient, unknown, strategies, reasonableness, mental computation, property
2 Report Card Language: The student can understand properties of multiplication and the relationship between multiplication and division. CCSS: 3.OA.5 Apply properties of operations as strategies to multiply and divide (commutative, associative, and distributive property) Evidence/ Assessments toward Meets Terms for students: operation, multiply, divide, factor, product, quotient, strategies, Properties Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = = 56. (Distributive property.) S The student needs significant teacher support to apply one or two of the following properties to solve multiplication and division problems; the commutative property, the associative property or the distributive property. The student can apply one or two of the following properties to solve multiplication and division problems; the commutative property, the associative property and the distributive property. * The commutative property would probably be the first property to be to master. The student can apply the commutative property, the associative property and the distributive property to solve multiplication and division problems. The student can make connections and communicate how two out of the three properties relate to each other using multiplication and division. Students need not use formal terms for these properties.
3 Report Card Language: The student can use models to represent and solve problems involving multiplication and division within 100. CCSS: 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. toward Meets Different models include: array models equal groups number lines partition model support the student can solve one step word problems involving multiplication and division within 50, using drawings and equations to represent the problem and the solution. one step word problems involving multiplication and division within 50; using drawings and equations to represent the problem and the solution. one step word problems involving multiplication and division within 100; using drawings and equations to represent the problem and the solution. one or twostep word problems involving multiplication and division within 100; using multiple strategies to represent the problem and the solution.
4 Report Card Language: problems involving the four operations (addition, subtraction, multiplication, division) and identify and explain patterns in arithmetic. CCSS: 3.OA.8 Solve twostep word problems using the four operations. Represent the problems using equations with a letter standing for the unknown quantity. 3.OA.9 Identify arithmetic patterns (including patterns in the addition or multiplication table) and explain them using properties of operations. toward Meets This is limited to problems with whole numbers. The student needs significant teacher support to solve two step word problems using the four operations. (Adding and subtracting numbers within 100, and multiplying and dividing singledigit factors with products less than 100.) The student needs significant teacher support to find patterns in addition and multiplication using a 100 s chart. two step word problems using the four operations. (Adding and subtracting numbers within 1,000, and multiplying and dividing singledigit factors with products less than 100.) The student can find patterns in addition and multiplication using a 100 s chart. two step word problems using the four operations. (Adding and subtracting numbers within 1,000, and multiplying and dividing singledigit factors with products less than 100.) When representing the problem the student can use an equation with an unknown quantity. The student can find and communicate patterns in addition and multiplication. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. two step word problems using the four operations. (Adding and subtracting numbers beyond 1,000, and multiplying and dividing singledigit factors with products beyond 100) When representing the problem the student can use an equation with an unknown quantity. The student can find and communicate many patterns in addition and multiplication. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
5 Report Card Language: The student can use the concept of place value to round whole numbers to the nearest 10 or 100. CCSS: 3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100. toward Meets Terms for students: place value, rounding addition, add, addend, sum, subtraction, subtract, difference, strategies, (properties)rules about how numbers work The student needs significant teacher support to round whole numbers to the nearest 10 using place value understanding. The student can use place value understanding to round whole numbers to the nearest 10 only. The student can communicate the reasoning about their answers. The student can use place value understanding to round whole numbers to the nearest 10 or 100. The student can communicate the reasoning about their answers. The student can use place value understanding to round whole numbers to the nearest The student can communicate the reasoning about their answers.
6 Report Card Language: The student can multiply one digit whole numbers by multiples of 10 (e.g., 5 X10, 5 X 300) CCSS: 3.NBT.3 Multiply onedigit whole numbers by multiples of 10 in the range using strategies based on place value and properties of operations. toward Meets help the student can multiply one digit whole numbers by 10 and but is not able to communicate and reason about the products. The student can multiply one digit whole numbers by 10 and is able to communicate and reason about the products. (not simply using the trick of add a zero) The student can multiply one digit whole numbers by multiples of ten (e.g., 9 x 80, 5 x 60) and is able to communicate and reason/defend the products. For example, for the problem 50 x 4, students should think of this as 4 groups of 5 tens or 20 tens, and that twenty tens equals 200. The student can multiply one digit whole numbers by multiples of ten (e.g., 9 x 80, 5 x 60) and is able to communicate and reason /defend the products by explaining that in a multidigit number, a digit in one place represents ten times what it represents in the place to its right. They can extend this understanding to multiply one digit numbers by 100 or 1000.
7 Report Card Language: The student can fluently add and subtract within CCSS: 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and /or the relationship between addition and subtraction. Evidence/ Assessments toward Meets Fluently means accuracy, efficiency, and flexibility. Know from memory should not focus only on timed tests and repetitive practice, but ample experiences working with manipulatives, pictures, arrays,word problems, and numbers to internalize the basic facts. support the student can add and subtract within 100, but does not demonstrate fluency. The student can fluently add and subtract within 100 and is able to communicate how the problem was solved. The student can fluently add and subtract within 1000 and is able to communicate how the problem was solved. The student can fluently add and subtract within 1000 using more than one strategy to communicate how the problem was solved. The student can use place value to solve addition and subtraction problems greater than 1000 by correctly setting up problems using the algorithm.
8 Report Card Language: The student can understand and represent fractions as part of a whole. CCSS: 3.NF.1 Understand a fraction of 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Performance Levels for Reported Standa toward Meets Fraction models in third grade include only area models (circles, rectangles, squares) and number lines. Terms for students partition(ed) equal parts fraction equal distance ( intervals), equivalent equivalence denominator numerator comparison compare justify The student required significant teacher support to identify halves of an area model and on a number line. The student can identify halves of an area model. Students can label unit fractions (fractions with numerator 1) of a whole with teacher support. The student can label/ identify fractions as fair sharing or parts of a whole, using various contexts (candy bars, fruit, and cakes) and a variety of models (circles, squares, rectangles, fraction bars, and number lines). The student can build fractions from unit fractions (seeing the numerator 3 in 3/4 as the quantity you get when putting 3 of the 1/4s together). *No need to introduce improper fractions initially. Using two or more models student can label/identify fractions as fair sharing or parts of a whole, using various contexts (candy bars, fruit, and cakes) and a variety of area models (circles, squares, rectangles, fraction bars, and number lines) and set models (parts of a group).
9 Report Card Language: The student can use models to order and compare fractions. CCSS: 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Evidence/ Assessments toward Meets help the student can identify the whole and the half on a number line. help the student can place a half onto the number line. The student can identify the whole and the half on a number line. The student can place a half onto the number line. With picture models the student can identify 1/2=2/4. With 1:1 support, the student can compare two simple fractions and identify which one is bigger. The student can identify a fractional amount on a number line, between 0 and 1. example 0, 1/4, 1/2, 3/4, 1. The student can list simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3) e.g., by using a visual fraction model.students should only explore equivalent fractions using models, rather than using algorithms or procedures. The student can compare two simple fractions with the same denominator and defend why one is bigger than the other. The student can use a number line to order fractions by size and communicate the reasoning. The student can list complex equivalent fractions, using a visual fraction model. Students should only explore equivalent fractions using models, rather than using algorithms or procedures. The student can compare two more complex fractions with the same denominator and defend why one is bigger than the other.
10 Report Card Language: The student can represent and interpret data using bar, line, and picture graphs. CCSS: 3.MD.3 Draw a scaled picture graph and scaled bar graph to represent a data set with several categories. Solve one and twostep how many more and how many less problems using information presented in scaled bar graphs. toward Meets Terms for students: picture graph bar graph line graph data title label key support the student can complete a template of a picture graph or a bar graph and fill in some of the required data sets. support the student can read a scaled bar graph and answer questions about the data. The student can complete a template of a picture graph or a bar graph and fill in the required data sets. The student can read a scaled bar graph and answer questions about the data. Example: How many kids like the color orange? The student can draw a picture graph and a bar graph to represent a data set with at least 3 categories. Using the information from scaled bar graphs to solve for one and two step problems about how many more or how many less. Example: How many more nonfiction books where read than fantasy books? Did more people read biography and mystery books or fiction and fantasy books? The student can draw a picture graph and a bar graph to represent a data set with more than 3 categories. The student can construct their own questions about the information in the graphs that they create and the can communicate about the reasons for those questions. Using the information from scaled bar graphs to solve for one and two step problems about how many more or how many less.
11 Report Card Language: The student can recognize perimeter as an attribute of rectangular arrays and distinguish between perimeter and area. CCSS: 3.MD.8 Solve real world and math problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas with the same area and different perimeters. toward Meets Terms for students: perimeter polygon side length unknown equal unequal support the student can solve real world math problems involving the perimeter of 3 and 4 sided regular polygons. support the student can find perimeter given the side lengths of 3 and 4 sided polygons. support the student can find the length of an unknown side of a square or rectangle. able to do the above even with real world math problems involving the perimeter of 3 and 4 sided regular polygons. The student can find perimeter given the side lengths of 3 and 4 sided polygons. The student can find the length of an unknown side of a square or rectangle (when equal side lengths are known) The student can identify rectangles that have equal perimeters and rectangles that have equal areas. real world math problems involving the perimeter of polygons. The student can find the perimeter of regular polygon, given the side lengths. The student can find the length of an unknown side of a polygon. The student can identify rectangles that have equal perimeters and differing area, as well as, rectangles with equal area and differing perimeter. real world multistep math problems involving polygons. The student can find the perimeter of irregular polygons given the side lengths. The student can find the length of multiple unknown sides of a polygon.
12 Report Card Language: The student can divide shapes into parts with equal areas and describe the equal parts represented as a fraction of the whole.
13 CCSS: 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as unit fraction of the whole. toward Meets equal parts numerator denominator fractional area partition label describe support the student can cut a shape into equal parts and label those parts with the correct fractional amount. able to complete the task even with The student can cut or fold a shape into equal parts and label those parts with the correct fractional amount. The student can cut or fold a shape into equal parts and label those parts with the correct fractional amount. The student is able to communicate and reason about how these equal parts have the same area. The student extends understanding to partitioning of wholes that involve collections of objects (set models). For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
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