3.OA.6 Biweekly Assessment administered: Approximately October 10 3.OA.3 3.OA.5 3.OA.7 3.OA.8 3.OA.1 3.OA.2 3.OA.4 3.OA.6 Distributive Property and Problem Solving Using Units of 2-5 and 10 Apply the distributive property to decompose units Solve two-step word problems involving multiplication and division and assess the reasonableness of answers. Solve two-step word problems involving all four operations and assess the reasonableness of answers Ch. 2 Ch. 5 Ch. 6 Ch. 7 Ch. 8 Ch. 9 Ch. 12 4 End of Unit Assessment administered: Approximately October 24 Essential Question: How are multiplication and division related? How do we use multiplication and division to solve problems? What are the properties of multiplication? What strategies can we use to memorize facts? Key Vocabulary: Array (a set of numbers or objects that follow a specific pattern, a matrix) Column (e.g., in an array) Commutative Property/Commutative (e.g., rotate a rectangular array 90 degrees to demonstrate that factors in a multiplication sentence can switch places) Equal groups (with reference to multiplication and division; one factor is the number of objects in a group and the other is a multiplier that indicates the number of groups) Equation (a statement that 2 expressions are equal. E.g., 3 × 4 = 12) Distribute (with reference to the Distributive Property; e.g. In 12 × 3 = (10 × 3) + (2 × 3) the 3 is multiplier for each part of the decomposition) Divide/division (partitioning a total into equal groups to show how many equal groups add up to a specific number. E.g., 15 ÷ 5 = 3) Fact (used to refer to multiplication facts, e.g., 3 × 2) Factors (i.e., numbers that are multiplied to obtain a product) Multiplication/multiply (an operation showing how many times a number is added to itself e.g., 5 × 3 =15)
Rubric Assessment Task Item and Standards Addressed STEP 1 Little evidence of reasoning without a correct answer. (1 Point) STEP 2 Evidence of some reasoning without a correct answer. (2 Points) STEP 3 Evidence of some reasoning with a correct answer or evidence of solid reasoning with an incorrect answer. (3 Points) STEP 4 Evidence of solid reasoning with a correct answer. (4 Points) 1 3.OA.2 3.OA.3 3.OA.4 3.OA.7 Student is unable to answer any question correctly. The attempt shows the student may not understand the meaning of the questions. Student answers at least one question correctly. Mistakes may include those listed in the box to the right, and/or Writes the incorrect factor in the multiplication sentence Does not show understanding of the meaning of the unknown factor Writes an incorrect division sentence Student answers at least two questions correctly. Mistakes may include the following: Incorrectly writes in the missing factor, but understands that it represents the number of cookies in each row Places the numbers incorrectly in the division sentence Student correctly: Draws an array Fills in the missing factor (6) and understands what it represents Writes a related division sentence (18 ÷ 3 = 6) 2 3.OA.2 3.OA.3 3.OA.5 Student attempts to draw the picture. The attempt, however, shows the student may not understand the meaning of the questions. Student answers at least one question correctly. Mistakes may include those listed in the box to the right, and/or: Draws incorrect pictures of the number of bags of chocolate chip cookies and sugar cookies Attempts to draw the 2 arrays, but inaccurately explains the relationship between them Student answers at least two questions correctly. Mistakes may include the following: Incorrectly calculates the number of bags either in Part (a) or Part (b) Draws the arrays correctly but explanation includes some inaccuracies Student answers every question correctly: Finds the number of bags Melanie packs for chocolate chip cookies and sugar cookies. Draws 2 arrays to represent the chocolate chip cookies and sugar cookies Provides an accurate explanation of the commutative property in Part (c)
word problems Fluently multiply and divide within 100 Fourth Grade Solve multi-step word problems posed with whole numbers and having whole-number answers Fluently add multi-digit whole numbers Fractions • Add mixed numbers with like denominators Fourth Grade Solve multi-step word problems posed with whole numbers and having answers Fluently subtract multi- digit whole numbers Fractions Subtract mixed numbers with like denominators Fourth Grade Solve multi-step word problems posed with whole numbers and having answers Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two- digit numbers Fractions • Multiply a fraction by a whole number Fourth Grade Solve multi-step word problems posed with whole numbers and having answers Find quotients and remainders with up to four-digit dividends and one-digit divisors Addition Subtraction Multiplication Division pg 2 Fifth Grade Fractions • Add fractions with unlike denominators (including mixed numbers) Decimals • Add decimals to hundredths Fifth Grade Fractions • Subtract fractions with unlike denominators (including mixed numbers) Decimals • Subtract decimals to hundredths Fifth Grade • Fluently multiply multi- digit whole numbers Fractions • Solve real world problems involving multiplication of fractions and mixed numbers Decimals Explain patterns in the placement of the decimal point when a decimal is multiplied by a power of 10 Multiply decimals to hundredths Fifth Grade • Find whole-number quotients of whole numbers with up to dividends and divisors Fractions • Divide unit fractions by whole numbers and whole numbers by unit fractions Decimals Explain patterns in the placement of the decimal point when a decimal is divided by a power of 10 Divide decimals to hundredths Sixth Grade Decimals Sixth Grade Decimals digit Sixth Grade Decimals Sixth Grade • Fluently divide multi-
• Fluently add multi-digit decimals Expressions, Equations & Inequalities Reason about and solve one-variable equations and inequalities. Represent and analyze quantitative relationships between dependent and independent variables. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers Write an inequality of the form x > c or x < c to represent a constraint or condition in a real- world or mathematical problem Represent solutions of inequalities on number line diagrams • Fluently subtract multi- decimals Expressions, Equations & Inequalities • Same as “Addition” Column • Fluently multiply multi- digit decimals Expressions, Equations & Inequalities • Same as “Addition” Column digit numbers Fractions • Divide fractions by fractions Decimals • Fluently divide multi- digit decimals Expressions, Equations & Inequalities • Same as “Addition” Column Addition Subtraction Multiplication Division pg 3 Seventh Grade Seventh Grade Seventh Grade Seventh Grade Add rational numbers Add and expand linear expressions with rational coefficients Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units Use proportional relationships to solve ratio and percent problems Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals) Subtract rational numbers Subtract and expand linear expressions with rational coefficients Multiply rational numbers Factor and expand linear expressions with rational coefficients • Divide rational numbers • Convert a rational number to a decimal using long division