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Number & Operations (Models of Multiplication and Division and number properties) Page 11 Computation & Estimation (CE)/Number Operations 3.2 NUMBERS AND OPERATIONS, ALGEBRA, AND DATA ANALYSIS: Most problems on the CBEST for multiplication and division center around story problems, number lines and sets. 3.2.1Represent and apply the concept of multiplication as repeated addition. 3.2.2Represent and apply the concept of division as repeated subtraction and forming equal groups. 3.2.3 Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal "Jumps" on number lines and hundreds charts ) and division (e.g., repeated subtraction, partitioning and sharing ) to solve problems. 3.2.4Apply increasingly sophisticated strategies based on the number properties ((e.g., place value, commutative, associative, distributive, identity, and zero) to solve multiplication and division problems involving basic facts. 3.2.6 Represent, analyze and extend number patterns using rules that involve multiplication and/or addition ((e.g., 3.2.7 Analyze frequency tables, bar graphs, picture graphs and line plots; and use them to solve problems involving addition, subtraction, multiplication and division. Grade 3 MATH: Oregon Department of Education Standards for Practice or Progress Monitoring. OAKS testing format These problems are presented in an OAKS testing format. A passing grade is 80% This booklet will focus on the items in This booklet will focus on ONLY the items in Bold Black [3.2.3] below table. In 2011-2012 these standards will be added to the OAKS assessments. 3.2.5 Apply the inverse relationship between multiplication and division (e.g.,and the relationship between multiples and factors Book #6 This booklet will focus on ONLY the items in Bold Black [3.2.3] Teachers: To assure that the above standards are understood, always remind, ask and show your students: 3.2.3 1.Multiplication is repeated addition, division is repeated subtraction. 2.Practice representing multiplication with manipulatives in arrays, hundred charts, & groups and number lines. 3.Always ask: What strategies can you use to solve a multiplication or division problem? 4.Extend and know number patterns ( skip counting). Teacher Information... Teacher Information... This booklet does not cover the core standards that will be tested in 2011- 2012. 3.2.3Apply models of multiplication (e.g., equal-sized groups, arrays, area models, equal "Jumps" on number lines and hundreds charts ) and division (e.g., repeated subtraction, partitioning and sharing ) to solve problems. The test samples and strand data for this booklet can be found on the Oregon State Departments of Education web site. The use of this booklet was designed for the Hillsboro School District based on HSD Power Standards along with the ODE strand categories. This booklet is paid for and furnished to teachers for instruction by the HSD. The concept of this booklet was created by Rick & Susan Richmond © Rick & Susan Richmond 2010 Revision: Original 03-2010 No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, without written permission from Rick & Susan Richmond and the Oregon State Department of Education and the Hillsboro School District.
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Page 1 Page 10 Rick & Susan Richmond based on ODE Standard 3.2.3 1.What is the perimeter of this rectangle? A.4 B.12 C.2 D.10 22 4 4 Do your work here: Rick & Susan Richmond based on ODE Standard 3.2.3 10.What is the best strategy for solving the perimeter? Each small box represents 1”. A.3 x 3 B.3 + 4 +3 +4 C.4 x 3 D.3 + 3 + 3 + 3 Do your work here:
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Page 9 Page 2 Do your work here: Rick & Susan Richmond based on ODE Standard 3.2.3 9.What number sentence could you write to go with this array? A.2 + 2 + 2 + 2 + 2 + 2 B.2 x 2 C.7 ÷ 7 D.7 x 2 2.Look at the number line. What is the best expression for the number line? A.2 x 6 B.2 x 2 C.2 x 5 D.2 x 4
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Page 8Page 3 Do your work here: Items of Difficulty from ODE (Standard 3.2.3) 3.Rachel played in 8 soccer games. She scored 4 goals in each game. Which number phrase shows the total she scored? A.4 + 4 + 4 + 4 B.8 x 4 C.8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 D.8 + 4 8.Jared is reading a book in 7 days. If he keeps the same pattern, how many pages are in the book? A.90 B.110 C.130 D.150 Items of Difficulty from ODE (Standard 3.2.3) DAYS 1234567 PAGES READ 103050
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Page 4 Page 7 Do your work here: Sample Practice Test from ODE (Standard 3.2.3) 4.The perimeter of a rectangle is 150. Which choice shows the possible numbers used for the sides? A.25 + 50 + 25 + 50 B.60 + 60 + 30 C.20 + 55 + 25 + 50 D.40 + 50 + 40 + 50 Group 1 Group 2 Group 3 Group 4 7.Look at the table showing people below. What is the best strategy for solving the total number of people? A.4 x 4 B.8 x 3 + 3 C.8 x 4 – 3 D.8 x 4 Rick & Susan Richmond based on ODE Standard 3.2.3
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Page 6Page 5 Do your work here: Rick & Susan Richmond based on ODE Standard 3.2.3 Sample Practice Test from ODE (Standard 3.2.3) 5.Which number on the number line is missing? A.22 B.21 C.17 D.16 6.Round the number 48 to the nearest ten. A.49 B.47 C.50 D.52
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