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1 Grade 4 Pacing Investigations 2009 Unit 1 - Factors, Multiples, and Arrays Unit 2 - Describing the Shape of Data S M T W T F S Unit 5 - Landmarks and Large Numbers Unit 6 - Fraction cards and Decimal Squares Sep-09 Unit 3 - Multiple Towers and Division Stories Unit 8 - How Many Packages? How Many Groups? Unit 4 - Size, Shape, and Symmetry Unit 9 - Penny Jars and Plant Growth Unit 7 - Moving Between Solids and Silhouettes/Geometry Packet Oct-09 Nov-09 Dec-09 S M T W T F S S M T W T F S S M T W T F S Jan-10 Feb-10 Mar-10 S M T W T F S S M T W T F S S M T W T F S Apr-10 May-10 Jun-10 S M T W T F S S M T W T F S S M T W T F S

2 PLEASE REFER TO EDC CALENDAR FOR ACTIVITIES AND DO THEM WHEN/IF POSSIBLE 9/2-9/25 Unit 1: Factors, Multiples, and Arrays See page 22 4.N.9,4.N.10, 4.P.1, 4.M.4 Students use arrays to represent multiplication situations. They use arrays to find factors and gain fluency with multiplication combinations up to 12 x 12. Continually emphasize area and perimeter. 4.P.2 can be taught in this Unit, as well as Units 3, 5, 6, and 8. Emphasize fraction elements, Investigation unit will not be until March. Daily Depositor can incorporate 4.P.2 (day=input, amount deposited = output.) 9/29-10/27 Unit 5: Landmarks and Large Numbers See page 54 See page 86 See page 58 OMIT 4.N.13, 4.N.13 4.N.1, 4.N.2, 4.N.7, 4.N.10, 4.N.12, 4.N.16, 4.N.17, 4.P.1, 4.P.3 4.N.1, 4.N.2, 4.N.7, 4.N.10, 4.N.12, 4.N.14, 4.N.16, 4.N.17 Students develop strategies for finding factors and multiples of 2- and 3-digit numbers. They continue to gain fluency with multiplication combinations up to 12 x 12 Students use what they know about the factors of 100 to find factors and multiples of 100. They explore the idea that factors of a number are also factors of a number that is a multiple of that number Students review place-value concepts to 1,000 by constructing 1,000 books. They add and subtract multiples of 10 and 100 and find the difference from a given number to 1,000. Students study the operation of addition as they solve addition problems accurately and efficiently. They study different types of addition strategies, including the U.S. algorithm. Reinforce the difference between factors and multiples. Continue practicing finding factors of smaller numbers as well. (ex. Factors of 24.) *Use rounding by place value as one strategy for estimation. *Model use of variables as one way to represent solving mileage problems. Emphasize fraction elements, Investigation unit will not be until March. Daily Depositor can incorporate 4.P.6 (n = number and d = day) Emphasize graph - Line graphs will not be explicitly taught until Unit 9 - after MCAS. 7/9/2009 1

3 Investigation 4 4.N.1, 4.N.2, Students practice solving subtraction Also cover addition and subtraction of See page N.7, 4.N.10, 4.N.12, 4.N.14, 4.N.16, 4.N.17, 4.P.3 problems accurately and efficiently. They consider different kinds of subtraction situations and solve addition and subtraction problems. large numbers with place value up to 100, /28-11/30 Unit 3: Multiple Towers and Division Stories See page 56 See page 94 Investigation 4 See page N.17 4.N.13, 4.N.17 4.N.13, 4.N.17 4.N.13, 4.N.17 Students solve multiplication problems Multiply by decomposing numbers, with small 2-digit numbers by breaking area/box model, and using clusters. the numbers apart and representing their solutions and arrays. Students solve and representing division problems in story contexts, including problems with remainders. Students solve and represent problems that involve multiples of 10. They examine the mathematical relationship that underlies the pattern they see when a number is multiplied by 10. Students develop strategies for solving multiplication problems with larger 2- digit numbers by breaking the problems apart in order to use the number relationships that they know. Introduce Partial Quotient Method for division. Daily Depositor can incorporate 4.N.1 by writing daily total in expanded notation and in word form. 12/1-12/22 Unit 4: Size, Shape, and Symmetry See page 52 4.M.1, 4.M.2, 4.M.4, 4.M.5 4.G.1, 4.G.2, 4.G.4, 4.G.5, 4.G.8, 4.G.9, 4.M.1, 4.M.5 Students estimate and measure length in U.S. standard and metric units, including lengths up to 100 feet. They practice using measurement tools accurately and review perimeter. Students investigate the attributes of polygons. They focus particularly on quadrilaterals, categorizing them by side length, angle size, and parallel sides. 7/9/2009 2

4 OMIT Skip to Investigation 4 - Standard 4.G.4 requires students be able to identify as acute, right, or obtuse. This is done in Investigation 4 See page 110. *See Notes* 4.M.1, 4.M.4, 4.M.5, 4.G.7, 4.G.8, 4.G.9 Student measure the area of polygons in both non-square* and square units of measure, by decomposing shapes and using symmetry. They focus particularly on finding the area of a triangle in square units by relating it to the area of a rectangle. Session 1: Skip activity 3:Finding Area on Triangular Grid Paper Session 2:OMIT *Finding area should focus on Square Units at this point to prevent confusion. Session 3:Eliminate Logo Paths E15; Workshop will Only be Crazy Cakes Sessions 4-6: Discuss Congruence when finding area of triangle using rectangle (ex. p. 131) 1/4-1/22 Unit 7: Moving Between Solids and Silhouettes/ Geometry Packet *See Notes* 4.G.1, 4.G.2 Students describe the properties and attributes of geometric solids. {They identify the shapes of silhouettes projected by these solids and visualize what objects look like from different perspectives.} - Focus on 3-D vocabulary. This activity can be revisited as a center in. ***OMIT Sessions 2-4**** OMIT See page 74 4.M.1, 4.M.5 Students find the volume of rectangular prisms in cubic units by constructing boxes to hold arrays of cubes and drawing patterns for those boxes. Not in frameworks 7/9/2009 3

5 Geometry Packet Geometry 1/25-2/26 Unit 2: Describing the Shape of Data 3/1-4/1 Unit 6: Fraction Cards and Decimal Squares See page 52 See page 92 See page 64 4.G.1, 4.G.2, 4.G.3, 4.G.4, 4.G.5, 4.G.6, 4.G.7, 4.G.8, 4.G.9, 4.M.1, 4.D.1, 4.D.3, 4.M.5, 4.M.2 4.D.1, 4.D.2, 4.D.3, 4.M.5 4.D.1, 4.D.4, 4.D.6 4.N.3, 4.N.4, 4.N.5, 4.M.1, 4.M.4 4.N.3, 4.N.4, 4.N.5, 4.N.18, 4.M.1, 4.M.4 Students record, organize, and represent data, including measuring the heights of fourth graders. They learn to use the median as one way to describe and compare data sets. Students use their own survey questions for data collection. They represent and analyze the data. They also draw conclusions based on evidence in different sets of data. Students learn to describe probability using words such as impossible and certain, and the number 0 to 1. They conduct probability experiments and describe and compare results. Students find fractional parts of the area of different-sized rectangles and of groups of objects or people. They compare fractions and find combinations of fractions that are equal to 1. Using representations and mathematical reasoning, students add fractions with like and unlike denominators. Students make fraction cards that show area representations for fractions and mixed numbers. They compare fractions to the landmarks 0, 1/2, 1, and 2, and place fractions and mixed numbers on a number line. Students make conjectures about general rules for comparing fractions. Choose some of activities supplied in geometry packet (can be found on P Drive) to support areas needed. ***4.G.3 and 4.G.6 are not taught in Investigations*** 4.D.5 can be taught during this unit. It is not in Investigations. Frameworks only call for adding and subtracting fractions with like denominators. Make sure to use clock element of March calendar - 4.M.3 is not addressed in Investigations. April calendar contains Fraction a Day that will reinforce the skills in this unit. 7/9/2009 4

6 4.N.3, 4.N.4, Students represent and compare See page N.5, 4.N.6, 4.N.18 decimals using 10 x 10 decimal squares. They use representations to combine decimals that include tenths and hundredths. Using a context of running or walking, students add distances in miles and in tenths and hundredths of miles. 4/5-5/7 Unit 8: How Many Packages? How Many Groups? See page 60 See page 86 4.N.17 4.N.10, 4.N.11, 4.N.12, 4.N.17 4.N.1, 4.N.2, 4.N.10, 4.N.11, 4.N.12, 4.N.13, 4.N.14, 4.N.15, 4.N.17 Students estimate products and practice for solving multiplication problems with 2-digit factors. Students practice strategies for solving 2-digit by 2-digit multiplication problems including breaking one or both factors apart or solving an easier problem and adjusting the answer. Students use representations and story contexts to develop strategies for solving division problems with 1-digit or 2-digit divisors. Continue using area model to help reinforce place value of each digit. Encourage students to make reasonable estimates before calculating. Reinforce area model and partial quotient methods. Introduce traditional algorithm for multiplication and division for those students who are ready. Make sure to use clock element of April calendar - 4.M.3 is not addressed in Investigations. 5/7-6/18 Unit 9: Penny Jars and Plant Growth See page 42 4.D.1, 4.D.3, 4.D.4 4.P.1, 4.P.4, 4.P.6, 4.D.1, 4.D.4, 4.D.3 Students examine graphs for temperature and speed. They determine values of the points on the graphs, identify changes in temperature or speed, and relate the changes that are represented on the graphs to the corresponding stories. Students work with situations of constant change to examine and make predictions about how values change. They use tables, graphs, arithmetic expressions, and symbolic notation to represent, describe, and compare situations of constant change. 7/9/2009 5

7 4.D.1, 4.D.3, Students make line graphs of plant See page D.4 growth, describe the change in growth that graphs represent, and match graphs with tables and stories. 7/9/2009 6