Multiplication and Division: Moving to Algorithms Guided Questions:

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1 Time Frame: 20 teaching days This unit examines how multiplication and division are related. There is emphasis on modeling problems as well as further developing the idea of the distributive property of multiplication. Additionally, skills that students tend to forget over the summer (as identified by fourth grade teachers) are included in this unit for review. 1. Can students relate multiplication to repeated addition? 2. Can students represent a multiplication problem? 3. Can students show mastery of basic multiplication facts? 4. Can students relate multiplication to skip counting? Guided Questions: 5. Can students find the missing product or factor in a multiplication number sentence? 6. Can students use calculators to solve addition, subtraction, and multiplication sentences? 7. Can students relate division to repeated subtraction? 8. Can students represent and solve a division problem? 9. Can students show mastery of basic division facts? 10. Can students relate multiplication and division? 11. Can students use calculators to solve addition, subtraction, multiplication, and division problems? 12. Can students apply their knowledge of fact families to solve real life problems? 13. Can students show mastery of multiplication and division facts with the use of algorithms? 14. Can students show mastery of basic multiplication and division facts from 0 through 12? 15. Can students recognize that the division algorithm is performed from left to right, while all others are performed from right to left?

2 Focus 8-1 Multiplying and Dividing: Moving to Algorithms (9 days) 5. Recognize and model multiplication as a rectangular array or as repeated addition (N4) (N7) Model a rectangular array Review skip counting by 2s, 5s, and 10s Develop concept of multiplication by having students create and recognize models and number sentences using rectangular arrays and repeated addition Harcourt: Chapter ; ; Linking Math:C1, C2, C3, C4, C5, C6, C Recognize and model division as separating quantities into equal subsets (fair shares) or as repeated subtraction (N4) (N7) Recognize, select, connect, and use operations, operational words, and symbols (i.e., +,, x, ) to solve real- life situations (N5) (N6) (N9 When given examples, recognize the model shows division as repeated subtraction or fair shares Model a given division problem as repeated subtraction or fair shares Use repeated subtraction and fair shares to solve division problems Identify basic operational words and symbols to solve real-life situations (choosing the correct operation based on a given word problem) Use and recognize basic operational words and symbols to solve story problems Review the terms operations, operational words, and symbols Harcourt: Chapter 13 and ; ; Harcourt: Chapter When given a story problem, select the correct operation or symbol to use to solve the problem 35

3 9. Know basic multiplication and division facts [0s, 1s, 2s, 5s, 9s, and turn-arounds (commutative facts), including multiplying by 10s] (N6) (N4) Identify the components of a multiplication problem (factor x factor = product) Identify the components of a division problem (dividend divisor = quotient) Absolutely know facts for 0s, 1s, 2s, 5s, and 9s, including turnarounds Harcourt: Chapters 8, 9, 13, ; ; ; ; ; ; Linking Math: C2, C3, C4, C5, C6, C9, C10 Focus 8-2: Place Value and Estimation (3 days) 1. Model, read, and write place value in word, standard, and expanded form for numbers through 9999 (N1) Recall basic facts 0, 1, 2, 5, 9, 10 (including turnarounds) without relying solely on tricks or memory aids Read and write in word (six hundred thirty-two), standard (632), and expanded form ( ) Interpret models made from place value blocks and other concrete or pictorial objects Associate place value words with how many digits in a number Review meaning of our base-10 number system (Our base-10 number system is based upon a simple pattern of tens, where each place is ten times the value of the place to its right. This is known as a ten-to-one place-value relationship.) Meaning of Numbers to 9999 Harcourt: Chapter 2 18, 19;22-29 Project LIFT: #1, #2, #21 Tell how the value of a digit changes because of its position/place in the number (Tell the value of 5 in 659 and 5,836) 2. Read, write, compare, and order whole numbers through 9999 using symbols (i.e., <, =, >, ) and models (N1) (N3) Model, compare, and order numbers through 9,999 Use <, >, =, to compare numbers Both signs can be used at this time Harcourt: Chapter 3 38, 39;42-47 Constructed Response: PA Unit 1 Task A pg.3 PA Unit 7 Task A pg

4 12. Round to the nearest 1000 and identify situations in which such rounding is appropriate (N7) (N9) Round to the nearest 1000 Review that estimation tells about how many or about how much Review rounding to the nearest ten and hundred before moving to the nearest 1000 Harcourt: Chapter Project LIFT: #3 Review rounding a 3 digit number to the nearest 10 Ensure that students understand fully the process of rounding before introducing them to rules FYI: The Process of Rounding: Use a number line or hundreds chart and locate a particular number. Have the students determine which 2 tens it falls between. Have students find which ten the number is closer to. Explain that this is why the number rounds to that particular ten. After the students show mastery, next repeat the same process to round to the nearest hundred and thousand Include rounding mentally. I have 382 jolly ranchers. About how many jolly ranchers do I have? Focus 8-3 Fractions to Tenths ( 2 days) 3. Use region and set models and symbols to represent, estimate, read, write, and show understanding of fractions through tenths (N1) (N2) Use concrete and pictorial models to represent sevenths, eighths, ninths, and tenths Use regions and sets/groups of objects to represent sevenths, eighths, ninths, and tenths Use words and symbols to read and write fractions through tenths (sevenths, eighths, ninths, tenths) Review that a fraction is used to name a part of one thing or a part of a collection of things Review that the bottom number in the fraction tells how many equal parts are in the whole or set Review that the top number in the fraction tells how many of those parts are being described Review the language of fractions fourths means 4 equal parts of a whole; 1/4 represents one of four equal parts when a candy bar is shared among 4 students Review the use of concrete and pictorial models, symbols, and fraction words to represent halves, thirds, fourths, fifths, and sixths Harcourt: Chapter

5 Focus 8-4 Addition and Subtraction 3-digit Numbers (2 days) 11. Add and subtract numbers of 3 digits or less (N8) (N7) Add numbers with 3 digits Add and subtract numbers requiring regrouping and no regrouping Review fact families to remind students that addition and subtraction are inverse operations; that is, one is related to the other For example, give one basic fact sentence for addition/subtraction have the students give the other three Review adding 1 and 2 digit numbers Harcourt: Chapters 1 and ;70-73 Project LIFT: #4, #5 13. Determine when and how to estimate, and when and how to use mental math, calculators, or paper/pencil strategies to solve addition and subtraction problems (N8) (N9) Estimate, use mental math strategies, or paper/pencil to add and subtract (students need to master these before working with calculators) Know when to estimate, use mental math strategies, or paper/pencil to add and subtract Know when an estimate or exact answer is needed Harcourt: Chapters 3 and ;74-79 Focus 8-5 Money (2 days) 10. Calculate the value of a combination of bills and coins and make change up to $5.00 (N6) (M1) (M5) Make change up to $5.00 Review identifying the value of U.S. coins (penny, nickel, dime, quarter, half-dollar) and bills ($1 and $5) Review skip counting by 5s and 10s, and 25s Harcourt: Chapter ; Project LIFT: #7, #20 Linking Math: B1, B3 Review making change from $1.00 Ensure students are fully capable of making change from $1.00 before moving on to $5.00 Review equivalent relationships between coins and bills, such as four quarters equal one dollar 38

6 Focus 8-6 Time and Elapsed Time ( 2days) 24. Find elapsed time involving hours and minutes, without regrouping, and tell time to the nearest minute (M1) (M5) Find elapsed time involving hours and minutes Review telling time to the nearest hour, half hour, and quarter hour on a standard and digital clock and watch Review whether a given time is a.m. or p.m. 39