MATH NUMBER SENSE 3 Performance Objective Task Analysis Benchmarks/Assessment Students: 1. Students understand place value of whole numbers.

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1 Students: 1. Students understand place value of whole numbers. 1. Count, read, and write whole numbers to 10,000. Count to 10,000 Which numbers are whole numbers? Whole number 0, 15.3, 4/5, 8, 25 1/2 Count up Count up 4 from 1,398. Count down Juan counted down 5 from 3,872. What was his new number? Number line Show the missing number on the number line. 1,591 1,593 Use the number line to show in which direction the numbers get larger. Smaller. Sequence Which number comes before 9, 000? Which number comes after 5,438? 1

2 Patterns Find the missing numbers. 9,991 9,992, 9,995 1,002 1,001 1, ,523 1,623 1,723 1,923 Extend the pattern. 8,231 8, 233 8,235 8,237, Odd / Even Read and write numbers to 10,000 Read zeros Will the next number be odd or even? Read the numbers 4,006 4,060 4,600. How are they alike? How are they different? Read the comma What does the comma in 8,674 represent? Standard notation Write a number for nine thousand five hundred sixty-four in standard notation. Write 9,503 in words as you would read the number aloud. Write 8,002. 2

3 Write a number between 5,898 and 5,998. Is there more than one number? Explain. Write a number that comes before 9,983. How many numbers could you write? Explain. 2. Compare and order whole numbers to 10,000. Write a number 100 more than 800. Write a number 200 less than 700. Compare More than / Less than Number line Magnitude Samuel scored 8,370 points on a video game. Josh scored 8,39l. Who had the most points? Use a number line to compare 5,200 to 5,198. 5,197 5,198 5,199 5,200 Which number is larger? How do you know? Which number represents the most? the fewest? 784, 794, or 790 After 9 innings, Bob s team had 12 runs and Leon s team had six runs. Whose team had more runs? 3

4 Use estimation to compare how many m&m s it takes to fill a can of soda as compared to how many it would take to fill a 2 liter bottle of soda. Relation Symbols Match the symbols with their definition. > equal sign = less than < greater than Write T or F > < = > 4115 Fill in the blank with >,< or = Order Numbers List numbers from greatest to least. 9,784 7,854 9,684 9,900 Use a number line to list the numbers from least to greatest. 4, , Which number is closest to 5,650? 5,540 or 6,000 or 5,600 4

5 *3. Identify the place value for each digit in numbers to 10,000. Name position Fill in the blanks to show place value for the number 9,325. 9, Tens Ones List the ones, tens, hundreds, and thousands place for 9,724. ones tens hundreds thousands What number is in the hundreds place? 1,296 Zero as place holder Value of each digit What does the 0 in 6,032 mean? How are 2,130 and 1,032 alike and different? How are these numbers different? 1, 10, 100, 1,000 and 10,000 In the number 1,234, which digit has the greatest value? The least value? 5

6 In the number 679 how many thousands are there? Hundreds? Patterns What place value is changing in these numbers? 5,677 6,677 7,677 8,677 What is the smallest whole number you can make using the digits 4, 3, 9, and 1? Use each digit exactly once ( FW). 4. Round off numbers to 10,000 to the nearest ten, hundred and thousand. About how many Number line Round 1,898 to tell about how many people attended the concert. Explain how to use the number line to round 568 to the nearest hundred Place Value Round to the indicated place value. 67 to the nearest ten 678 to the nearest ten 678 to the nearest hundred 1,572 to the nearest thousand 1,347 to the nearest hundred 6

7 Round 7,495 to the nearest ten, hundred, and thousand. Round 3,258 to the nearest ten, hundred and thousand. *5. Use expanded notation to represent numbers. Standard notation Component parts Write the following numbers in standard notation. 6 hundreds and 4 tens 5 hundreds + 6 tens + 1 one 8, , Write 6,583 in expanded form. Here is a number sentence: 2, = What number should go is the blank to make the sentence true? ( FW) 7

8 Students: 2.0 Students calculate and solve problems involving addition, subtraction, multiplication and division. *1. Find the sum or difference of two whole numbers between 0 and 10,000. Add without regrouping Line up place value Find the sum of the following: , , ,231 1, Cheryl got 1,032 students to sign a petition. Libby got 937 students to sign. All together, how many students did they get to sign the petition? Subtract without regrouping Find the difference of the following: ,748-8,215 5, , Shonda had $3,375 saved for college. She used $1,250 to buy a computer. How much money does she have left? Add with regrouping in one or more columns Find the sum of the following: , ,133 4, ,735 5, ,434 5, , ( FW) 1, ,074 ( FW) 8

9 Subtract with regrouping in one or more columns Subtract with regrouping that includes zeroes Find the difference of the following: ,376-1,283 5,384-4,972 8,325-7,436 3,215-2,876 ( FW) ( FW) ( FW) Add columns of numbers Combine operations Recognize the relationship between addition and subtraction What number sentence is missing? = 16, = 16, 16-9 = 7 Use addition to check the answer to the subtraction problem. 3, Compare Use >, <, or = *2. Memorize to automaticiy the multiplication table for numbers between 1 and 10. 9

10 Repeated Addition How are and 5 x 6 related? There are 3 circles with 4 stars inside each circle. How many stars are there altogether? Multiples How does skip counting relate to multiplication? Fill in the blanks. 3 = 3 x 1 6 = 3 x 2 9 = 3 x 3 12 = 15 = = 3 x 6 Arrays How do arrays show multiplication? There are 3 rows and 5 columns of square tiles. How many square tiles are there altogether? Commutative property Why is 5 x 6 the same as 6 x 5? Fill in the blank. 3 x 4 = 4 x Use multiplication vocabulary (twice, three times, product, factor) How do you find twice the number 12? Three times? 10

11 Identify the factors and product for 3 x 5 = 15 *3. Use the inverse relationship of multiplication and division to compute and check results. Solve for the missing factor. 7 x = 56 and 56 7 = x 9 = 36 and 36 9 = How are these multiplication and division facts related? 20 5 and 5 x 4 Martin wants to buy 18 tennis balls. They come in cans of 3. How many cans should he buy? (3 x = 18) How can you check your answer to know it is correct? Use arrays of rectangles to show relationship of multiplication and division x 5 = 10 squares 11

12 Use arrays to learn division facts with dividends between 0 and 100 Given 15 squares and a side of 3, find the length of the other side.? 3 15 squares Check the division problem by using multiplication 15 5 = 3. Check answers Check the multiplication problem by using division. 6 x 3 = 18. *4. Solve simple problems involving multiplication of multi-digit numbers by one-digit numbers (3,671 x 3) True or false? 24 x 0 = = x 1 = 63 ( FW) Use base ten blocks (or pictures) to show 166 x 2. Array Draw an array for 2 x 100. Repeated addition Partial products Use repeated addition to solve 137 x 3. Mike solved the following multiplication problem. Fill in the blanks to explain what he did. 12

13 555 x 7 35 Multiplied ones 350 Multiplied 3500 Multiplied 3885 Solve without partial products 555 Mary used a short x 7 cut way to solve the 3885 problem. What did she do? Find the product. 721 x 6 2,073 x x 3 3,005 x 2 True or false? 3,105 x 3 = 9, ( FW) A price list in a store shows: pen sets, $3; magnets, $4, sticker sets, $6. How much would it cost to buy 5 pen sets, 7 magnets, and 8 sticker sets? ( FW) 5. Solve division problems in which a multi-digit number is evenly divided by a one-digit number. Equal Sharing $135 was put into 5 piles. How much money was in each pile? 13

14 Array Use the multiplication table to find the answer to this division problem Find the quotient What is the difference between the following two problems? There are 12 children and four cars. How many children can travel in each car? There are a total of 12 children. Four children can ride in a car. How many cars do you need for the 12 children? Recognize a remainder A class of 73 students go on a field trip. The school hires vans each of which can seat a maximum of 10 students. The school policy is to put as many students as possible into a van before using the next van. How many vans are needed? ( FW) 6. Understand the special properties of 0 and 1 in multiplication and division. Use the pattern to write a rule for multiplying any number by 0. 1 x 0 = 0 2 x 0 = 0 3 x 0 =0 99 x 0 =0 14

15 Use the pattern to write a rule for multiplying and dividing any number by 1. 4 x 1 = = 6 8 x 1 = = 9 28 x 1 = = x 1= = 689 Use the inverse operation of multiplication and division to show it is impossible to divide by 0. (12 4 = 3 because 3 x 4 = is impossible because there is not a number times 0 that equals 12) 7. Determine unit cost when given the total cost and number of units Find total cost Find unit cost 8. Solve problems which combine two or more of the skills above 15 If one giant bag of potato chips cost $2.00, how much would 8 bags cost? Jeff paid $125 for 5 soccer balls. How much did 1 soccer ball cost? There are 54 marbles, and they are put into 6 bags, so that the same number of marbles are in each bag. How many marbles would 2 bags contain? ( FW) A tree was planted 54 years before How old is the tree in 1998? ( FW)

16 3.0 Students understand the relationship between whole numbers, simple fractions and decimals. Students: 1. Compare fractions represented by drawings or concrete materials to show equivalency. Show equivalency How are these circles alike? different? What part is shaded? How are these circles alike? different? What part is shaded? Are they equivalent? Use pictures or manipulatives to compare fractions Robert ate 1/4 of a pizza. Shane ate 1/3. Who ate the most? Which is more? 1/3 of a glass of milk or 1/8 a glass. Draw a picture. Which is less? 1/4 of a candy bar or 1/5 of the same candy bar. 16

17 Which is more? 1/8 or 3/8 Which is larger? How do you know? 2/3 or 1/3 2/5 or 4/5 Compare fractions with like denominators using >, <, and =. Use >, <, or = to compare. 1/5 22/5 3/5 3/5 3/4 1/4 Leonard walks 5/8 of a mile to school. Sam walks 7/8 of a mile. Who walks the greater distance? Order fractions with like denominators using diagrams Order the fractions from greatest to least. 3/8, 5/8, 2/8, 8/8 Order unit fractions with denominators less than 6 Put these fractions in order from least to greatest. 1/3, 1/6, 1/5, 1/2, 1/4 *2. Add and subtract simple fractions and determine that 1/8 + 3/8 is the same as 1/2. John ate 1/4 a pizza and Mike ate 2/4 of the same pizza. How much did they eat all together? Draw a picture to show how much pizza is left. 17

18 Janis, Maija, and their mother were eating a cake. Janis ate 1/2 of the cake. Maija ate 1/4 of the cake. Their mother ate 1/4 of the cake. How much of the cake is left? ( FW) Draw a picture to show 1/8 + 3/8. What other fraction(s) shows the same amount? Add or subtract. 1/3 + 1/3 1/8 + 6/8 3/10 + 5/10 7/15-3/15 Add or subtract and find an equivalent fraction. 1/6 + 1/6 1/8 + 1/8 5/6-1/6 3/10-2/10 *3. Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation using whole number nultiliers and divisors. Recognize different ways to write cents Write 15 cents two other ways. 18

19 Compare decimals Use >, < and = to compare these decimals. $.50 $.40 $.37 $.73 $1.30 $1.70 $1.25 $1.32 $.10 $ $.25 Add and subtract using money in decimal notation Erik had 3 nickels, 4 pennies, 2 dimes, and 3 quarters. How much money did he have? Jorge bought a sandwich for $5.00 and a soda for $1.10. How much did he spend? Linda had $ She spent $13.80 How much money does she have left? Solve $.17 + $.13 $ $.25 +$.25 Jerry bought an ice-cream for 62 cents and paid for it with a $10 bill. How much change will he receive? ( FW) Multiply and divide money amounts in decimal notation using whole numbers for the multiplier and divisor. Josh earned $2.50 an hour. He worked 3 hours. How much did he earn? 19

20 Material costs $9.35 a yard. How much would 3 yards cost? Tootsie Rolls cost 3 cents each. How much would 25 Tootsie Rolls cost? How would you divide $ into 5 equal groups? 4. Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1/2 dollar, 75 cents is 3/4 of a dollar). How are 25 cents and $.25 related? Fill in the blanks..25 = 1 quarter = 1/4 a dollar.50 = = 2/4 or 1/2 a dollar = 3 quarters = 3/4 a dollar Use a 10 by 10 grid, with each square equal to 1 cent, to show that 25 cents or $.25 is the same as 1/4. Use the number line to show the relationship between fractions and decimals. (Fill in the blank) 0 1/4 1/2 1 (Fraction) (Decimal) 20

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