The document outlines goals for a 5th grade math unit, including writing and solving open sentences, rounding numbers, estimating products, and finding actual products of multi-digit numbers and decimals. It provides examples and instructions for each goal such as how to set up and solve word problems using open sentences, the process for rounding numbers to certain places, how to make magnitude estimates before calculating products, and methods for multiplying multi-digit numbers and decimals while keeping place value aligned.

1. Unit 2 5 th Grade

2. Unit Goals Write and solve open sentences for number stories Round numbers to designated places Make magnitude estimates Find the product of multi-digit whole numbers and decimals Identify the maximum, minimum, median, mode, and mean for a data set (see data landmarks power point for more information)

3. Write and solve open sentences for number stories An open sentence is a number sentence or equation that contains a variable I had three fish and bought some more at the pet store. After two died, I had eight fish left. How many fish did I buy? f = fish bought 3 + f – 2 = 8 1 + f = 8 f = 7 Define your variable (the quantity you don’t know) Describe what took place using math operations Combine like terms Solve for the variable

4. Write and solve open sentences for number stories It often helps to look for key words to help you decide what operations to use. Try one! per a out of ratio of quotient of percent ÷ Is Are Was Were will be gives yields sold for of times multiplied by product of increased/decreased by a factor of decreased by minus less difference between/of less than fewer than increased by more than combined together total of sum added to = X - +

5. Which open sentence describes the following number story? Lucas was comparing prices on a pair of mini-speakers. At one store, the pair of speakers cost $19.95. At a second store, the same speakers cost $24.70. At a third store, they cost $18.50. If he buys the speakers at the lowest price, how much will he save over the highest price? $24.70 + $19.95 = s S= savings $24.70 x $19.95 = s S= savings $24.70 - $19.95 = s S= savings $24.70 ÷ $19.95 = s S= savings

6. Correct! The correct open sentence is $24.70 - $19.95 = s because the phrase “save over the highest price” is asking you to find the DIFFERENCE (subtraction) between the highest and lowest prices. Lucas was comparing prices on a pair of mini-speakers. At one store, the pair of speakers cost $19.95. At a second store, the same speakers cost $24.70. At a third store, they cost $18.50. If he buys the speakers at the lowest price, how much will he save over the highest price ? Click here to return to the goals page

7. Keep Trying! The correct open sentence is $24.70 - $19.95 = s because the phrase “save over the highest price” is asking you to find the DIFFERENCE (subtraction) between the highest and lowest prices. Lucas was comparing prices on a pair of mini-speakers. At one store, the pair of speakers cost $19.95. At a second store, the same speakers cost $24.70. At a third store, they cost $18.50. If he buys the speakers at the lowest price, how much will he save over the highest price ? Click here to return to the goals page

8. Round numbers to designated places Remember place value! Underline the value to which you are rounding Circle the digit to its right- this is the number you will need to look at If the circled digit is 5 or more, change the underlined digit to the next highest number and make the rest of the digits to the right into zeros If the circled digit is 4 or less, leave the underlined digit alone and make the rest of the digits to the right into zeros

9. Round numbers to designated places Round 1,342,365.1427 to the nearest thousand. Underline the thousands place. Circle the hundreds place. The hundreds place is less than 5 Leave the 2 alone and change 3 and everything to the right of it into zeros You are being asked to tell whether 1,342,365.1427 is closer to 1,342,000 or 1,343,000. 1,342,000.0000 Try one on your own!

10. Round numbers to designated places Round 234,567,890.0987 to the nearest million. 200,000,000 235,000,000 234,000,000 230,000,000

11. Correct! The correct answer is 235,000,000. Click here to return to the goals page Round 234,567,890.0987 to the nearest million. Millions Is 234,567,890.0987 closer to 234 million or 235 million? 23 4 ,567,890.0987 235,000,000 5 or more, round up!

12. Keep Trying! The correct answer is 235,000,000. Click here to return to the goals page Round 234,567,890.0987 to the nearest million. Millions Is 234,567,890.0987 closer to 234 million or 235 million? 23 4 ,567,890.0987 235,000,000 5 or more, round up!

13. Make magnitude estimates A magnitude estimate is a ballpark estimate of what your answer should be. It’s very helpful to use magnitude estimates to determine if your answer is reasonable. Round the factors to the nearest multiple of 10 38 is close to 40 42 is close to 40 2. Find the product of the two rounded factors 40 x 40 = 1600 3. The answer should be in the 1000s 38 x 42 =1596 38 x 42 =

14. Make a magnitude estimate for 339 x 38= s. Make magnitude estimates 300 x 40 = 12,000 The answer should be in the 10,000s 400 x 40 = 16,000 The answer should be in the 10,000s. 300 x 40 = 1,200 The answer should be in the 1,000s 400 x 40 = 1,600 The answer should be in the 1,000s

15. Correct! The correct answer is 300 x 40 = 12,000… The answer should be in the 10,000s. Click here to return to the goals page 339 x 38 = 3 3 9 X 3 8 ________ 2 7 1 2 1 0 1 7 0 ________ 1 2, 8 8 2

16. Keep Trying! The correct answer is 300 x 40 = 12,000… The answer should be in the 10,000s. Click here to return to the goals page 339 x 38 = 3 3 9 X 3 8 ________ 2 7 1 2 1 0 1 7 0 ________ 1 2, 8 8 2 Be sure to round to the nearest multiple of 10- the number’s highest place value! 339 is closest to 300 38 is closest to 40 300 x 40 = 12,000

17. Find the product of multi-digit whole numbers and decimals When multiplying multi-digit numbers, remember to keep place value lined up! . 5 3 4 . 0 x 2 . 3 0 2 2 5 1 Multiply 5340 x 3 0 0 8 6 0 1 Multiply 5340 x 20 0 2 0 2 2 1 Add the products Multiply by .01 Divide each number by .1

18. Find the product of multi-digit whole numbers and decimals You can also multiply this way: 5 3 4 x 2 3 0 1 Multiply 20 x 500 0 0 6 Multiply 20 x 30 2 8 2 2 1 Add the products 0 0 0 0 8 5 1 0 0 9 0 1 2 Multiply 20 x 4 Multiply 3 x 500 Multiply 3 x 30 Multiply 3 x 4

19. Find the product of multi-digit whole numbers and decimals A third way to multiply is: 5 3 4 x 2 3 0 1 Multiply 20 x 500 0 0 6 Multiply 20 x 30 2 8 2 2 1 Add the products 0 0 0 0 8 5 1 0 0 9 0 1 2 Multiply 20 x 4 Multiply 3 x 500 Multiply 3 x 30 Multiply 3 x 4

20. The Lattice Method Click here for a demonstration of the lattice method of multiplication. Another demonstration page

21. Find the product of multi-digit whole numbers and decimals Use a method of multiplication to solve the following open number sentence: 43.25 x 36 = N N = 15570 N = 125.7 N = 1557 N = 1257

22. Correct! The correct answer is 43.25 x 36 = 1557. Click here to return to the goals page 43.25 x 36 = 4 3 . 2 5 X 3 6 . 0 0 ___________ 2 5 9 5 0 0 0 1 2 9 7 5 0 0 0 ___________ 1 5 5 7. 0 0 0 0

23. Keep Trying! The correct answer is 43.25 x 36 = 1557. Click here to return to the goals page 43.25 x 36 = 4 3 . 2 5 X 3 6 . 0 0 ___________ 2 5 9 5 0 0 0 1 2 9 7 5 0 0 0 ___________ 1 5 5 7. 0 0 0 0