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Common Core Learning StandardsGRADE 5 Mathematics

NUMBER & OPERATIONS IN BASE TEN

Common Core Learning Standards Concepts Embedded Skills Vocabulary

Understand the place value system. place value Define a number in one place as 1/10 of its value in the place to its left.

place value names

base ten value (of digit) decimal digit5.NBT.1.

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Define a number in one place as 10 times its value in the place to its right.

SAMPLE TASKSI. What number is ten times greater than 128? __________________________

Explain how you know.

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II. What number is one-tenth as much as 83? ____________________________Explain how you know.

_______________________________________________________________________________________________________

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Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

III. Billy said that the number 0.05 has a value 10 times greater than 0.005. A. Is he correct? Explain your answer.

_________________________________________________________________________________________________________

_________________________________________________________________________________________________________

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B. What number is ten times greater than 0.5? ___________________________________________________________________

Explain your answer._________________________________________________________________________________________________________

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Understand the place value system. powers of 10 Explain the pattern in the number of zeros in a product when multiplying by powers of 10.

powers of ten exponents product place value

names base decimal digit scientific

notation

Explain the pattern in moving the decimal point when multiplying or dividing by powers of 10.

5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 1.

Write whole number exponents to denote powers of 10.

SAMPLE TASKSI. Lynn was asked to multiply 7 x 600. Explain how you would help her solve it mentally.

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II. A marker costs $0.15. How much will 10 markers cost? _________________________________________

How much will 100 markers cost? ________________________________________

How much will 1,000 markers cost? _______________________________________

Explain the pattern you notice with your answers above.

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III. Mrs. Russo wrote two expressions on the board.

4.325 x 103 4.325 ÷ 102


A. Find the value of the expression 4.325 x 103. Explain how you found your answer.

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B. Find the value of the expression 4.325 ÷ 102. Explain how you found your answer.

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Understand the place value system. decimals to the

thousandths

Read and write decimals to the thousandths using base 10 numerals.

base-ten numerals

number names

expanded form/notation

expanded form with multiplication

place value names

standard form/notation

word form/notation

decimal digit

Read and write decimals to the thousandths using number names.

5.NBT.3a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

Read and write decimals to the thousandths using expanded form (with fractions of 1/10, 1/100, and 1/1000 to denote decimal places).

SAMPLE TASKSI. Write the following number in expanded form using multiplication so that every value uses one

factor from the factor bank.

637.415

______________________________________________________________________________________________


Factor Bank

1,000 110

100 1100

101

1,000

1

II.

Use the place value chart above to write the number in the following ways:

A. base-ten numeral: _____________________________________________________________________________________________

B. number name: ________________________________________________________________________________________________

____________________________________________________________________________________________________________

C. expanded form with multiplication: _______________________________________________________________________________

____________________________________________________________________________________________________________

III. Write the number four hundred seventy-six and three hundred ninety- five thousandths in expanded form with multiplication.

____________________________________________________________________________________________________________


Hundreds Tens Ones . Tenths Hundredths Thousandths4 6 8 . 7 2 1


Understand the place value system. Comparing decimals

Compare two decimals to the thousandths using greater than, less than, and equal to symbols.

greater than less than equal to place value

names decimal digit

5.NBT.3b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

SAMPLE TASKSI. Jackson and Nate ran a 200-meter race. Their times, in seconds, are listed below.

Jackson: 34.067 Nate: 34.56

Which runner had the fastest time? Explain your answer.

_______________________________________________________________________________________________________

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II. Circle all of the decimals below that make the following number sentence true: 17.2 > ___________.

17.025 17.212 17.18 17.009 17.25Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

Choose ONE of the decimals you circled above, and explain how you know that it makes the number sentence true.

____________________________________________________________________________________________________

III. Mrs. Jones wrote these two decimals on the board:

III.46 3.460

Mary claims that 3.460 is greater than 3.46. Sally says they are worth the same. Who is correct? Explain how you know.

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Understand the place value system. Rounding decimals

Round decimals to any place (up to thousandths). Round estimation place value

names decimal digit

Justify the reasonableness of a solution using estimation.

5.NBT.4. Use place value understanding to round decimals to any place.

SAMPLE TASKSI. Martin rounded a number to the nearest tenth and got 4.0. What is a possible number that she rounded? Explain your answer.

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II. Cara’s dog weighs 7.25 pounds. Her cat weighs 6.75 pounds.

A. Round the weight of each pet to the nearest whole pound.

_______________________________________________________________________________________________________

_______________________________________________________________________________________________________

B. What do you notice about the rounded weights? Explain your answer.Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

_______________________________________________________________________________________________________

_______________________________________________________________________________________________________

III. Round 9.847 to the place value named.

A. tenths B. hundredths C. ones

_________________ _________________ _________________



Perform operations with multi-digit whole numbers and with decimals to hundredths.

Multiplying multi-digit

whole numbers

Multiply multi-digit whole numbers using the standard algorithm.

factors product multi-digit algorithm digit decimal fluency

(Maintenance of fluency with basic math facts).

5.NBT.5. Fluently multiply multi-digit whole numbers using the standard algorithm.

SAMPLE TASKSI. A restaurant has seating for 365 people. The restaurant offers a $27 buffet. If the restaurant is full and everyone orders the

buffet, how much money will the restaurant earn? Give an estimate and an exact answer. Show all your work.

Estimate: _________________________________

Exact answer: ______________________________

II. There are 658 seats in each of the 48 sections of an arena. How many seats are there in all? Give an estimate and an exact answer.


Estimate: _________________________________

Exact answer: ______________________________



Dividing whole

numbers (4-digit

dividends and 2-digit

divisors)

Divide whole numbers with up to 4-digit dividends and 2-digit divisors.

divisor dividend quotient equation rectangular

array area model digit decimal

Illustrate and explain quotient (solution) through equations, rectangular arrays, and/or area models.

5.NBT.6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

SAMPLE TASKSI. A farmer has 2,664 pounds of oats. If he divides the oats equally among 32 bags, how many pounds of oats will be in each bag?

Show all your work.

_____________________________

II. Kali has 288 inches of ribbon. She wants to cut the ribbon into 25-inch pieces.

A. Write an equation that shows how many 25-inch pieces of ribbon Kali will have and how much will be left over. Show your Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

work.

B. Write a mixed number that represents the ribbon after Kali cuts it. Explain what each part of the mixed number represents. _______________________________________________________________________________________________________

_______________________________________________________________________________________________________

_______________________________________________________________________________________________________

III. A florist had 215 flowers. He used 12 flowers to make each bouquet and had some flowers left over. Show all your work.

A. How many full bouquets did the florist make? _______________________________________________________________

B. How many flowers were left over? ________________________________________________________________________

C. Write an equation that proves your answer is correct. _________________________________________________________




operations with decimals

Add decimals (to hundredths place). operation names

sum hundredths place value

names minuend subtrahend addend difference dividend divisor quotient decimal digit factor product

Subtract decimals (to hundredths place).

5.NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Multiply decimals (to hundredths place).

Divide decimals (whole number divisors and dividends to hundredths place).Explain method used to solve problems in all four operations.

SAMPLE TASKSI. Carrie earned $43.85 doing her paper route. She spent $7.50 at the movie theater and $16.42 at the mall. How much money does

Carrie have left? Show all your work.


II. A sculptor bought 15 blocks of wood for a total of $139.50. The three large blocks cost a total of $25.50. The remaining small blocks each cost the same amount. How much did each small block cost? Explain your answer.

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III. A. Quinn bought 3.4 pounds of bananas. He paid $0.65 per pound. How much money did Quinn spend in all?

____________________________________________________

B. If Quinn pays with a $5 bill, how much change will he receive?

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