HOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE

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number that is divided by another number.

1 MCC6.NS. Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE Dividend A number that is divided by another number. Divisor A number by which another number is to be divided. Quotient A number that is the result of division. HOW TO DIVIDE: 1

Thousandths Hundredths Tenths Ones Tens Hundreds

REMAINDER INTO A DECIMAL: Step 1: add a decimal and a

Step : Divide Multiply Subtract Check Bring Down Step :

stop and round to the nearest hundredth.

place value 1,000,000 100,000 10,000 1,000 100 10 1 1

and Underline the place value you are rounding to.

If the number to the right is FIVE or MORE, increase

2 Thousandths Hundredths Tenths Ones Tens Hundreds Thousands Ten Thousands Hundred Thousands Millions MAKE REMAINDER INTO A DECIMAL: Step 1: add a decimal and a zero to the dividend. Step : Divide Multiply Subtract Check Bring Down Step : If you still have a remainder, continue to add a zero and bring down. Step 4: Go out three numbers past the decimal, then stop and round to the nearest hundredth. Sometimes it helps to think of money when dealing with place value 1,000, ,000 10,000 1, ,000 Dime Penny Mill token STEP ONE: Find and Underline the place value you are rounding to. STEP TWO: Look at the number to the right. If the number to the right is FIVE or MORE, increase the underlined number by 1 and turn everything to the right into zeroes. If the number to the right is FOUR or LESS, leave the underlined number the same and turn everything to the right into zeroes. Round 1.89 to the nearest whole number The eight is five or more so round the 1 up to 1.

MCC6.NS. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Use the grid to find the quotient..1 1.04= The model below represents.

3 MCC6.NS. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Use the grid to find the quotient = The model below represents. Separate the model into groups of How many groups do you have? = When dividing by a decimal, change the divisor to a by moving the decimal (or by multiplying by a power of ten). Move the decimal in the dividend the same number of places (or multiply by the same power of ten) ) to see what the answer should be close to. (1.04 rounds to 1 and.1 rounds to ) ) Move the. Move the decimal to make the divisor a whole number (or multiply by a power of 10) Move the decimal the same number of spaces in the dividend (or multiply by the same power of 10) ) DIVIDE.

4 4

5 5 Just be sure to line up the terms so that all the decimal points are in a vertical line.

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Prime WORD DEFINITION IN YOUR WORDS EXAMPLE A positive number that is divisible only by itself and the number one

Thus, all non-prime numbers are composite numbers The expression of a composite number as a product of prime

Sometimes all integers not divisible by are considered to be odd numbers A whole number that is divisible by.

And occasionally, zero will not be considered an even number 1,, 5, 7, 9, 11, 4, 6, 8, 10, 1, 14.

Continue to break down any composite numbers.

7 Prime WORD DEFINITION IN YOUR WORDS EXAMPLE A positive number that is divisible only by itself and the number one Composite Prime Factorization A composite number is a number that has factors in addition to one and itself. Thus, all non-prime numbers are composite numbers The expression of a composite number as a product of prime numbers x x 7 Odd Even A whole number not divisible by. Sometimes all integers not divisible by are considered to be odd numbers A whole number that is divisible by. Sometimes all integers divisible by are considered to be the even numbers. And occasionally, zero will not be considered an even number 1,, 5, 7, 9, 11, 4, 6, 8, 10, 1, STEP 1: Break down the number as a product of two numbers (DO NOT USE 1) STEP : Circle any prime numbers. Continue to break down any composite numbers. STEP : Continue until all composite numbers are broken into prime numbers. (DO NOT USE 1) STEP 4: Write the prime numbers in order with exponents and multiplication symbols. ANSWER: x x 5 This is a factor tree, NOT a prime factorization. It s what you use to find it! This is the prime factorization of 90. Remember means x.

8 MCC6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 1. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4(9 + ). WORD DEFINITION IN YOUR WORDS EXAMPLE Factor Multiple Least Common Multiple (LCM) When two or more integers are multiplied, each integer is a factor of the product. "To factor" means to write the number or term as a product of its factors The product of a given whole number and an integer The smallest multiple (other than zero) that two or more numbers have in common. Factors of 1: Multiples of 1:,,,,, Find the LCM of 8 and 1: Greatest Common Factor (GCF) The largest factor that two or more numbers have in common. Find the GCF of 16 and 4: List the multiples of each number. Find the first multiple they have in common. Find the LCM of 8 and 6: 8: 8, 16, 4,, 40 6: 6, 1, 18, 4 8

9 Find the GCF of 18 and 15: List the factors of each number. Find the largest factor they have in common. 18: 1,,, 6, 9, 18 15: 1,, 5, 15 1) Write the numbers side by side with an L around it. ) Think of a and write it on the left side of the L. Find the GCF of 18 and 4: 18 4 ) Divide the numbers inside the L by the common factor and write the quotients the numbers. 4) If nothing goes into of the quotients evenly, go to step 5. If there is a common factor for the quotients, repeat step. 5) Use the numbers on the of the ladder to help you find the GCF and LCM: To find the GCF: Multiply all of the numbers on the outside LEFT of the L. Find the LCM of 1 and 8: 8 1 To find the LCM: Multiply all of the numbers outside to the left and below the L, or all around the L 9 Find the GCF for 48 and 7 Step 1: Find the prime factors for 48: x x x x 7: x x x x Step : Multiply each factor that has a match GCF = x x x = 4 Find the LCM of 1 and 6 Step 1: Find the Prime factors for 1 = x x 6 = x x x Step : Multiply each prime factor the greatest number of times it appears in any one factorization. The most number of times appears in either factorization is twice. The most number of times appears in either factorization is twice. Thus, LCM = x x x = 6

10 Do we have to split two or more things into smaller equal sections? Are we trying to figure out how many people we can pass two or more things out to evenly? Are we trying to arrange something into rows or groups? Is it asking for a greatest number that divides into two or more numbers? Do we have an event that is or will be repeating over and over? Will we have to purchase or get multiple items in order to have enough? Are we trying to figure out when something will happen again at the same time? MCC6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 1. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4(9 + ). 10 WORD DEFINITION IN YOUR WORDS EXAMPLE Distributive Property The sum of two addends multiplied by a number is the sum of the product of each addend and the number

11 1) List the of each addend. ) Identify the common. ) Use the greatest common factor (GCF) to write an equivalent expression: each addend by the GCF and write the quotients inside the parentheses as a sum. Write the GCF outside of the parentheses. Using the distributive property, write as a multiple of a sum of two whole numbers with no common factor The factors of ADDEND 4: COMMON FACTORS The factors of ADDEND 16: Factor out the GCF from each addend to create an equivalent expression. 11 Using the distributive property, write as a multiple of a sum of two whole numbers with no common factor 1. Use the ladder method to find the greatest common factor (see page 9). The remaining (the numbers below the ladder) are the addends that will be inside the parentheses.. Write the expression as the product of the GCF and the sum of the remaining (the numbers below the ladder).

$1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of$ $fractions with like denominators. WORD DEFINITION IN YOUR WORDS EXAMPLE Numerator Denominator Common Denominator The term above the line in a fraction.$

12 MCC5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. WORD DEFINITION IN YOUR WORDS EXAMPLE Numerator Denominator Common Denominator The term above the line in a fraction. The numerator tells how many parts are being talked about or considered The number below the line in a fraction. The denominator indicates what kind or size of parts the numerator counts. A whole number that is a common multiple of the denominators of two or more fractions. Simplify Mixed Number Improper Fraction To use the rules of arithmetic and algebra to rewrite an expression as simply as possible. A fraction that contains both a whole number and a fraction A fraction where the numerator is equal to or larger than the denominator. Identify what fractional part of each figure at right is shaded: a) b) c) 1 d)

$If your answer is a fraction, YOU HAVE TO SIMPLIFY IT. To simplify a fraction: 1)Find a common factor for the numerator AND denominator.$ $4) Repeat steps and until there are no other common factors. To simplify an improper fraction: 1)Divide the numerator by the denominator.$ $4)Keep your whole number, and simply the fraction (see above). 1)Write both fractions in a table. )List multiples of denominators until you find a common one.$

13 If your answer is a fraction, YOU HAVE TO SIMPLIFY IT. To simplify a fraction: 1)Find a common factor for the numerator AND denominator. )Divide the numerator by the common factor, and write it as the new numerator. ) Divide the denominator by the common factor, and write it as the new denominator. 4) Repeat steps and until there are no other common factors. To simplify an improper fraction: 1)Divide the numerator by the denominator. )Take your remainder and put it as your new numerator. )Slide your divisor ( knocking at the door ) and make it your new denominator. 4)Keep your whole number, and simply the fraction (see above). 1)Write both fractions in a table. )List multiples of denominators until you find a common one. )Fill in the numerators to find your fraction. 1 1)Find the lcm of the denominators (see LCM pg.8-9). )Write the LCM after the equal sign as the denominator. ) Multiply the top and bottom of each fraction by the same number to get the common denominator.

X = - 4 X = 9 If you have a factor that cannot

$of the first fraction. ) Keep the the same.$ 4) Now subtract the numerators.

BORROWING FROM A WHOLE NUMBER 14 8 7 1 11 1

14 X = - 4 X = 9 If you have a factor that cannot subtract, then borrow! 1) from the whole number. ) Add the denominator (a whole) to the numerator of the first fraction. ) Keep the the same. 4) Now subtract the numerators. 5) Don t forget the whole numbers. BORROWING FROM A WHOLE NUMBER MODELING THE EXAMPLE ABOVE. Draw 8 circles. Shade in 5 /4. The amount left unshaded is your answer.

$STEP : Take the and make it the numerator of a fraction with the divisor as the denominator. Write each improper fraction as a mixed number.$

15 Multiply the. Multiply the. Simplify! MIXED NUMBERS TO IMPROPER FRACTIONS + x STEP 1: Multiply the by the whole number. STEP : Add your answer to the. STEP : Put your number over your original denominator. 8 x + 1 = IMPROPER FRACTIONS TO MIXED NUMBERS r r STEP 1: Divide the by the denominator. STEP : Take the and make it the numerator of a fraction with the divisor as the denominator. Write each improper fraction as a mixed number Write each mixed number as an improper fraction

$Write mixed numbers as fractions. Put whole numbers over. Multiply the numerators. Multiply the denominators.! No improper fractions as an answer. MCC6.NS.$

16 Write mixed numbers as fractions. Put whole numbers over. Multiply the numerators. Multiply the denominators.! No improper fractions as an answer. MCC6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Rewrite the problem using common denominators. Draw a bar to model the dividend. Determine how many times the numerator of the divisor goes into the numerator of the dividend. The remaining pieces are written as the new numerator and the denominator of the answer is the numerator of the divisor. Adapted from a lesson from SHMS 16

17 Make mixed numbers improper. Keep the first fraction (the dividend) the same. Multiply by the reciprocal of the second fraction (the divisor). Multiply the numerators. Multiply the denominators. Simplify. KEEP the first fraction 1 = 5 8 CHANGE divide to multiply FLIP the second fraction (reciprocal) X = 15 17

18 Write mixed numbers as improper fractions. Put whole numbers over one. KEEP the first fraction, CHANGE divide to multiply, FLIP the second fraction (reciprocal) Multiply the numerators. Multiply the denominators. SIMPLIFY! No improper fractions as an answer = Write the mixed numbers as improper fractions x = KEEP the first fraction the same. CHANGE to multiplication. FLIP to make the reciprocal of the second fraction CROSS SIMPLIFYING 18

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Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6

Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6 NUMBER SENSE & OPERATIONS 3.N.1 Exhibit an understanding of the values of the digits in the base ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999. Our