Associative Property of Addition – the property that states when the grouping of addends is changed, the sums is the same Example: (2 + 5) +7 = 2 + (5 + 7)Common Factor – a number that is a factor of two or more numbers Example: factors of 4: 1, 2, 4 factors of 6: 1, 2, 3, 6 - 1 & 2 are the common factorsCommutative Property of Addition – the property that states that when the order of two or more addends is changes, the sum is the same Example: 4 + 6 = 6 + 4
Composite number – a whole number having more than two numbers Example: 2 (1,2)Divisible – a number is divisible by another number if the quotient is a whole number and the remainder is zeroFactor Tree – a diagram that shows the prime factors of a number
Greatest Common Factor (GCF) – the greatest factor that two or more numbers have in commonExample: 2 – (1, 2) 4 – (1. 2. 4) 6 – (1, 2, 3, 6)2 is the GCF of 2, 4 & 6Ladder Diagram – a diagram that shows the steps of repeatedly dividing by a prime number until the quotient is 1Prime Factorization – a number written as the product of all its prime factors
6.1 Additionwith LikeDenominatorsCompleteInvestigate pg. 231with a partnerMaterials needed:pattern blocks
Explain how the sum is related to the number of same-shaped pattern blocks.Explain how you could add fractions that have the same denominator without using the model?Analyze in the Investigate, you modeled 5/6 + 3/6 = 8/6 using pattern blocks. Use blue quadrilaterals and two yellow hexagons to model a different equation with an equivalent sum. What is your equation?Explain why you can use different-shaped pattern blocks to model the same sum.
6.1 Addition with Like Denominators Use a number line to add fractions.?
6.1 Additionwith LikeDenominatorsComplete ProblemSolving pg. 234Sense or Nonsense?
How can you use modelsto add fractions with likedenominators?
6.2 Subtractionwith LikeDenominatorsCompleteInvestigate with apartner (pg. 235)Materials: patternblocks
Explain how you subtracted in the take-away model.Explain how you subtracted in the comparison model.Analyze How is the comparison model different from the take-away model?Explain how you could subtract fractions that have like denominators without using models.
6.2 Subtractionwith LikeDenominatorsUse a number lineto subtractfractions.
How can you usemodels to subtractfractions with likedenominators?
A number is divisible by: Example Your Example2 – if the last number is even 963 – if the sum of the digits is 96 (9+6 =15)divisible by 3 15 ÷ 3 = 54 – if the last two digits form 128a number divisible by 4 28 ÷ 4 = 75 – if the last digit is 0 or 5 3556 – if the number is divisible 96by 2 and 3 6 is even (9+6=15) 15÷39 – if the sum of the digits is 396 (3+9+6=18)divisible by 9 18 ÷ 9 = 210 – if the last digit is 0. 550
6.3 Problem Solving pg. 16. Dirk bought a set of stamps that has fewer 242 stamps than the set for Germany. The number Use the table to of stamps in the set he solve 16 – 19 bought is divisible by 2, 3, 5, 6 and 10. Which set is it?17. The number of stamps in one set is divisible only by 5.Which set is it?18.Tina collects stamps. She wants to purchase two differentsets of stamps so that she can put 9 stamps on a page in hercollector’s notebook and not have any stamps left over.Which two sets of stamps should she purchase?19. Geri wants to put 10 stamps on some pages in her stamp book and 9 stamps on other pages. Explainhow she could do this with the stamp set for Japan.
How can you tell if anumber is divisible by 2, 3,4, 5, 6, 9 or 10?
Prime numbers – a whole number greater than 1 that has exactly two factors, 1 and itselfExample: factors of 13: 1, 13Composite numbers – a whole number greater than 1 that has more than two factorsExample: factors of 12: 1, 2, 3, 4, 6, 12
PrimeNumbersStep 1: Cross out 1,because it is not a primenumber (it has only onefactor)Step 2: Circle 2, since it isprime (factors: 1,2) Crossout all other multiples of2.Step 3: Circle the nextnumber that is notcrossed out & then crossout all of multiples of thatnumber.Step 4: Repeat Step 3 untilevery number is eithercircled or crossed out.
How can you tell whethera number is prime orcomposite?
E very composite number can be written as a product of factors that are all prime numbers.A factor tree can be used – a diagram that shows the prime factors of a numberThere are two ways to begin a factor tree – using basic facts of the number or divisibility rules Which ever strategy you use continue with it until the only factors remaining are prime numbers
4 + 8 = 12 (12 is divisible by 3 thereforeBasic fact: 6 x 8 = 48 48 is also)
LadderDiagramStart by choosinga prime factor bywhich thenumber isdivisible. Thendivide.Continue dividingby a prime factoruntil the quotientis 1.
21. The 4-digit code number is made up of the prime factors of 140. The factors are entered in order from Problem greatest to least. What is the code number? Solving pg. 25022. This 5-digit code is made up the prime factors of Use the information 108. The factors are entered in order from least to below to solve 21-24 greatest. What is the code number? Each customer of a23. This 6 –digit code number is made up of the prime bank must enter a 4 – factors of 900. Each factor repeats twice, and the 6 digit code number to use his or her cash numbers are entered in order from greatest to least. card at an ATM What is the code? machine.24. This 6-digit code number is made up of the prime Suppose the code factors of 1260. The factors are entered in order number is made up of from least to greatest. What is the code number? prime factors that are part of the25. Find the prime factorization of 240. Write your account number. answer as an expression using exponents.26. Which shows the prime factorization of 144?
How can you find all theprime factors of a number?
A common factor is a number that is a factor of two or more numbers.Factors of 6: 1, 2, 3, 6Factors of 9: 1, 3, 9The common factors are 1 and 3.Greatest Common Factor is the greatest factor that two or more numbers have in common.Greatest Common Factor (GCF) of 6 & 9 is 3.
CommonFactors &Simplest FormSimplest form iswhen thenumerator anddenominator bothhave 1 as their onlycommon factor
18. What fraction of the 50 states are part of the Southeast region? Write your answer in simplest form.19. What fraction of the 50 states are part of the Northeast region? Write your answer in simplest form.
Maths Mansion: Show 25: Do the Same to the Bottom as th
20. What fraction of the 50 states are part of the West and Southwest regions? Write your answer in simplest form.21. Florida borders both the Atlantic Ocean and the Gulf of Mexico . Thirteen states border only the Atlantic Ocean. Four other states border only the Gulf of Mexico. Use simplest form to write the fraction of the 50 states that border one or both of these bodies of water.
How can you find the greatest common factor of two or more numbers?
How can you renamefractions greater than 1 asmixed numbers and renamemixed numbers as fractionsgreater than 1?
6.9 Add &SubtractFractions***importantinformation***before you can addfractions thedenominators mustbe the same!
6.9 Add &Subtract LikeFractions***importantinformation***Before you cansubtract fractionsthe denominatorsMUST be the same!
19. What fraction of the students chose summer or spring as their favorite season? Write your answer in simplest form.20. What fraction of the students chose fall or winter as their favorite season? Write your answer in simplest form.
21. What fraction of the students chose summer or winter as their favorite season? Write your answer in simplest form.22. Which is greater, the fraction of the students whose favorite season is summer, or the fraction of the students combined whose favorite season is winter, spring, or fall combined? By how much?
How can I add or subtract fractions with like denominators?
How can I add or subtract mixed numbers with like denominators?
Step 1 – rename the mixed number as a fraction greater than 1.Step 2 – subtract the mixed numbers. Write the answer in simplest form.
Step 1 – Rename both mixed numbers as fractions greater than 1.Step 2 – Subtract the fractions greater than 1. Write the answer in simplest form.
How can you rename a mixed number to subtract a larger fraction?
The commutative property of addition states that when the order of two addends is changed, the sum is the same. For example: 4 + 5 = 5 + 4The associative property of addition states that when the grouping of addends is changed, the sum is the same. The grouping of addends is usually shown by parentheses. For example: (5 + 8) + 4 = 5 + (8 + 4)
How can you add fractionswith like denominators usingthe properties of addition?