5th Grade Math Notes Common Core PDF

5th Grade Math Notes Common Core Basic Fraction Mixed Numbers and Improper Fractions When converting a mixed number into an improper numerator - (the # of pieces shaded or unshaded) fract...

5th Grade Math Notes Common Core Basic Fraction Mixed Numbers and Improper Fractions When converting a mixed number into an improper numerator - (the # of pieces shaded or unshaded) fraction you multiply the denominator by the whole denominator - (the total number of pieces) number, then add the numerator. Example: Example: 5 3 12 x 3 + 5 = 41 5 12 12 **Hint: The denominator does NOT change.** When converting an improper fraction into a mixed number you divide the numerator by the denominator. **Hint: Zero can NEVER be a denominator.** 3 R5 41 12 41 5 3 12 - 36 12 5 **Hint: The dividend becomes the whole number and the remainder becomes the numerator and your denominator does NOT change.** Equivalent Fraction Adding Fractions ~ For the numerators add straight across. ~ The denominator does not change. Ex. 12 2 + = = 24 4 2 3 5 + = 6 6 6 The rule when converting fractions is that what ever Ex. you do to the top you must also do to the bottom. 1 1 12 4 = 24 4 ~ If your denominator is 24 and it changes to 4 you 2 1 have to determine which operation was used. + 4 ~ You divided 24 by 6 which equals 4. ~ Since you divided 24 by 6, you also have to divide 12 by 6. 3 2 ~ 12 divided by 6 equals 2 4 12 2 * Hint: Make sure you have a common = 24 4 denominator before you add.  5th Grade Math Notes Common Core Adding & Subtracting with UNLIKE Denominators Multiplying Fractions 1 2 ~ Multiply the numerator by the numerator. + 2 3 ~ Multiply the denominator by the denominator. 1. Find the least common multiple (LCM) by listing the multiples of each denominator in the problem. Circle Ex. 3 2 6 x = the least common multiple and use it as your common 4 6 24 denominator. (Ex: the LCM of 2 and 3 is 6. Use 6 as your common denominator.) 2: 2, 4, 6, 3: 3, 6 2. Rename the fractions using the new common denominator. 1 3 2 4 = = 2 6 3 6 3. Perform the operation & keep the new denominator. 3 4 7 + = 6 6 6 *HINT: remember to simplify your answer. 4. Write the answer in simplest form. Ex. 6 1 7 1 24 4 = 1 6 6 Dividing Fractions Geometry Formulas ~ Invert the fraction P = perimeter (The distance around a figure.) ~ multiply the fractions A = area (The measure, in square units, of the inside of a plane figure.) 1 3 1 4 4 V = volume (The number of cubic units a space of ÷ = x = a solid figure takes up, count the cubes needed to 2 4 2 3 6 fill a fiqure.) 6 in. 2 ft. 6 in. 10 ft. 6 in. 4 2 V=lxwxh = 6 3 V=6x6x6 ~ Draw a picture to represent the first fraction and draw a V = 216 in.3 picture beneath that to represent the second fraction. ~ Draw a line where the second fraction ends and that V= area of the base x height 2 ft. fraction has a new denominator. V= B x h V=lxwxh ~ See how many squares on the bottom picture match the V = 2 x 2 x 10 top picture and that is the new fraction. V = 40 ft.3  5th Grade Math Notes Common Core Operations With Decimals Measurement Conversions Adding Decimals: 12 inches = 1 foot 1. Line up the decimal points and add as usual. 3 feet = 1 yard 2. Drag the decimal straight down. 1,760 yard = 1 mile distance Subtracting Decimals: 5,280 feet = 1 mile 1. Line up the decimal points and subtract as usual. 2. Drag the decimal point straight down. 1 kilometer = 1,000 meters Multiplying Decimals: 1. Multiply as usual. 1 gallon = 4 quarts 2. Count the digits behind the decimals. 1 quart = 2 pints capacity 3. Place your decimal point in the product (answer). 1 pint = 2 cups Make sure the product and the original problem have 1 cup = 8 ounces the same number of digits behind the decimal. Dividing Decimals: 16 oz. = 1 lb. 1. Move the decimal in the divisor so it is a whole 1 8 oz. = lb. weight number. Move the decimal in the dividend the same 2 number of spaces. 1 4 oz. = lb. 3. Divide as usual. 4 4. In your answer, place the decimal directly above the decimal in the dividend. Measurement Measurement Metric System Gallon Land three basic units gram measures weight meter measures length liter measures capacity thousandths hundredths hundrdeds thousands basic unit tenths tens 1,000 100 10 1 0.1 0.01 0.001 meter gram o- i- - - i- - ca ci nt lo ct ill de de ki ce m he liter A millimeter is about how thick a dime is. A centimeter is how wide one of your fingers is. A kilometer is a little more than half a mile.  5th Grade Math Notes Common Core Place Value Rounding Rap hundred thousands Yo, find that place value hundred millions Circle that digit ten thousands Move to the right, underline get it. ten millions thousands hundreds 0-4 circle stays the same millions 5-9 add one is the game ones tens Now flex your muscles like a hero , , Digits to the right change to zero All the other digits stay the same Whole Numbers Yo! You’re the winner of the rounding game! hundred thousands ten thousands thousandths hundredths thousands hundreds tenths ones tens , Parts of a Whole Numbers Whole Place Value Rounding This standard refers to rounding. Students 347.392 should go beyond simply applying an algorithm or procedure for rounding. The expectation is that Three hundred forty seven and three students have a deep understanding of place value hundred ninety two thousandths and number sense and can explain and reason 1 (3 x 100) + (4 x 10) + (7 x 1) + (3 x /10) + (9 about the answers they get when they round. x 1/100) + (2 x 1/1000) Students should have numerous experiences using a number line to support their work with rounding. 2 1 (3 x 10 ) + (4 x 10 ) + (7 x 1) + (3 x 0.1) + (9 x 0.01) + (2 x 0.001) Example: Round 14.235 to the nearest tenth. Students recognize that the possible answer must be in tenths thus, it is either 14.2 or 14.3. They then identify that14.235 is closer to 14.2 (14.20) than to 14.3 (14.30).  5th Grade Math Notes Common Core Multiplying & Dividing Whole Numbers Algebraic Thinking Standard Algorithm Order of Operations 4, 3 2 7 P ( ) (14 + 2) x 12 - 52 x 3 4 E x2 16 x 12 - 52 1 7 3 0 8 M x 16 x 12 - 25 + 1 2 9 8 1 0 D ÷ 192 - 25 1 4 7, 1 1 8 A + S - Multiple Towers 36 27 Simple Expressions 32 24 Johnny had 12 apples that he gave to Susan. 28 21 He then picked some more. 24 18 20 15 12 - 6 + a 16 12 12 9 8 6 4 3 Multiplying & Dividing Whole Numbers Data Analysis Relating Division to Multiplication Line Plot 14 x 12 = 168 Shows frequency of data along a Factor 100 number line 10 + 2 20 Factor 40 10 10 x 10 = 100 10 x 2 = 20 + 8 + 168 4 4x2=8 4 x 10 = 40 (10 + 2) divisor 12 or quotient divisor or quotient Dividend (10 + 4) 168 14  5th Grade Math Notes Common Core Division Strategies Division Strategies Partial Quotient Dealing Out 135 ÷ 4 36 ÷ 4 4 36 3 x 4 = 12 - 12 3 10 10 10 10 3 x 4 = 12 24 10 3 10 3 10 3 10 3 10 10 10 10 3 x 4 = 12 - 12 3 12 - 12 3 135 - 40 = 95 0 9 -40 55 -40 156 ÷ 5 5 156 15 20 x 5 = 100 - 100 20 -12 10 x 5 = 50 56 3 1x5=5 - 50 10 6 - 5 1 1 31 r 1 Division Strategies Division Strategies Breaking the Dividend into Multiples of Breaking Dividend Apart the divisor 84 ÷ 4 135 ÷ 4 80 ÷ 4 = 20 80 4 20 + 1 = 21 4÷4=1 100 + 30 + 5 100 ÷ 4 = 25 135 ÷ 4 80 30 ÷ 4 = 7 r 2 80 ÷ 4 = 20 40 5÷4=1r1 135 40 ÷ 4 = 10 12 33 r 3 12 ÷ 4 = 3 3 33 r 3 5th Grade Math Notes Common Core Comparing 0.207 (2 x 0.1) + (0 x.01) + (7 x 0.001) 0.26 (2 x 0.1) + (6 x 0.1) The digit 6 in the hundredths place is larger than the o digit. Adding Decimals Model 1.25 + 0.40 + 0.75 Subtracting Decimals with Models 4 - 0.3  5th Grade Math Notes Common Core Multiplying Decimals Students should be able to describe the partial products displayed by the area model. For example, “3/10 times 4/10 is 12/100. 3/10 times 2 is 6/10 or 60/100. 1 group of 4/10 is 4/10 or 40/100. 1 group of 2 is 2.” Divide Decimals Example of division: finding the number in each group or share. Students should be encouraged to apply a fair sharing model separating decimal values into equal parts such as 2.4 ÷ 4 = 0.6 Example of division: finding the number of groups. Students could draw a segment to represent 1.6 meters. In doing so, s/he would count in tenths to identify the 6 tenths, and be able identify the number of 2 tenths within the 6 tenths. The student can then extend the idea of counting by tenths to divide the one meter into tenths and determine that there are 5 more groups of 2 tenths.  5th Grade Math Notes Common Core Volume (3 x 2) represented by first layer (3 x 2) x 5 represented by number of 3 x 2 layers (3 x 2) + (3 x 2) + (3 x 2) + (3 x 2)+ (3 x 2) = 6 + 6 + 6 + 6 + 6 + 6 = 30 6 representing the size/area of one layer Students will extend their work with the area of composite figures into the context of volume. Students will break apart (decompose) 3-dimensional figures into right rectangular prisms in order to find the volume of the entire 3-dimensional figure.  5th Grade Math Notes Common Core Multiplying Fractions Models 2 3 x 3 4 2 4 x 3 5 2 x 7 is less than 7 because 7 is multiplied by a factor less than 1 so the product must 3 be less than 7. 7 3 of 7 4