Adding/Subtracting DecimalsADDING: When you are adding decimals, please follow the following steps.
1. Stack it 2. Line up your decimals 3. Add moving from right to left - Don't forget to carry your 1 4. Drop your decimal down. (Make sure it is the same number of spaces over in your answer as it was in your problem) Example: SUBTRACTING: When you are subtracting decimals, please follow the following steps.
1. Stack it! 2. Line up your decimals 3. Subtract moving from right to left. 4. If your minuend (number on top) is smaller than your subtrahend (number on bottom), then go to the neighbor and see if they can help you out. ** If that neighbor can't help, keep going down the neighbors until you find one that can. Make sure you pass his help all the way down the line to where it is needed. 5. Drop your decimal down. Make sure it is the same number of spaces over in your answer as it was in your problem) *** If there is not a number in the tenths/hundreths place of your minuend/subtrahend, then add a ghost zero!*** Example: Adding/Subtracting Fractions with Like DenominatorsADDING: When you are adding fractions that have the same denominator, you are adding together parts of the whole so your denominator stays the same. All you need to do is add together your numerators.
Example: 4/9 + 3/9 = 7/9 SUBTRACTING: When your are subtracting fractions that have the same denominator, you are taking away parts of the whole so your denominator stays the same. All you need to do is subtract your numerators. Example: 7/8 - 5/8 = 2/8 AnglesRight Angle
90 degrees, make a square corner, "Post-it note trick" Acute Angle Less than 90 degrees, "a cute little angle" Obtuse Angle Larger than 90 degrees, "big, lazy, stretched out angle" Straight Angle 180 degrees, looks like your arm straightened out Angles-Complementary and SupplementaryComplementary Angles
-2 angles that come together to form a right angle -the measurement of the angles, when added together, totals 90 degrees. Example: A + 34 = 90
A = 90-34 A = 56 degrees Supplementary Angles
-2 angles that come together to form a straight angle -the measurement of the angles, when added together, totals 180 degrees. Example: A + 39 = 180
A = 180 - 39 A = 141 degrees AreaArea is the number of units needed to cover a flat surface without any overlaps or gaps.
Area = length x width A = L x W Example: Area = L x W
Area = 5 x 5 Area = 25 sq. cm. Example:
Area = L x W
Area = 9 x 4 Area = 36 sq. cm. Comparing Fractions-Creating Common Denominators1. Stack it
2. Multiply the denominators 3. The product is the new denominator 4. What you do to the bottom, you have to do to the top 5. Compare the new fractions ***Parents*** We will work on finding the Least Common Denominator at a different time. I would like the kids to get used to this method first. Thank you! Comparing Fractions-Cross Multiplying1. Multiply the numerator of the first fraction by the denominator of the second fraction.
2. Write the product above the first fraction and circle it 3. Multiply the numerator of the second fraction by the denominator of the first fraction 4. Write the product above the second fraction and circle it 5. Compare the circled numbers Comparing Fractions-With ModelsUse the model to compare fractions (>, <, =).
Comparing NumbersGreater than >
Less than < Equal to = For large numbers, start with the beginning digit (the digit with the highest place value) and compare those. If they are the same, cross them out and move to the next digit. Continue this process until you can determine which number is greater. Decimals - HundredthsDecimals - TenthsDistributive Property (Multiplication)Where multiplication and expanded form meet!!!
Example: 8x56 1. Make sure both numbers are in expanded form: 8X(50+6) 2. Spread the wealth: (8x50) + (8x6) 3. Handle what's inside the parenthesis: (400) + (48) 4. Add together: 448 Division: Please see "Long Division" below!Dot PlotsA DOT PLOT is a graph that shows the frequency of data along a number line.
Example: 1. Look at your data. Find the least amount. That is where your number line with start. 2.Order your number line from least to greatest. 3. Count how many times you see a specific number in your data. That is how many dots you will put above the number on the number line.
4. Count how many dots are above each point on the number line, write the total, and circle it.
Equivalent Fractions (Cross Multiplication Method)1. Draw bubbles
2. Multiply the numbers in the bubbles and write the product.
3. Are the products equal or not equal?
Equivalent Fractions (Creating Them)1. Circle the numerators.
2. Look at the numerator with the smallest digit. 3. What would I multiply this by to make the other numerator? 4. What I do to the top, I have to do to the bottom. 5. If I multiply the denominator of that fraction, do I get the denominator of the other fraction? 6. If yes, then they are equivalent. If no, then they are NOT equivalent. ***Parents*** The kids have not been taught "reducing" yet. Once their division skills become stronger, we will work on that strategy Creating equivalent fractions: Multiply the numerator and the denominator by the same number to create equivalent fractions. Example: Estimating (Sums, Differences, Products)To estimate, just round each part and perform the operation.
Example #1: Estimate 327 + 456 1. Round 327 to the nearest hundred = 300 2. Round 456 to the nearest hundred = 500 3. Perform the operation 300+500=800 Example #2: Estimate 9,542 - 6,374 1. Round 9542 to the nearest thousand = 10,000 2. Round 6374 to the nearest thousand = 6,000 3. Perform the operation 10,000 - 6,000 = 4,000 Example #3: Estimate 5,248 x 8 1. Round 5248 to the nearest thousand = 5,000 2. DO NOT round 8 (it is already easy to work with!) 3. Perform the operation 5,000 x 8 = 40,000 Example #4: Estimate 37 x 42 1. Round 37 to the nearest ten = 40 2. Round 42 to the nearest ten = 40 3. Perform the operation 40 x 40 = 1,600 Frequency TableA table that uses numbers to record data about how often something happens. The frequency is the number of times the data occurs.
Example: Create a frequency table using the data below. Step 1: Order the data from least to greatest.
30, 30, 30, 30, 30, 60, 60, 60, 60, 90, 90, 90, 120, 120, 120 Step 2: Draw/complete frequency table. Step 3: Answer questions about the frequency table. Pay close attention to the vocabulary!
Improper FractionsWhen the numerator is larger than the denominator.
Example: 13/6 Changing an improper fraction to a mixed number: 1. Build a house
2. Follow division steps.
3. Create your mixed number.
***The DENOMINATOR stays the same ***The quotient is the number of WHOLE times it divided so that is your WHOLE NUMBER ***The remainder is the NUMERATOR
Input/Output TablesLines, Rays, Line Segments, PointsLINE - a straight path of points that continues in both directions with no end. Has arrows on both ends to show it continues.
EXAMPLE: When we line up to travel. The line can move forward and the line can move backward. RAY - part of a line that has one endpoint and continues without end in one direction.
EXAMPLE: a ray of sunshine. Starts at the sun and shoots out in one direction. LINE SEGMENT - part of a line between 2 endpoints EXAMPLE: a segment of a worm. It starts and stops. POINT - an exact location in space Line of SymmetryA line of symmetry divides a figure into 2 parts that are the same size and shape.
If you fold along the line, both sides will match exactly. Example: Long Division (without remainders)Use the following acronym to remember the steps:
Does Ms. Sangdahl Cook Brownies? Division Multiplication Subtraction Check Bring Down Tip: Use graph paper to help keep your numbers straight! Remember that Academic Language... Divisor - number you are dividing by (number at the door) Dividend- number you are splitting into equal groups (number in the house) Quotient - answer to division problem (on the roof) 1. Write the problem on graph paper. Each digit gets its own box. 2. DIVIDE: How many times will the divisor (number at the door) go into the first digit of the dividend (number in the house)? Write that number on the roof. (Remember-if its not perfect, you want to choose a product less than - NOT greater than!)
***If the first digit in the house (dividend) is too small for the divisor (number at the door) to go into, place a zero on the roof and then look to the next digit. Look at examples from class on Thursday!*** 3. MULTIPLY: Multiply the number on the roof by the divisor. Write the product under the first digit of the dividend.
4. SUBTRACT: Subtract the product from the dividend.
5. CHECK: Is your difference smaller than your divisor (number at the door)? If yes, keep going. If no, the number on the roof isn't big enough.
6. BRING DOWN: The next number in the house drops down.
7.. DIVIDE: How many times will the divisor go into the dividend? (door into house). Write that number on the roof. MULTIPLY: Multiply the 2nd digit on the roof by the divisor. Write the product under the dividend.
8. MULTIPLY: Multiply the 2nd digit on the roof by the divisor (roof times door). Write the product under the dividend. .
9. SUBTRACT: Subtract. When you get "0" you know you are finished.***If there is an amount left, this is a remainder (left-over)!***
CHECK: Multiply your quotient (top of roof) and your divisor (at the door). The product should match your dividend (in the house).
Mixed NumbersA mixed number is a combination of a whole number and a fraction.
Example: 2 1/4 Changing a mixed number to an improper fraction: Strategy 1: Strategy 2:
Multiplication: 10, 100, 10001. Circle the non-zero numbers
2. Multiply the circled numbers 3. Count how many zeroes 4. Put that many zeroes at the end Multiplication: 2 Digit by 1 Digit1. Stack it
2. Bubble the numbers 3. Multiply the 2 numbers in the bubble starting on the right 4. If your product is greater than 9, carry over 5. Multiply the 2 numbers in the bubble. If you have a number above your bubble from carrying over, add it to the product. ****** INSIDE THE BUBBLE-MULTIPLY ****** OUTSIDE THE BUBBLE-ADD Multiplication: Multiple DigitFollow the same steps as above for 2 digit by 1 digit multiplication. Remember to bubble/loop all of your numbers!
Multiplication: 2 Digit by 2 Digit***PLEASE SEE the instructional video under the video header OR access it here***
http://youtu.be/6Pu2ZAfODEg 1. Stack it 2. Cover the tens place with finger 3. Bubble 4. Multiply 5. PEN- place marker, place value lines, addition sign, bubbles 6. Multiply 7. Add 8. Finished! Multi-Step Addition Problems1. Read the problem.
2. Draw your strip diagram. 3. Fill in the information you have. 4. Label what you are solving for as "X" in your strip diagram. 5. Solve for missing piece 6. Use information to solve for x Example: The birding club counted 344 seagulls on their last visit to the ocean. The club saw 215 more seagulls today than they did on their last visit. How many seagulls did the club see on the two visits to the ocean? -Draw your strip diagram
-Fill in the information you have. -Label what you are solving for as "x" -Solve for the first missing piece
-Use the information you have to solve for x
Multi-Step Subtraction Problems1. Read the problem.
2. Draw your strip diagram. 3. Fill in the information you have. 4. Label what you are solving for as "x" in your strip diagram 5. Solve Example: For next year, the campground director wants to make 4,000 new bundles of wood. The crew made 1,238 bundles in September and 1,141 bundles in October. How many more bundles do they need to make? -Draw your strip diagram
-Fill in the information you have -Label what you are solving for as "x" -Solve for the first missing piece
-Use the information you have to solve for x
One Tenth of/Ten Times as Much asWhen a number is 1/10 of another number, it is one space to the right of the other number on the place value chart.
Example: 70 is 1/10 of 700 Example: 700 is 1/10 of 7,000 Example: 7,000 is 1/10 of 70,000 Example: 0.07 is 1/10 of 0.7 *** Trick- for 1/10 of, add a zero to the end of your number to get your answer. When a number is 10 times as much as another number, it is one space to the left of the other number on the place value chart. Example: 70 is 10 times as much as 7 Example: 7,000 is 10 times as much as 700 Example: 70,000 is 10 times as much as 7,000 Example: 0.7 is 10 times as much as 0.07 *** Trick - for 10 times as much as, take a zero away from the end of your number to get your answer. Parallel and PerpendicularParallel Lines
2 lines that are always the same distance apart and will NEVER cross. Example = Perpendicular Lines 2 lines that form right angles when they cross each other. Example + PatternsA pattern is an ordered set of numbers or objects.
Number patterns follow a RULE. Identify what the rule is and you can continue or fill in the pattern. Example: Perimeter
The distance around a figure.
Perimeter of a Rectangle Formula: p=(2 x L) + (2 x w) or p= 2L + 2w "Plug and Chug" Plug - Take what you know, enter it into the formula Chug - Do the math Example: p= (2 x L) + (2 x w)
p= (2 x 9) + (2 x 4) p= 18 + 8 p = 26 Perimeter of a Square
Formula: p = 4 x s Example: p = 4 x s
p = 4 x 5 p = 20 Place Value (decimals)Place Value (whole numbers)ProfitProfit is the amount of money you make after all of your expenses are covered.
Example: Sweet Wendy's spent $100 on ingredients to make a wedding cake. The bride and groom paid $500 for the cake. What is Sweet Wendy's profit? $500-$100=$400 profit Protractors (reading a picture)When determining the measurement of an angle using a protractor (that is drawn on the paper), please follow these steps:
1. Look at the angle. Is it right, acute or obtuse? Write this above the angle.
2. What is the rule for my type of angle?
Right = 90 degrees Acute < 90 degrees Obtuse > 90 degrees Write the rule next to the angle type. 3. Where does the ray intersect the protractor? In other words, what 2 numbers (or tick marks) crosses the arc of the protractor? Write these 2 choices in the middle of the protractor.
4. Which one of the measurements makes my rule true? That is my answer!
Protractors (using it to measure an angle)When using a protractor to measure an angle, please follow these simple steps.
1. Look at the angle. Is it right, acute or obtuse? Write this above the angle. 2. What is the rule for my type of angle? Right = 90 degrees Acute < 90 degrees Obtuse > 90 degrees Write the rule next to the angle type. 3. Place hole/circle on bottom of protractor directly over the angle's vertex.
4. Make sure the bottom of the protractor is straight and lines up with the bottom ray
5. Use your note card (or other straight edge) and line the edge up with the ray
6. Read the 2 measurements on the protractor and write them on your angle
***Remember to play very close attention to if you should be counting up or counting down!!!*** 7. Decide which measurement follows the rule for the type of angle you have
QuadrilateralsRemainders
A "left-over" in a division problem.
Rounding1. Underline the digit you are rounding to
Example: Round to the nearest hundred thousand 12,248,698 2. Circle the neighbor (digit to the right of the underlined number). 3. Look at the circled number and ask the question "Is it greater than, less than, or equal to 5?" 4.Follow these rules: ** If it is greater than 5, the underlined digit will increase by 1 and all of the digits after it will become a zero. ** If it is less than 5, the underlined digit remains the same and all of the digits after it will become a zero. ** If it is equal to 5, the underlined digit will increase by 1 and all of the digits after it will become a zero. ** ALL digits BEFORE the underlined digit will remain unchanged. Example Answer: 12,200,000 Example 2: Round to the nearest 10 thousand 56,968 Answer: 60,000 Stem and Leaf PlotsA stem and leaf plot shows groups of data arranged by place value.
"Stem" - the digit that is in common (tens place) "Leaf" - the digit that is different (ones place). Example: Use the data table to create a Stem and Leaf Plot. Step 1: Put the numbers from the table in order from least to greatest.
Step 2:
Put the STEMS (digit in the tens place) on the left side of the vertical line. PUt the LEAVES (digit in the ones place) on the right side of the vertical line. How many stems are there? 3 (1,2,3)
How many leaves are there? 8 (0,1,2,0,2,5,6,1) Which stem has the most leaves? 2 (4 leaves) How do I read a stem and leaf plot? Put the stem with the leaf-so... 1 l 0 would be 10 2 l 0 would be 20 2 l 2 would be 22 3 l 1 would be 31 Which could be a key? The combination that makes sense! Key just means answer in these types of questions! Strip DiagramsStrip diagrams are a tool we can use to find missing pieces. They contain variables (numbers dressed up in a letter costume) that you need to solve for.
In the example below, top part of the diagram represents the "whole" and the bottom 2 parts of the diagram represent "parts of the whole". Example: TrianglesUnit FractionDecomposing a fraction into units.
Numerator is always 1. Example: 3/4 = 1/4 + 1/4 + 1/4 Writing NumbersStandard Form
-written with numbers "what you are used to seeing" Example: 245,158,268 Word Form -written in words "what it sounds like when you read the numbers out loud" Example: two hundred forty five million, one hundred fifty eight thousand, two hundred sixty eight Expanded Form -broken down by place value "stretched out with + signs" Example: 200,000,000 + 40,000,000 + 5,000,000 + 100,000 + 50,000 + 8,000 + 200 + 60 + 8 |
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