Mid over Math 280

Draw diagram state # of units in shape add the units Base -5: 0,1,2,3,4One= 5Five=5 (units) 25= 5(square)125= 5 (flat) times 3

Flat 100Long 10 Cube Ones If we are working in base six, what we know about the blocks we would use to build numbers in base six?We know hat each long will be equal to 6 unis. and each flat will be equal to 6 longs or 36 units What does the base tells us?The base tells us the numbers of units needed to create 1 long Example:23+42= 6 longs and 5 ones II ooo+ IIIoo= IIIIIIooooo What makes a "good" algorithms 1) expanded 2)Efficent3) Base on math Traditional Algorithms 237+185Add units: 7+5=12( write 2, carry over 1) add ten's: 3+8+1=12(write 2, carry out 1) Add hundreds: 2+1+1=4 Final answer: 422It is expandable, Efficient but not base one Math Expanded Form 237+185237 expanded form: 200+30+7185 expanded form: 100+80+5Add the hundreds place value: 100+200=300Add the tens place value: 30+80=110Add the one's place value: 7+5=12 300+110+12=422Its expandable, Effiecient and Base on math Left-to-Right ( being with the left digit)237+185 Add the hundreds place: 200+100=300 Add the tens place: 30+80= 110Add the ones place: 7+5= 12 300+110+12= 422Its expandable, Effiecient and Base on math Friendly number #'s that end with zero 32+58Round 32 to 30 by subtracting by 2 and adjust 58 by adding 2 to the 8 to make it 60 32 become 30 58 becomes 60 Add them together 30+60=90Its expandable, Effiecient and Base on math Scatch Method Add Digit by Digit with Scratches 456+789Add Units place: 6+9=15 Write down 5, make a scratch for 10 carry 1 Add tens place: 5+8=13plus carry 1, total 14 ,write down 4, make scratch for 10 cary 1 Add hundreds Place: 4+7=11 Plus carry 1 total 12, write down 2 make a scratch for 10 carry 1Its expandable, Effiecient but is questionable to be Base on math 

Subtraction= take way Flats 100 longs 10 units 1's Expanded Form: 40 - 6 -(20 + 4)__________ 20+2=22 Yes expandable Not efficient Yes is base on solid mathLeft-to-Right (start from left )9-3=66-5=196- 35________61Yes expandableOkay efficientYes is base on solid mathEqual Addends 64-38Add +2 on both sides 64 becomes 66 and 38 becomes 40 Now add the two answers together 66-40=26Yes expandableYes efficientYes is base on solid math

3x4 3= # of group (circle)4= inside (square) Describe how the order in witch we should beach our muliplication table 1-10 1st(1,2,5,10) 2nd(3,9,double). 4th(4,6,7,8)Expanded form: 34 x 28Multiple 20x30= 600Multiple 20x4 = 80 Then Multiple 8x30=240Multiple: 8x4=32 Add all together 600+80+240+8=952 Left to Right 38x26tens : 3 become 30 tens: 2 become 20Multiple 30x20=600Multiple 30x6=180Multiple 8x20=160Multiple 8x6=48Add all together 600+180+160+48=988Area Model Draw a rectangle divided into two parts virtically and horizontally, representing 12 and 26Multiple 10 x20=200Multiple 10x 6= 60 Multiple 2x20=40 Multiple 2x6 = 12 Then Add 200+60= 260 Add 40+12= 52 Add both answer together 260+52= 312

Traditional Division 649/5 5 goes into 64 12 times( 5x12=60)subtracted 64-60=4 Now bring dow the next digit 95 goes into 49(5x9=45)subtract 49-45=4 Answer is 129 r4Reapeated Subtraction 832-700=132(subtracted 70) 132-70=62 (subtracted another 70) Now 62 remains. We will subtract 7 repeatedly from here 62-7=5555-7=4848-7=4141-7= 3434-7= 2727-7= 2020-7=1313-7=6 70+70+7(8)= 208 Area model Draw rectangle to represent the total area of dividend, 649 First, determine a large multiple of 5 that fits into 649 5x100= 500Subtract 500 from 649 649-500=149Now, we know that 5 goes into 649 at least 100 timesNow divide 149 by 5: 5x20=100Subtract 100 from 149 149-100=49We know that 5 goes into 149 at least 20 Divide 49 by 5 5 x 9=45Subtract 45 to 49 49-45=4We know that 5 goes into 49 at least 9 timesNow put them all together 100+20+9=129

What does numerator tell us about our fraction How many piece we have What does the denominator tells about the fraction The size of the piece What do the parts of a fraction mean? 2/5 1/4 2= # we have 1= 1 # of pieces5= size of piece 4= how big the piece areWhy are fractions so hard for some people?Because they introduce an inverse relationship: a smaller denominator means larger pieces 2/5 2/3small big When and why do we need to find common denominator? Because when I'm adding two fractions together or subtracting two fraction, I need to adding or subtracting the same size pieceComparing Fraction1) over half way 6/11 or 15/34= 6/11 bigger2) same number of pieces 4/15 or 4/13= 4/13 bigger 3) missing one piece 15/16 or 5/6= 15/16 is bigger 4) over half way 23/50. or 354/700= 354/700 is bigger5) missing two piece 13/15. or 25/27= 25/27 bigger

Adding fraction:Find common denominator: LCM Convert each fraction to an equivalent fraction with common denominator Add fraction Subtracting fraction Find common denominator: LCMConvert each fraction to an equivalent fraction with common denominatorSubtract the fraction Multiplying Fractions Multiply the numerators Multiply the denominaators Write the products as a new fractionsSimplify the fraction (if possible) Divison Fraction Keep: Keep the first fraction as it is Change: change the division sign to a mulitiplication sign Flip: flip the second fraction What are the Fact Families 2+4=6 4+2=66-4=26-2=435 / 5= 735/7 = 5 5x7=35 7x5=35

2 color3 color More colors if possible Addition Use 1 pink tile to represent 1/2 of the total area Use 2 yellow tiles to represent 1/4 Since 2 yellow tiles represent 1/4 together cover the dame area as 1 pink tile representing 1/2 Subtraction Represent 2/3 ( Shade 2 out of the 3 parts of the circle)Represent 1/3 (shade 1 out of the 3 part of another circle) Subtract 1/3 from 2/3 ( remove 1 shaded part from the 2/3) After removing 1 part, we are left with 1 shaded part out of the 3 Multiplying Divide the circle into 3 equal part Shade 2 out of the 3 parts to represent 2/3

Solving SubtractionDifferent symbol subtract same symbols Add Example -18 - (-15)= It turns out to be -18 + (15) - - becomes a + Show Diagram Sub 4-3 ++++ take away 3 = 1-2-(-6) + + + + + + _ _ _ _ _ _ _ _ Dark blue is the answer (4) Blue and red become zero bank green is -6 thats what we need to take awaySolving Multiplication/ Division Different sign= neg Same sign= positive Example 3(-7)= -21 diff sign negative -41(-60)= 2460 same sign positive-40 / (-20)= 2 same sign positive 300 / (-100) = -3 different sign negative

Problem Solving

Order of Operation P E M D A S or GEMDAS () xp x / + -A problem where the P doesn't stand for Parethesis -4-2(8)/4 What does the world percent mean? Its a ratio 30% = 30 ------- 100Solving percent mentally what is 10% of 90= 9 What is 30% of 70= 3x7= 21What is 42% of 120 = 4x12=48 1.2x 2 =2.4 add them together answer is 50.4