Mid over Math 280

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Mid over Math 280

Week 8

Problem Solving

Week 7

Week 6

Building Fraction Add,Sub,Mult

2 color

3 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

Homework 6

Week 5

Solving fraction/adding/Mult/Sub

Adding fraction:

• Find common denominator: LCM
• Convert each fraction to an equivalent fraction with common denominator
• Add fraction

Subtracting fraction

• Find common denominator: LCM
• Convert each fraction to an equivalent fraction with common denominator
• Subtract the fraction

Multiplying Fractions

• Multiply the numerators
• Multiply the denominaators
• Write the products as a new fractions
• Simplify 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=6

6-4=2

6-2=4

35 / 5= 7

35/7 = 5

5x7=35

7x5=35

Homework 5

Week 4

Understand Fraction/

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 pieces

5= size of piece 4= how big the piece are

Why are fractions so hard for some people?

Because they introduce an inverse relationship: a smaller denominator means larger pieces

2/5 2/3

small 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 piece

Comparing Fraction

1) over half way

6/11 or 15/34= 6/11 bigger

2) 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 bigger

5) missing two piece

13/15. or 25/27= 25/27 bigger

Homework 4

Exam

Week 3

Multiplication Building/showing/Alt algorithms

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 28

Multiple 20x30= 600

Multiple 20x4 = 80

Then

Multiple 8x30=240

Multiple: 8x4=32

Add all together

600+80+240+8=952

Left to Right

38x26

tens : 3 become 30

tens: 2 become 20

Multiple 30x20=600

Multiple 30x6=180

Multiple 8x20=160

Multiple 8x6=48

Add all together

600+180+160+48=988

Area Model

• Draw a rectangle divided into two parts virtically and horizontally, representing 12 and 26

Multiple 10 x20=200

Multiple 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

Division Building/showing/Alt algorithms

Traditional Division

649/5

• 5 goes into 64 12 times( 5x12=60)
• subtracted 64-60=4
• Now bring dow the next digit 9
• 5 goes into 49(5x9=45)
• subtract 49-45=4

Answer is 129 r4

Reapeated Subtraction

• 832-700=132(subtracted 70)
• 132-70=62 (subtracted another 70)

Now 62 remains. We will subtract 7 repeatedly from here

• 62-7=55
• 55-7=48
• 48-7=41
• 41-7= 34
• 34-7= 27
• 27-7= 20
• 20-7=13
• 13-7=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= 500

• Subtract 500 from 649

649-500=149

Now, we know that 5 goes into 649 at least 100 times

• Now divide 149 by 5:

5x20=100

• Subtract 100 from 149

149-100=49

We know that 5 goes into 149 at least 20

• Divide 49 by 5

5 x 9=45

• Subtract 45 to 49

49-45=4

We know that 5 goes into 49 at least 9 times

Now put them all together

100+20+9=129

Homework 3

Exam 1

Weeks 2

Building addition/Alt algorithms/Friends and number

Flat 100

Long 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)Efficent

3) Base on math

Traditional Algorithms

237+185

Add 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: 422

It is expandable, Efficient but not base one Math

Expanded Form

237+185

237 expanded form: 200+30+7

185 expanded form: 100+80+5

Add the hundreds place value: 100+200=300

Add the tens place value: 30+80=110

Add the one's place value: 7+5=12

300+110+12=422

Its 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= 110

Add the ones place: 7+5= 12

300+110+12= 422

Its expandable, Effiecient and Base on math

Friendly number

#'s that end with zero

32+58

Round 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=90

Its expandable, Effiecient and Base on math

Scatch Method

Add Digit by Digit with Scratches

456+789

Add Units place: 6+9=15

• Write down 5, make a scratch for 10 carry 1

Add tens place: 5+8=13

• plus 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 1

Its expandable, Effiecient but is questionable to be Base on math



Building Subtraction/Alt Algorithms

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 math

Left-to-Right (start from left )

9-3=6

6-5=1

96-

35

________

61

Yes expandable

Okay efficient

Yes is base on solid math

Equal Addends

64-38

Add +2 on both sides

64 becomes 66 and 38 becomes 40

Now add the two answers together

66-40=26

Yes expandable

Yes efficient

Yes is base on solid math

Homework 2

Week 1

Different bases

1. Draw diagram
2. state # of units in shape
3. add the units

Base -5: 0,1,2,3,4

One= 5

Five=5 (units)

25= 5(square)

125= 5 (flat) times 3

Homework 1