Elementary Mathematics - Madison Smalley

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Elementary Mathematics - Madison Smalley

Week 8

Extra Notes

When adding, negatives go in the front

Positives on top, negatives on bottom, and keep them in pairs

Adding a pair of 1 negative and 1 positive = Zero pairs

Red side of tiles = negative

Add/Sub Integers

Subtracting Integers

Show X using Y tiles

Zero Bank

A group of zero pairs = zero bank

Show

++ - - - - - - - - -

Model

Demonstrate Numbers

Week 9

Multiplication/Division Rules

Same sings = Positive Different signs = Negative

Notes / Answers

Build Multiplication

2(3) / -2(3)

Solve Sub

-37+(15)

Show Sub

-5-(-2)

Week 10

Fraction

Algorithms +/-/X/

Intro to Fractions

Models

Area

Finding the fraction of a specific area from a bigger area

Set

Example: 3/7 Red or 4/7 Not Red

Linear

using length for fraction

Greater/Less/Equal

Numerator/Denominator Understanding

Numerator = what we have Denominator = the size of the pieces we have

Week 11

Exam 2 Review

Week 12

Build and Show Fractions

Week 13

Solve: Multiple Division

Solve Multi/Div Fractions

Draw Diagram to show how to Add, Sub, and Multiply Fractions

Week 14

Solve expressions using the appropriate Order of Operations

Week 15

Final Review

Week 7

Division

Upward Division

Number Sorting

Group 3

6,7,8,9: Harder to count or do any math problems

Group 2

3 and 4: small numbers

Group1

2,5,10: Easy to count, multiply, divide, add, and subtract

Divisibility Rules

Look at the last three digits, divide by 8, then yes

Look at the last two digits, divide 4, then yes

If two and three work, then yes

Sum of the digits, divide by 9, then yes

Find the sum of the digit. If the whole number could be divided by three, then yes

If the one's digit is a zero, then yes

If the number ends in a 5 or a zero, then yes

If the number is even, then yes

Groups

5&10, 3&9, 4&8, 2,3&6

Repeated Sub

Week 6

Exam Review

Multiplication

Lattice/Area Model

Expanded Form/Left To Right

Subtopic

Left To Right: 32(29)

Expanded: 23(16)

Week 5

Multi-Digit Multiplication

Model Base ten

Array Model

Chinese

Multiplication Automaticity

FC/Best order to each to teach Multiplication Facts

1. Start with 1,2,5,10. Skip counting. 2. 3,9, doubles, also skip counting. 3. The rest of the numbers.

3 different groups:

Timed Test

Timed tests are not beneficial for students. It is more for the teachers to take the results and teach the class on the subjects that need it more.

What does 2(3) mean?

2(3) mean 2 groups of 3. (3)(3).

The difference between 2(4) and 4(2)

The difference between 2(4) and 4(2) is 2(4 is two groups of 4, while 4(2) is 4 groups of 2.

Week 4

Equal Add Ons

63-35/ +5 to both sides to make 68-40=28. This makes it easier to sub/add numbers when there is a zero in the second number.

36-24= 30&20 - 6&4 = 10&2=12

Week 3

Subtraction

469-264= 205. Take 4-2, 6-6, then 9-5. This makes it easy for student to keep place value.

Expanded

46-12/ 40-10&6-2 = 34

Equal Additions

30-17/ +3 to both sides, making 33-20= 13

28-16/ Taking the 28 and turning it into the base ten blocks, having two longs and eight units. Then turn the 16 into one long and 6 units. You would take one long from each number, the take away 6 units from each. This allows students to keep place value as well as seeing it physically.

Addition

Friendly Numbers

24+43+76+39+17/ Bring numbers that will add up to 10 together. Such as 4, from 24, and 6, from 76, making the 24 a 30, and a 70. Then the 7 from 17, to 3 from 43. making the 17 to 10, then 43 to 50. Then you will have 30+50+70+10. Adding 199.

Trade Off

37+88/ Taking numbers away from one number and adding it to the other to create a number ending in zero. You would take 2 from the 37, then add it to the 88. Creating 35+90= 125

Scratch

24=68=37=59/ Adding number until you get to ten. You would start by writing the numbers vertically, leaving space between the numbers. You would start with the units. 4+8= 12, so you would draw a line through the 8, then write a 2 next to it, signally 12. You would then add that 2 to the 7, creating 9, you then add the next number, 9. Creating 18, so you would draw a line through 9, then write a 8 next to it, signally 18. You would write the 8 at the bottom, then count the lines through the numbers. Since there was 2, you would put 2 about the 2 in 24. Then you add the 10's digits together. 2+2+6, this creates 10, so you would draw a line through the 6, then put a 0 next to it, signally a 10. Add the rest the numbers continuing this process. At the end you will have 8 at the bottom. You will then count the lines, then put that on top of the 100's place. Since there is no other number, that 1 will just drop down. Meaning 24+68+37+59=188.

Lattice Addition

246+159/ You would rewrite the numbers vertically. You would then make a box from the bottom line. Then draw two more lines creating 3 boxes for the three place values. You will then draw diagonal lines, causing the boxes to turn into triangles. You then add normally, 6+9 is 15, so you would write 15 in the triangles under 6&9. You will the same process for the rest of the numbers. After you will add diagonally. so 5+nothing=5, 1+9 is 10, so you would write a zero then bring the one to the next number, so 1+0+3=4, and so on. You will end up with 405.

Left to Right

537+265/ Take 5&2, add those two numbers together, creating 7, then 6+3=9, 7+5=12. You then can re write the number out again with the correct place value, but older students could process the 12 adding to the 10's digit. 537+265= 802.

Expanded Form

224+437/ You would write each number at based on their place value. 200+400, 20+30, 4+7. Making 600+50+11. Making 661.

Base Ten block

Using 10 Frames to visually show the numbers, and adding them together.

Understanding Triples

2-3-5 All go together. 2+3=5, 3+2=5, 5-2=3,5-3=2

What Makes an algorithm a good algorithm?

A good algorithm is based off; no new learning strategies(using information we already know), does it implement place value, is it expandable, and is it efficient.

Week 2

Convert from bases ten to other bases

Diagrams would just be drawing it out.

13 to base eight/ you would represent 13 with 1 base ten long and 3 extra units. Turning this into base eight, you can use 10 blocks to represent a long so it is easier to add together. Since it is being turned into base eight, you would take out eight units creating one loneg, then you have 5 units left over creating 15eight.

Convert from other bases to base ten:

Using diagrams would just be drawing it out instead of using the units squares.

24six being turnined into base ten. You can use the units squares to show the number of units in each long. Knowing that the base is six, this mean that there are 6 units in each long. There are 2 longs so, 2x6=12, then add the remaining 4 units, adding up to 16. So 24six is 16.

Base Ten Blocks

Place Values of 10, 10 units make 1 long, 10 longs make a flat. In different bases it would different number. Example: in base seven, it would be 7 units make a long, and 7 longs make a flat.

Week 1

Into to Bases

Video

Five and Ten Block Frames

Five and Ten blocks are used to help students count in an organized fashion, but also understand place value. In each, creating a "long" 10 longs creates a "flat"