Elementary Mathematics

Week #1

The first week we went over the syllabus the supplies needed and how we will view and interact with the content videos.

Ploya's problems, 7 problem solving strategies

Ploya's Problems-UnDevCarLoUn- understand the problem -reread the problem -explain the problem to someone else -break it downDev- develop a plan -brainstormCar- Carry out a planLo- look back to see if your answer makes sense -work backward7 problem-solving strategies--Guess and check-Diagram-lists-algorithm

Week #2

This week we learned about building bases and 5-10's frames. We learned how to convert numbers from and into their bases. As well as adding numbers and their bases.

Converting bases

To convert to a numbers base you need to understand place valueFor example for a base of 61 long=6 small cubes6 small cubes=1 longnow to convert a base it takes some addition for example 25 base 6 would be represented like this-4 longs(6)= 41 small cube= 1 = 41and if you converted 41 base 6 you would prove the same

Week #3

This week we learned about alternative ways to do addition. We used methods like Friendly Numbers, Scratch, Lattice, and trading off.

Friendly numbers

Friendly numbers:Friendly numbers are numbers that end in zero.Example:364+136You would add 4 to 136 to get a friendly 140360+140 You would add 40 to 360 to get a friendly 400400+100=500

Trading off numbers

Trading off:Trading off is just like using friendly numbers, but you can do it with more numbers more than once to answer your questions concisely and make them all friendly numbers.

Scratch

Lattice

Week #4

In this week we learned how to use manipulatives to demonstrate subtraction. We also learned alternate methods to use to subtract.

Expanded form

Expanded form:Students would be given a subtraction problem just like this:56-23and they would have to put it into expanded form:50+6-(20+3)= 30+3=33

Equal addends

Equal Addends:This is similar to friendly numbers. You will add the same amount to both sides.One side will become a friendly number, then you can subtract everything else.

Diagrams

Week #5

In this weeks lesson we learned how to demonstrate multiplication using base ten blocks, picture drawings, and alternate solving methods.

Expanded form

Expanded form multiplication:When doing expanded form multiplication, it is the same as expanded form subtraction36 x 4430+6x 40+4Then you start multiplying diagonally To add the answers together to get a final answer

Left to right

Left-to-right multiplication is similar to the expanded formInstead of breaking the numbers apart into smaller pieces You will multiply diagonally all the way acrossUntil you add all the answers from multiplying diagonallyto get your final answer.

Area model

Lattice

Week #6

The overview of the lesson was how to tell the difference between numerator and denominator.

Numerator is the number of parts you haveThe denominator is how many pieces the whole is broken into

Repeated subtraction

Set up your division problem as normal, but add a long line for what you multiply your outside number byThe number that you get after multiplying you subtract from the inside number, you repeat the process until you can no longer multiply into the outside number. The final number you get from subtracting will be your numerator, and your denominator will be the original outside number. The numbers outside the line we drew need to be added together, then used as the whole number in the fraction.

Area model

Prime factorization

Prime numbers are the numbers that only have 2 factors 1 and itself as a factor.A number that isn't a prime is a composite.you take one large number and break it into its smallest possible form that it can be multiplied into. Those will be the prime numbers.

Week 12

Using two color counters to subtract

Week #1

We demonstrated how to add, subtract
and multiply using pictures.

Using two color counters to add integers

Week #10

We learned how to solve
fractions with reasoning
and understanding.

Solving addition and subtraction fractions
with different denominators and problems with mixed factors

When solving addition fractions to a mixed number you simply put them togetherwhen subtracting mixed numbers you subtract one from the mixed number then put the one less mixed number as the mixed number to the denominator on top and bottom. Then subtract the mixed number and fraction from the original fraction straight across and get a mixed number and your new fraction.to multiply different denominators you must factor and find similar prime numbers use the number it would be multiplied by and multiply it to your fraction take those new fractions and add or subtract to get your answer.Keep change flip

Week #9

Use drawings add, subtract,
and multiply fractions

Area model: Drawing a circle and coloring in the portion of the fractionLinear model: Drawing a rectangle, creating equal portions in the rectangle, filling portions of it in, and labeling the filled-in portion as a fraction.Set model: One color against another color causing a fraction in the whole to be one of the colors.

Week #8

Using manipulatives to demonstrate
addition, subtraction, and
multiplication

Using the fraction pieces to add numerators together and form larger fraction pieces, and vice versa for subtraction.

Week #7

Using manipulatives to divide

Using manipulatives to build
equivalent fractions

Using fraction pies etc. to show that wholes are fractions and inside fractions are even more fractions!