Elementary Mathematics

Number line

subtracting integers using keep- change method

simplify fractions

common denominators (+/-)

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Q. Why do we need to find common denominators when we add and subtract fractions?A: the same size pieces

Pigs and chickens, we found that there was more then five ways to find out that there was 18 animals and they counted 52 feet. The answer was 10 chickens and 9 pigs.

We also learn base 10 and base 5

Base 10 refers to the numbering system in common use that uses decimal numbers. Base 10 is also called the decimal system or denary system.

Division can be done as repeated subtraction or through building and analyzing rectangular arrays.
By letting the cube, flat, rod, and unit represent 1, 0.1, 0.01, and 0.001, respectively, older students can explore and develop decimal concepts, compare decimals, and perform basic operations with decimal numbers.
The squares along each face make the blocks excellent tools for visualizing and internalizing the concepts of perimeter and surface area of structures. Counting unit blocks in a structure can form the basis for understanding and finding volume.

A divisibility test is a rule for determining whether one whole number is divisible by another. It is a quick way to find factors of large numbers. Divisibility Test for 3: if the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

Problem Solving Strategies

Move to base 5

multiplication in base 5

1208 / 26 = 46 R 12
46 / 26 = 1 R 20

Comparison -Diff models

11/15/16

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20- 15/920 - 1 6/9 +19 - 6/918 6/9 - 6/9 = 18 3/9

whole numbers

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Step 1: Separate the whole number from the fraction part of each number. Step 2: Add the whole numbers and then add the fractions. Again, we will need to get common denominators so that we can add the fractions. The second fractionalready has 10 as the denominator, so we are ready to add.

Backwards C

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134/9 + 71/9 121/9 + 64/9+ 188/920 5/9

11/15/16

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15+2 4/717 9/7

Now, think about the last answer (1 R 20), it means that 1208/26/26 = 1 (plus bits), in other words it tells us that we should put a "1" in the "262" column

Next we should put a 20 in the "261" column, and lastly a 12 in the units.

Why?

Because our first division work has really said that:

1208 = 46 × 26 + 12

So, 12 belongs in the units column, and from here on we are dealing with the first power of 26:

46 = 1 × 26 + 20 (so 20 belongs in the ×26 column, and we put 1 in the ×26×26 column)

So the answer is:
262 261 1s
1 20 12

divison

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divison of integerspartition model-12/4nnn nnn nnn nnnmeasurement (repeated subtraction)-12/ (-4)pppp pppppppp

integers and their arithmetic

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integers: negative and positive numbers that include 0 but are not fractions or decimals

Multiplication

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multiplication of integers3x4pppppppppppppppp pppp pppp-3x4nnnnnnnnnpppppppppremoves 3 groups of positive 4nnnnnnnnnnn=-12

fractions

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Multiple by what is missing. For example,1/8 + 5/6 ---> (3/3) 1/8 + 5/6 (4/4)

fraction concepts and operations

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models: area model, set model and liner4 strategies for comparing fractions:1. same size whole (denominator)2. same number of the parts (numerator)3.more or less than one4. closeness to 1/2 or 1

Repeated subtraction


Base 10 Blocks


Upwards


Long/short

modeling integers: number lines

prime