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Reference - Operations, Decimals, Fractions, Mixed Numbers, Benchmark Numbers

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Common Core Standards
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1 MB|12 pages
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These student reference sheets cover all the basics. I suggest having students keep the reference sheets on their desks while they are working on problems so you can refer them back to the appropriate section of the reference sheet instead of reteaching everything when a student forgets how to do something.

The Five Operations of Arithmetic (yes, five!)

1. Explains what each operation means and if the commutative property holds for that operation. Includes examples written as mathematical expressions and in words.
2. Describes grouping (multiplication) as repeated addition when the number of groups is a whole number and taking a piece when the number of groups is a fraction. Establishes the commutative property for each interpretation.
3. Describes division as two separate operations (hence five operations total), "splitting up" and "fitting into". Explains that both of these operations lead to the same numerical answer, even though they ask different questions, which is why we only use one symbol for both of them.

Adding with Decimals

1. Explains the rules for adding with decimals.
2. Gives a step-by-step example of how to add with decimals.

Subtracting with Decimals

1. Explains the rules for subtracting with decimals.
2. Gives two step-by-step examples of subtracting with decimals including borrowing across zeros.

Multiplying with Decimals - Matrix Method

1. Explains how to multiply with decimals using the matrix method.
2. Gives two step-by-step examples of multiplying with decimals using the matrix method.

Multiplying with Decimals - Traditional Method

1. Explains how to multiply with decimals using the traditional method.
2. Gives a completely worked out example of multiplying with decimals using this method.

Long Division

1. Explains the four steps of the long division algorithm.
2. Explains what to do if there are no more digits to bring down but you didn't get a zero the last time you subtracted.
3. Shows examples of putting the decimal in the same place in the dividend and quotient.
4. Reminds students not to be afraid of putting a zero in the quotient (a lot of my students neglect to put zeros in for some reason).
5. Explains the importance of putting the digits of the quotient in the correct place.
6. Explains to move a decimal if it is in the divisor (and to do the same thing to the dividend).
7. Explains repeating decimals.

Multiplying and Dividing by Powers of 10

1. Explains the rule for multiplying and dividing by powers of 10.
2. Explains what is really happening to the value of the digits when multiplying or dividing by a power of 10.

Introduction to Fractions and Mixed Numbers

1. Explains what a fraction is as well as the difference between proper fractions, improper fractions, and mixed numbers.
2. Reminds students that the fraction bar can also mean division.
3. Reminds students that a fraction with a 1 in the denominator is equivalent to the numerator.
4. Gives examples of writing a number as an improper fraction, mixed number, or whole number plus proper fraction.
5. Explains how to convert between mixed numbers and improper fractions.

Equivalent Fractions

1. Explains what equivalent fractions are.
2. Explains how you can tell if two fractions are equivalent.
3. Explains simple strategy (assuming numbers are multiples of each other) for determining the missing number that would make two fractions equivalent.
4. Explains how to create equivalent fractions.
5. Explains how to reduce fractions.

Operations with Fractions

1. Explains how to add and subtract fractions with like or unlike denominators.
2. Explains how to divide fractions.
3. Explains how to multiply fractions.
4. Explains how to reduce before multiplying.
5. Explains how to cancel before multiplying.

Operations with Mixed Numbers

1. Explains how to add mixed numbers including what to do if you wind up with an improper fraction inside the mixed number.
2. Explains how to subtract mixed numbers including what to do if the fraction part of the subtrahend is larger than that of the minuend.
3. Explains how to multiply and divide with mixed numbers.

Benchmark Numbers

1. Charts all benchmark numbers that students should be familiar with (halves, thirds, fourths, fifths, eighths, and tenths).
2. Explain how to quickly derive the benchmark numbers.
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