Top Seven Things a 7th Grader should know…
#1) Four Basic Operations for Fractions, Mixed Numbers and Decimals
Addition, Subtraction, Multiplication, Division
For Fractions:
· Add/Subtract: Denominators the same—add or subtract the numerator, the denominator stays the same
o Denominators different—Make the denominators the same by using the LCM of existing denominators. Rewrite the fractions with the same denominators (remembering to change the numerator when necessary), then add/subtract.
· Multiply—Numerator X Numerator, Denominator X Denominator
· Divide—invert the 2nd fraction and multiply
For Decimals:
· Add/Subtract: line up the decimals, add zeros where necessary, and add/subtract as normal.
· Multiply – Multiply as usual. Count the number of digits to the right of any decimal(s). Fine final answer has the same number of digits to the right of the decimal as the numbers in the problem.
· Divide – if the divisor contains a decimal, move it so that there are no digits to the right of the decimal. If you move a decimal in the divisor, you must also move it in the dividend. Add zeros to the dividend if necessary, and then divide as usual.
For Mixed Numbers:
· Add: Rewrite the mixed numbers as fractions with common denominators. Add, then simplify.
· Subtract: Rewrite the mixed numbers as fractions with common denominators. Decide if you need to regroup. Subtract the fractions first, and then subtract the whole numbers. Simplify your answer.
· Multiply: Write the mixed number as an improper fraction. Multiply the numerators then multiply the denominators. Simplify your answer.
· Divide: Write the mixed number as an improper fraction. Multiply by the reciprocal of the divisor. Write the product in simplest form.
#2) Simplifying Fractions/Finding Common Denominators of 2 or more Fractions
· A fraction is in simplest form when its numerator and denominator have no common factor other
than 1.
· Writing fractions so that they have a common (the same) denominator allows you to add or subtract fractions, or compare two different fractions
o Find a common multiple of the denominators. Remember to multiply the numerator by the same number you multiplied the denominator!
#3) Conversions between fractions, decimals, and percents
· Fraction to Decimal—Divide the numerator by the denominator.
· Decimal to Fraction—Place the numbers to the right of the decimal in the numerator of the fraction. The denominator is the same as the place value used in the decimal. Simplify.
· Decimal to Percent—Move the decimal two places to the right and add the % sign.
· Percent to Decimal—Move the decimal two place to the left and drop the % sign.
· Fraction to Percent—Change the fraction to a decimal then the decimal to a percent.
· Percent to Fraction—Change the percent to a decimal then the decimal to a fraction
#4) Rounding whole numbers, fractions and decimals
Round to the nearest 1, 10, 100, 1000, 1/10, 1/100, 1/1000 place.
· Rounding is a way to estimate. Find the “place” you are rounding to (i.e. the tens place). Look at the digit one place to its right.
o If the digit to the right is 5 or greater, round up.
o If the digit to the right is less than 5, round down – the digit in your rounding place will stay the same
o When rounding decimals – after you round the decimal number you drop the digits to the right of the place you are rounding to.
o When rounding fractions, if the fraction part is equivalent to ½ or greater, round up. If the fraction part is equivalent to less than ½, round down.
#5) Greatest Common Factor (GCF) and Least Common Multiple (LCM)
· The GCF is the largest factor that will go into a set of numbers
o To find the GCF, consider the factors of each number separately and find the largest number that is in both lists
· The LCM is the smallest number that any given set of numbers will all divide into evenly.
o Consider the multiples of all the numbers separately. Find the smallest number that each have in their respective lists. Sometimes the LCM is the product of the set of numbers.
#6) Using formulas to find the area and perimeter/circumference of 2-dimensional figures
Shapes to include triangles, quadrilaterals and circles.
Formulas and calculators are provided.
#7) Graphing in the First Quadrant (x,y)
Graph and identify points in the first quadrant of the coordinate plane using ordered pairs.
Remember that coordinate pairs are written in (x,y) format, with the x-coordinate first.
In addition, all seventh graders should be comfortable with their multiplication facts through 12s. This is a great thing to work on through the year. Flash cards, multiplication tables and online practice are good options to improve their speed and accuracy. If they need more help, please have them see their math teacher before school or during Opportunities.