Key Words:
Addition - increased by, more than, combined, together, total of, sum, added to, larger than, longer than
Subtraction - decreased by, minus, less, difference between, less than, fewer than
Multiplication - of, times, multiplied by, product of
Division - per, out of, ratio of, quotient of, percent (divide by 100)
Equals - is, are, was, were, will be, gives, yields
Translating Phrases into Algebraic Expressions:
Remember? "Less than" is backwards in the math from how you say it in words!
Here are some more wordy examples:
The expression they're looking for is "w + 30".
Addition - increased by, more than, combined, together, total of, sum, added to, larger than, longer than
Subtraction - decreased by, minus, less, difference between, less than, fewer than
Multiplication - of, times, multiplied by, product of
Division - per, out of, ratio of, quotient of, percent (divide by 100)
Equals - is, are, was, were, will be, gives, yields
Translating Phrases into Algebraic Expressions:
- Translate "the sum of 8 and y" into an algebraic expression.
- Translate "4 less than x" into an algebraic expression.
Remember? "Less than" is backwards in the math from how you say it in words!
- Translate "x multiplied by 13" into an algebraic expression.
- Translate "the quotient of x and 3" into an algebraic expression.
- Translate "the difference of 5 and y" into an algebraic expression.
- Translate "the ratio of 9 more than x to x" into an algebraic expression.
- Translate "nine less than the total of a number and two" into an algebraic expression, and simplify.
Here are some more wordy examples:
- The length of a football field is 30 yards more than its width. Express the length of the field in terms of its width w.
The expression they're looking for is "w + 30".
Summer Math Review for Students Entering 6th Grade
By the end of 5th grade, your child should be proficient in the skills listed below. For your convenience,
we listed some recommended websites to help your child practice these skills. We encourage parents to
monitor students’ use of the Internet.
Add, Subtract and Multiply Fractions and Mixed Numbers:
http://www.sheppardsoftware.com/ mathgames/fractions/FruitShootFractionsAddition. html
http://www.mathplayground.com/ fractions_sub.html
http://www.math-play.com/Multiplying-Fractions-Millionaire/Multiplying-Fractions-Millionaire.html
http://www.math.com/school/subject1/practice/S1U4L7/S1U4L7Pract.html
Convert Mixed Numbers into Improper Fractions and Improper Fractions into Mixed Numbers:
http://www.sheppardsoftware.com/ mathgames/
fractions/mathman_improper_fractions. html
http://www.quia.com/cb/186132.html
Place value:
http://www.topmarks.co.uk/maths-games/7-11-years/place-value
Multiplication of Decimals through the Hundredths Place:
http://www.funbrain.com/cgi-bin/fb.cgi?A1=start3&A2=Medium&ALG=No&INSTRUCTS=1
Long Division of Whole Numbers:
http://www.kidsnumbers.com/long-division.php
Please Note: All children should have multiplication and division facts through 12 committed to
memory. For enrichment at any grade level, students can practice word problems. Please note the key
words in the word problems before solving.
OTHER WEBSITES:
http://www.mathplayground.com/wordproblems.html
https://www.khanacademy.org
http://www.purplemath.com
http://reflexmath.com
By the end of 5th grade, your child should be proficient in the skills listed below. For your convenience,
we listed some recommended websites to help your child practice these skills. We encourage parents to
monitor students’ use of the Internet.
Add, Subtract and Multiply Fractions and Mixed Numbers:
http://www.sheppardsoftware.com/ mathgames/fractions/FruitShootFractionsAddition. html
http://www.mathplayground.com/ fractions_sub.html
http://www.math-play.com/Multiplying-Fractions-Millionaire/Multiplying-Fractions-Millionaire.html
http://www.math.com/school/subject1/practice/S1U4L7/S1U4L7Pract.html
Convert Mixed Numbers into Improper Fractions and Improper Fractions into Mixed Numbers:
http://www.sheppardsoftware.com/ mathgames/
fractions/mathman_improper_fractions. html
http://www.quia.com/cb/186132.html
Place value:
http://www.topmarks.co.uk/maths-games/7-11-years/place-value
Multiplication of Decimals through the Hundredths Place:
http://www.funbrain.com/cgi-bin/fb.cgi?A1=start3&A2=Medium&ALG=No&INSTRUCTS=1
Long Division of Whole Numbers:
http://www.kidsnumbers.com/long-division.php
Please Note: All children should have multiplication and division facts through 12 committed to
memory. For enrichment at any grade level, students can practice word problems. Please note the key
words in the word problems before solving.
OTHER WEBSITES:
http://www.mathplayground.com/wordproblems.html
https://www.khanacademy.org
http://www.purplemath.com
http://reflexmath.com
Summer Math Review for Students Entering 7th Grade
By the end of 6th grade, your child should be proficient in the skills listed below. For your convenience,
we listed some recommended websites to help your child practice these skills. We encourage parents to
monitor students’ use of the Internet.
All children should have multiplication and division facts through 12 and divisibility rules for
2, 3, 4, 5, 6, 8, 9 and 10 committed to memory.
For enrichment at any grade level, students can practice word problems. Please note the key words
in the word problems before solving.
WEBSITES:
http://www.mathplayground.com/wordproblems.html
www.khanacademy.org
www.purplemath.com
www.mathplayground.com
www.tenmarks.com
http://math.about.com/cs/ arithmetic/a/timestables.html
http://reflexmath.com
By the end of 6th grade, your child should be proficient in the skills listed below. For your convenience,
we listed some recommended websites to help your child practice these skills. We encourage parents to
monitor students’ use of the Internet.
- Fraction and decimal equivalents
- Decimal equivalents for unit fractions
- All operations involving whole numbers, decimals and fractions
- Estimation
- Order of operations
- Area of rectangles, triangles, and trapezoids
- Volume of rectangular and triangular prisms
- Mean, median and mode
All children should have multiplication and division facts through 12 and divisibility rules for
2, 3, 4, 5, 6, 8, 9 and 10 committed to memory.
For enrichment at any grade level, students can practice word problems. Please note the key words
in the word problems before solving.
WEBSITES:
http://www.mathplayground.com/wordproblems.html
www.khanacademy.org
www.purplemath.com
www.mathplayground.com
www.tenmarks.com
http://math.about.com/cs/ arithmetic/a/timestables.html
http://reflexmath.com
Summer Math Review for Students Entering 8th Grade
By the end of 7th grade, your child should be proficient in the skills listed below. For your convenience,
we listed some recommended websites to help your child practice these skills. We encourage parents to
monitor students’ use of the Internet.
- All operations involving rational numbers (whole numbers, decimals, fractions and integers)
- Order of operations and algebraic properties
- Identify polygons to 10 sides
- Identify prisms by their congruent and parallel bases
- Identify angles and angular relationships
- Identify triangles based on sides and angles
- Application of formulas for perimeter, circumference, area, and volume
All children should have multiplication and division facts through 12 and divisibility rules for
2, 3, 4, 5, 6, 8, 9 and 10 committed to memory.
For enrichment at any grade level, students can practice word problems. Please note the key words
in the word problems before solving.
WEBSITES:
http://www.mathplayground.com/wordproblems.html
www.khanacademy.org
www.purplemath.com
www.mathplayground.com
www.tenmarks.com
http://math.about.com/cs/arithmetic/a/timestables.html
http://reflexmath.com