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HOME OF THE PATRIOTS! |
6th Grade Mathematics (TEAM 6A)
GRADE 6 MATHEMATICS
Dear Parents,
Below are examples of what your child is learning in Grade 6. We hope you find this useful.
GRADE 6 MATHEMATICS - UNIT 8 ALGEBRA
Students need to:
• Draw pictures and use manipulatives to demonstrate a conceptual understanding
of proportion.
• Solve problems using proportional reasoning.
• Represent and recognize direct variation graphically, numerically, and symbolically.
• Identify and interpret the constant of proportionality in direct relationships.
1. Karen is mixing paint. She mixed 3 cups of red with 5 cups of white to make her favorite shade of pink. Her brother, Phil,dumped in another cup of red paint. How much white paint must Karen add to make the mixture return to her favorite shade of pink?
Sample Response:
To get the desired pink color we need a white to red ratio of 5:3. So, Karen needs about 6.67 cups of white paint. She has already poured in 5 cups of white so she must add 1.67 cups.
2. A rectangle has sides 3 cm and 5 cm. Draw a smaller and a larger rectangle with sides in the same proportion.
3. At the spring sale, prices were marked 20% off. How much would you pay for an item that regularly costs $10.50?
Sample Response:
When prices are marked off 20%, you must pay 80% of the regular price (100% - 20% = 80%). You will pay $8.40 for the item.
4. Karen discovered that ¾ of a gallon of paint would cover 25% of her walls. How many gallons will she need to cover all of her walls?
Sample Response:
Karen needs 3 gallons of paint to cover all her walls.
VOCABULARY
Constant of proportionality: The constant value of the ratio of two proportional quantities x and y; usually written y= kx, where k is the constant of proportionality. In a proportional relationship, y=kx, k is the constant of proportionality,which is the value of the ratio between y and x.
Direct Proportion (Direct Variation): The relation between two quantities whose ratio remains constant. When one variable increases the other increases. When A changes,
then B changes by the same factor: A=kB, where k is the
constant of variation.
Equation: A mathematical sentence that contains an equals sign.
Proportion: An equation which states that two ratios are equal.
Proportional: Two quantities are proportional if they are multiples of each other
Rule: A description or an equation that indicates the relationship among variables. An example might be: CD’s cost $12 each. The variables are number of CD’s and total cost. We could represent their relationship with an equation: T=12n.
WAYS PARENTS CAN HELP
Here are some activities you and your students can do together:
•Look for situations in which one quantity can be expressed as a multiple of another. For example, when figuring how much ground beef to buy, we might calculate ¼ pound perperson. We can represent this relationship as
g=1/4p. If everyone gets 3 cookies for dessert, the number of cookies we need (c)equals 3 times the number diners (d) or c =3d.
•If your student earns an allowance or has a job, make a graph showing how much money is received. Show pay periods on the horizontal axis and total amount received on
the vertical axis.
•Identify quantities in your environment that vary in the same way. For example, the more movie tickets you buy, the more money you pay. When you enlarge a photograph,
how do the dimensions change?
•Read ads that contain percent reductions and determine how much sale items will cost solving proportions.
•Identify best buys by comparing prices
for unit amounts.
Some links to try:
http://www.figurethis.org/challenges/c77/challenge.htm
http://www.figurethis.org/challenges/c47/challenge.htm
http://www.figurethis.org/challenges/c25/challenge.htm
http://www.math.com/school/subject1/lessons/S1U2L2GL.html
http://cne.gmu.edu/modules/dau/algebra/fractions/frac5_frm.html
http://www.aaaknow.com/pct68_x3.htm
Text References
If you have futher questions or concerns, please contact me at school. This will be a very challenging unit for our sixth grade students as they work with these algebraic concepts!
Ms. Kem Carter
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To Contact Ms. Carter:
Class Schedule:
Homeroom 7:30-7:35
1st period 7:35-8:35
2nd period 8:35-9:35
3rd period 9:35-10:35
4th/5th period 10:35-12:05 (planning)
6th period 12:05-1:35
(lunch 12:10-12:40)
7th period 1:35-2:35
School Voice Mail: (706) 855-2514, ext.# 310
Email Address: kem.carter@ccboe.net
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