The end of the year is fast approaching. We are working on our final unit in both 6th and 7th grade mathematics. We will be focusing on linear equations and functions for the remainder of the year. I will be giving make up tests after school on Monday May 19th for any student who is missing a test or quiz grade. Feel free to come by on this day to make up any missing work!
The middle field projects are coming alone nicely! Make sure your 7th grade student is ready for critiques and revisions on Wednesday and Thursday.
Our seventh graders are working hard on their middle field project. Final rough drafts of the map, proposal, and materials list are due on Friday!
We have studied three ways to solve a proportion. 1) (for pricing) Find the unit cost In dollars per unit, then multiply by the number of units you want to buy. Solve using mental math. Solve using cross products. Use a variable to represent the unknown. Next, find the cross products. Finally solve the equation.
A proportion is an equation stating that two ratios are equal. For example 1/2 = 2/4. If the cross products of two ratios are equal, the ratios are equivalent. The cross products are found by multiplying the denominator of each by the numerator of the other.
A rate is a ratio that compares two quantities in different units. For example: 15 grams of fat in every 5 servings. A unit rate is the rate for one unit of a given quantity. For example: 3 grams of fat per serving. A unit cost is a unit rate involving cost. Hints: a unit rate always has a one on the bottom. We use the word "per" to describe the comparison of quantities.
A ratio is a comparison of two quantities by division. A ratio can be written in three different ways; ":" "/" or "to." take the ratio of a 5 by 7 photo for example. It can be written 5:7, 5/7, or 5 to 7. Equivalent ratios are two ratios that represent the same number.
Here are some examples of how to graph inequalities.
Solving inequalities is very similar to solving equations. There conceptual difference is that equations we are working with usually have one solution and wine qualities have many solutions. Follow the same rules as door equations, except make sure to switch the direction of the symbol if you multiply or divide by a negative number.
Now we are getting into equations with many steps. For these kinds odor equations you can either distribute, the add or subtract, and then multiply or divide. This is the way we did it in class. The other option is to divide both sides by what is outside the parenthesis, then add or subtract away the constant.
Two step equations can be a challenge sometimes. Just make sure you use reverse PEMDAS. You need to first undo addition or subtraction. Then you must undo multiplication or division.
In seventh grade we are starting to tackle positive and negative numbers. We use the word "integers" to talk about all whole numbers and their opposites (negatives). Adding and subtracting integers can become rather confusing if we try to memorize all of the rules. Instead we change all subtraction problems to adding the opposite of a number. For example 8 - 9 is the same thing as 8 + -9 (read 8 plus negative 9), And 7 - -4 is the same thing as 7 + +4. This way we only need to master addition rules. If you are adding two negative number we add them together and our sum is negative. If we have a positive number and a negative number, we find the difference and use the sign of the larger number. For example 8 - 9 = - (9 - 8) = -1. Happy adding!
This is the most important skill for your child to know to get ready for Algebra. We need to be able to find the solution to an equation. That means we need to be able to figure out what number we can substitute in for x to make the equation true. Sometimes we can find this number using mental math, but at this point we are practicing our skills to get ready for more difficult problems. in case we discussed using inverse operations to solve for x. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. There is one example for each pair of inverses.
We are making "I can" books in 7th grade, which will be a catalogue of all the skills that we are learning in class. I am so excited for the kids to have a record of all the things they are learning so that they will have a reference to look back on. each page on the inside will contain the name of the skill on the top of the page, the steps to complete the skill on the left, and one perfect example on the right. So far we have completed 4 pages in class. I will be uploading examples of the pages as we complete them. :)