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10.1 Pan-Balance Problems

10.1 Pan-Balance Problems. Tuesday, April 22 nd. What is a pan balance? What is an algebraic expression?. A pan balance allows numeric or algebraic expressions to be entered and compared. You can "weigh" the expressions you want to compare by entering them on either side of the balance.

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10.1 Pan-Balance Problems

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  1. 10.1 Pan-Balance Problems Tuesday, April 22nd

  2. What is a pan balance? What is an algebraic expression? A pan balance allows numeric or algebraic expressions to be entered and compared. You can "weigh" the expressions you want to compare by entering them on either side of the balance. An algebraic expression is an expression that contains a variable.

  3. Math Work In your math notebook, title the page 10.1, and answer the following questions. 6 / 3 = ? 60 / 3 = ? 600 / 3 = ? 81 / 9 = ? 810/ 9= ? 819/9 =?

  4. Practice with Pan Balance Problems Follow the link to practice solving pan balance problems. http://illuminations.nctm.org/Activity.aspx?id=3529

  5. 10.2 Pan Balance Problems with Two Balances Wednesday, April 23rd

  6. Math Work In your math notebook, title the page 10.2, solve the following riddles: What number am I? If you double me and add 6, you get 20. If you add 5 to me, you get 0. If you double me, add 4, subtract 4, and then divide by 2, you get 9. If you double me and double the result, you get 0.

  7. Pan Balance Problem To Review 1. One block weighs as much as 2 circles.

  8. Pan Balance Problem with Two Balances. One block weighs as much as 4 marbles. One triangle weighs as much as 6 marbles. We will explain this example more in class.

  9. 10.3 Algebraic Expressions Thursday, April 24th

  10. Math Work In your math notebook, title the page 10.3, complete the following tasks. 1. Read SRB page 218 2. Complete the Check for Understanding # 1,3,5

  11. Key Points to Remember Expressions use operation symbols (+, -, *, /) to combine numbers, but algebraic expressions combine variables and numbers. A situation can often be represented in several ways; in words, in a table, or in symbols. Algebraic expressions use variables and other symbols to represent situations.

  12. Examples of Algebraic Expressions Sue weighs 10lbs less than Jamal. If J = Jamal’s weight, then J-10 represents Sue’s weight. Isaac collected twice as many cans as Alex. If A= the number of cans Alex collected, then 2 *A, or 2A, represents the number of cans Isaac collected.

  13. 10.4 Rules, Tables, and Graphs: Part 1 Friday, April 25th

  14. Rate Rate describes a relationship between two quantities. In the problem above, we are comparing two quantities, miles and hours. Rates are often expressed with phrases that include the word per Rates can also be expressed as fractions: 3 apples/$1

  15. Rate of Speed A plane travels at a speed of 480 miles per hour. At that rate, how many miles will it travel in 1 minute? The answer above is 8 miles per minute. Since there is 60 minutes in 1 hour, divide 480 by 60. Thus the distance traveled in 1 minute is 8 miles. Answer the following for math work: At 8 miles per minute, how far will a plane travel in 10 minutes? In 2.5 minutes?

  16. 10.6 Rules, Tables, and Graphs: Part 2 Monday, May 5th

  17. Math Work In your math notebook, title the page 10.6, answer the following questions. My number times 25 will equal 100. What is my number? 15 divided by my number will equal 6. What is my number? Let y represent my number. 3y = 60. y = ?

  18. Double-Line Graphs Please watch the following video. http://studyjams.scholastic.com/studyjams/jams/math/data-analysis/double-line-graphs.htm

  19. 10.7 Reading Graphs Tuesday, May 6th

  20. Interpreting Mystery Graphs A mystery plot in math is a way of representing data in line plots normally a graphical presentation. However, the graphs are unlabeled. They are used to identify data sets and draw conclusions from the data sets by just studying the plots. Please watch the following example of a mystery graph: https://www.youtube.com/watch?v=KU2KbDxEOPI

  21. Math Work In your math notebook, title the page 10.7, answer the following questions to the nearest whole number. 25.4 = 36.9 = 89.7 = 50.92 = 74.09 = 63.52 =

  22. 10.8 Circumference of a Circle Wednesday, may 7th

  23. Math Work In your math notebook, title the page 10.8, find the following definitions in your SRB. 1. Circumference 2. diameter 3. radius

  24. Circumference of a Circle The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. Pi is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to Pi. This relationship is expressed in the following formula: Circumference/ diameter = Pi

  25. Radius of a Circle The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius. This relationship is expressed in the following formula: diameter formula, where diameter is the diameter and radius is the radius.

  26. Relationship between circumference, diameter, and radii Circumference, diameter and radii are measured in linear units, such as inches and centimeters. A circle has many different radii and many different diameters, each passing through the center. A real-life example of a radius is the spoke of a bicycle wheel. A 9-inch pizza is an example of a diameter: when one makes the first cut to slice a round pizza pie in half, this cut is the diameter of the pizza. So a 9-inch pizza has a 9-inch diameter. Let's look at some examples of finding the circumference of a circle. In these examples, we will use Pi = 3.14 to simplify our calculations.

  27. Example of Finding the Diameter Example 1: The radius of a circle is 2 inches. What is the diameter? Solution: d = 2 * r (diameter formula) diameter = 2 · (2 in) diameter = 4 in

  28. Circumference Video Please watch the following video: http://studyjams.scholastic.com/studyjams/jams/math/measurement/circumference.htm

  29. 10.9 Area of Circles Thursday, may 8th

  30. Area of a Circle The area of a circle is π (Pi) times the Radius squared, which is written: A = π × r2 Example: What is the area of a circle with radius of 3 m ? Radius = r = 3 Area = π × r2 = π × 32 = π × (3 × 3) = 3.14159... × 9 = 28.27 m2 (to 2 decimal places)

  31. Math Work In your math notebook, title the page 10.8, answer the following questions using the appropriate unit of measure. Amount of carpet needed to carpet a bedroom. Length of a dollar bill. Amount of juice the average person drinks in a week.

  32. 10.10 Review Friday, may 9th

  33. Key Concepts to Review Interpret mystery graphs and line plots. Use formulas to find circumference and area of a circle. Distinguish between circumference and area of a circle. Write algebraic expressions to represent situations. Solve one-step pan-balance problems. Solve two-step pan-balance problems. Represent rate problems as formulas.

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