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Michael spent the following amounts of time building a bookcase: drawing up the plans: 2 hours cutting wood: 1 ½ hours assembling the bookcase: 2 hours Sanding and sealing: 3 ½ hours   What is the ratio of time spent cutting the wood to total time spent on the project? 1:9 1:6 1:5 3:7   Solution: We need to find two pieces of information in order to solve this problem: Time spent cutting the wood Total time spent on the project We find that it took 1 ½ hours to cut the wood from looking above at the information provided in the question. Next, find the time the entire project took by adding up all the times. We get 9 hours to complete the whole project. Now we solve our problem by doing the following steps: Our ratio is: time spent cutting wood : total time spent of the project We plug in the numbers to get: 1 ½:9 We multiply each term of the ratio by... read more

In math or science we come across terms such as inverse proportion and direct proportion. When two variables are directly proportional an increase in one variable causes an increase in the other variable. When two variables are inversely proportional an increase in one variable causes a decrease in the other variable.    Inverse Proportion: To illustrate inverse proportionality, I will use a common physics problem. Two golf balls are thrown down from a tall building at the same time and one ball has twice the velocity of the other ball. Which ball hits the ground first assuming only velocity is different?  We already know that velocity is approximately equal to distance / time. Let the velocity of the slower ball be v. Assuming only the velocity of the two balls is different, we can say approximately v = d / t. We can eliminate wind force, atmospheric force, and force of gravity since both balls will be affected equally. If you increase v,... read more

Often times experienced mathematicians tend to get comfortable with certain problem-solving strategies. For example, in a problem one might use a system of equations to solve a problem rather than employing a simpler more easy way to solve it. Though using system of equations are great, knowing how to solve problems using different approaches is important, not just for oneself, but for their students.   Take for example the following problem: A farmer has both pigs and chickens on his farm. There are 78 feet and 27 heads. How many pigs and how many chickens are there?   Solution 1: (Using Algebra System of Equations) 4p+2c=78 (pigs have 4 feet and chickens have 2 feet with 78 feet in total) p+c=27 (27 heads mean that the number of chicken and pigs total 27) Then by algebra p=27-c. Therefore by substitution, 4(27-c)+2c=78. 108-2c=78. 2c=30. c=15. Since, c=15, p+c=p+15=27. p=12. Therefore, the farmer has 15 chickens and 12 pigs... read more

Simply put, a graphic organizer is a visual way to communicate complicated material. Here is a graphic organizer that can be used to help students who are struggling to solve word problems: Click Here to Download Graphic Organizer  . This organizer teaches kids to go through the following 5 steps as they tackle a problem and includes helpful hints to a few of the most common phrases used in word problems. What Do I Know? Draw a picture Write down information  What I Need to Know? What are they asking me to find? What is My Plan? Use the helpful clues below to help set up a number sentence. Solve the Problem Use the plan and solve the problem. Check My Answer Did I  go back to the question to make sure that all the parts were answered? Does my answer to make sense? Write my final answer and circle it. If you have a student who is struggling... read more

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