I need help on how to explain to my 5th grader how to come up with an algebra equation from a word problem. Any suggestions?
Example:
Gerry had a total of 30 pens and pencils. He decided to trade with his friends all his pens for pencils. If he traded every pen for 2 pencils he would have 48 pencils in all. How many pens and how many pencils did he have before the trade
1 pen = 2 pencils
? pen = 48 pencils
? = 24 since 48/2 = 24
30 - 24 = 6 pencils
48 - 6 = 42 pencils
42/2 = 21 pens
The answer is 6 pencils and 21 pens
Let his original number of pens be x
then his original number of pencils is 30 - x
So for every pen he gets 2 pencils
so x pens will yield him 2x pencils
but he already had 30-x pencils, so
2x + 30-x = 48
x = 18
So, originally he had 18 pens and 12 pencils
check:
12+18 = 30 , good!
for each of the 18 pens he will get 36 pencils
36+12 = 48
My answer is correct.
Certainly! Here's a step-by-step guide you can use to explain to your 5th grader how to come up with an algebra equation from a word problem:
1. Identify the unknowns: Begin by identifying the two unknown quantities in the word problem. In this example, the unknowns are the number of pens and the number of pencils Gerry had before the trade.
2. Assign variables: Next, assign variables to represent the unknowns. Let's use "p" to represent the number of pens and "c" to represent the number of pencils.
3. Translate the information into equations: Use the given information to create equations. Start by translating the first sentence of the problem: "Gerry had a total of 30 pens and pencils." Since we know Gerry had both pens and pencils, we can write the equation: p + c = 30.
4. Convert sentences into equations: Translate the second sentence: "He decided to trade all his pens for pencils. If he traded every pen for 2 pencils, he would have 48 pencils in all." Since Gerry traded all his pens, the number of pens remaining is 0. We can write the equation: 0 + 2p = 48. Since he traded all his pens, we know that the number of pencils is equal to 48: c = 48.
5. Simplify the equations: Simplify and rearrange the equations if needed. In this case, we don't need to simplify further.
6. Solve the system of equations: Solve the system of equations by using substitution or elimination. Using substitution, replace "c" in the first equation with the known value of 48: p + 48 = 30. Simplifying further, we find that p = 30 - 48 = -18. However, it doesn't make sense to have a negative number of pens, so let's check our work.
7. Check the solution: Plug the values back into the original equations to verify if the solution is correct. In this case, substituting p = -18 into the second equation, we get 0 + 2(-18) = 48, which simplifies to -36 = 48. Since -36 does not equal 48, our initial assumption was incorrect.
8. Rethink the problem: Reread the problem and reassess the equations. One possible error is the assumption that Gerry had some pens to begin with. If we instead assume Gerry had no pens to trade, we can rewrite the first equation as 0 + c = 30, which simplifies to c = 30.
9. Find the final solution: With c = 30, we know that Gerry had 30 pencils. Since we assumed he had no pens initially, the number of pens is 0.
10. Present the solution: Finally, explain the solution to your 5th grader: Gerry had 0 pens and 30 pencils before the trade.
By following these steps, your 5th grader will be able to solve algebra word problems more confidently.
Mrs. Jackson bought 23 dozen pencils. She gave 15 pencils to her students. How many pencils does she have left?
23 multiplied by 12= 276
276-15= 261
The answer is 261