MATH ASSIGNMENTS FOR THE GARDEN
Apr. 4th, 2008 05:10 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
olgateaQUICK-AND-EASY LESSON PLAN #28
MATH ASSIGNMENTS FOR THE GARDEN
Spring: allegies, runny eyes ... and then, finally, ah ... gardening.
I love to garden, myself, but it wasn't until this year, working with a homeschooler who wanted to start his own garden that I realized how much math can be involved in the pursuit.
Sure, you can always just turn some dirt over, sprinkle some seeds, and hope that something sprouts. But if you want to do it in a more disciplined way, the possibilities are enormous for math/gardening problems.
What I'd like to do in this month's lesson plan is simply show how as a teacher or homeschooler, we educators can use gardening as a springboard to get children interested in some neat math problems.
The best way for me to do this is to describe what I've been doing with this one student, and then you'll see how you can take the same kinds of situations to develop questions and lesssons for the children with whom you work.
This boy, Chris, is an 18 year old Santa Fean, who has worked a bit with a landscaper, and who wanted to see what he can accomplish himself in terms of growing vegetables.
(By the way, this boy is in the Clonlara School program, whereby he gets credit for everything he does during this project. If you'd like to check out the Clonlara School, which I personally find wonderful, visit: clonlara.org)
Anyhow, here are some problems that have come up as he has been trying to plan out his garden:
PROBLEM 1: BEST DIMENSIONS OF THE GARDEN -
Chris was on a budget, and we determined that, based on his budget (lots of arithmetic here, as you can imagine), he could afford, at most, 48 linear feet of chicken wire for fencing. With that in mind, he started to think about the dimensions for his garden. Then he said, and I do quote: "You can use the same amount of fencing and still have the same area for different gardens. Can't you?"
Oh boy! I couldn't have scripted that question any better. This question launched us into an exploration into the relationship between perimeter and area of rectangles. I asked Chris to test out several rectangular plots with perimeter of 48, and to see if their areas all come out the same.
Chris tested three rectangular plots with perimeter of 48 (20 x 4; 10 x 14; 12 x 12), Chris started to see the light: that area increases as the rectangle more and more approximates a square. As a follow-up problem, I asked Chris to calculate the area of his garden if he took his fencing and used it as the circumference of a circular garden (he was amazed when he came up with the answer - see this month's POTM below for the challenge stated formally.)
Classroom teachers: here is a problem that is worthy in its own right. As your students explore such a question, you might also ask them why they think a square maximizes the area of all rectangles with the same perimeter.
Homeschoolers: whether or not you are planning a garden, this would be an interesting problem for any student who has studied area and perimeter of rectangles. What's great about this problem is that the answer defies children's "common sense," and thereby engages their sense of wonder.
PROBLEM 2: TESTING THE SOIL -
Once Chris decided on the shape of his garden (10 x 14, only because it fits better with the contour of his land), we decided that we had better test the soil. To do this, we ordered a Garden Soil Test Kit out of the Edmund Scientific catalog (800/728.6999 or www.scientificsonline.com) [Maybe I should start charging for all these free ads, huh?]
The kit is very cool, and it allows you to test your soil for pH, and then for concentrations of nitrogen, phosphorous and potash. Doing the tests involves both chemistry and a lot of arithmetic. We found out that Chris' soil has good pH for vegetables (6.5), but that it is extremely weak in nitrogen, phosphorous and potassium.
Classroom teachers: there's no reason why, if your school allows for interdisciplinary projects, you couldn't have your children use such a soil test kit to evaluate the soil for a school garden.
Homeschoolers: here's a fun way to blend the studies of horticulture, chemistry and math. Not only that, you'll get better tasting vegetables and prettier flowers!
PROBLEM 3: HOW TO ENRICH THE SOIL & CALCULATING UNIT PRICES FOR SOIL ENHANCERS -
Armed with our soil-test information, we visited the local greenhouse. We were all set to purchase separate bags of nitrogen, phosphorous and potash to make our own customized blend of fertilizer for Chris' soil. But the salesman who waited on us warned us that this would be something of a waste, since Chris' soil had never been cultivated. Turns out that when dealing with virgin soil, you must first use mulch and compost to give it fiber, and peat moss to help your plants grow. Once your soil has a good fiber content, then you can also add fertilizer in the customized manner we'd been planning.
The salesman at this first greenhouse recommended that we use equal parts of mulch, compost and peat moss.
We did some comparison shopping to find the best prices on these three enhancers. To do this, Chris called up five different nurseries and made a chart with headings like the one below:
Store Product Cost Cubic Feet Cost / Cubic Foot
He found these best deals:
mushroom mulch: $1.67/1.25 cubic feet = $1.33/ cubic foot cotton compost: $2.90/2 cubic feet = $1.45 cubic foot peat moss: $9.97/5.5 cubic feet = $1.81/ cubic foot
Classroom teachers: you could have your own students do research on this in the same way that we did our research. Have your students present their information in a spreadsheet (a computer spreadsheet if you have access to computers).
Homeschoolers: You can do this sort of project just as we did it.
PROBLEM #4: FIGURING OUT WHAT WE COULD AFFORD -
Using the information we had, we set out to find out if we could afford to purchase equal quantities of the three soil enhancers.
Our budget for soil enhancers was $100, and we had previously calculated that we needed a total of 70 cubic feet of enhancers for Chris' 10 x 14 foot garden (70/140 = .5 cubic feet of enhancer for every square foot of garden space, a previous calculation we had made).
I asked Chris how to figure out whether or not we could afford a 1:1:1 ratio of enhancers, recommended by the salesman at the first greenhouse. To do this, Chris divided the number of total cubic feet needed by 3 (70/3 = 23.33 cubic feet) and then he did this calculation:
23.33(unit cost of mulch) + 23.33 (unit cost compost) + 23.33 (unit cost peat moss).
Factoring out the 23.33 and plugging in values, he got: 23.33(1.33 + 1.45 + 1.81) = $107.08. Pretty close to our $100 budget, but budgets are budgets. This led to the next question: could we still use 70 cubic feet of enrichers and stay within budget?
We spoke to more greenhouse people to find out where we should cut back, and most of those we spoke to said that when dealing with virgin soil, the least important ingredient is peat moss, so we decided to cut back on that. No problem, since that was the most expensive enhancer anyhow.
The math question then became: if we keep the two quantities of compost the same and decrease the peat moss, how much do we have to decrease it to hit our target of $100.
Chris set up an algebraic equation as follows:
let x = the amount of mushroom mulch in cubic feet
Since we want to use the same amounts of compost as mushroom mulch, x is also equal to the amount of compost.
Since all three enhancers must add up to 70 cubic feet, the amount of peat moss may be expressed as 70 - 2x
Using our unit prices, we can then come up with an equation to give us the information we need, namely:
(cost mushroom mulch) + (cost cotton compost) + (cost peat moss) = $100
Plugging in our values, we got:
$1.33x + $1.45x + $1.81(70 - 2x) = $100
Solving this, Chris got: x = 31.78, which we rounded to 32, meaning that to get the budget down to $100, we must use 32 cubic feet of the mushroom mulch and compost. That leaves us room for just 6 cubic feet of the peat moss. (70 - 32x2 = 6)
Classroom teachers:
You can give your students a problem like this, or let them set a budget, set a cubic foot amount of enhancers, and have them use their actual data to get the answer.
Homeschoolers: Once again, this sort of problem gives you a chance to use a real-life math. And it's more motivating, of course, if you actually use the information to create a garden.
That's all for now.
Happy gardening!
http://www.algebrawizard.com/nuzltrs/105.html#lesson
MATH ASSIGNMENTS FOR THE GARDEN
Spring: allegies, runny eyes ... and then, finally, ah ... gardening.
I love to garden, myself, but it wasn't until this year, working with a homeschooler who wanted to start his own garden that I realized how much math can be involved in the pursuit.
Sure, you can always just turn some dirt over, sprinkle some seeds, and hope that something sprouts. But if you want to do it in a more disciplined way, the possibilities are enormous for math/gardening problems.
What I'd like to do in this month's lesson plan is simply show how as a teacher or homeschooler, we educators can use gardening as a springboard to get children interested in some neat math problems.
The best way for me to do this is to describe what I've been doing with this one student, and then you'll see how you can take the same kinds of situations to develop questions and lesssons for the children with whom you work.
This boy, Chris, is an 18 year old Santa Fean, who has worked a bit with a landscaper, and who wanted to see what he can accomplish himself in terms of growing vegetables.
(By the way, this boy is in the Clonlara School program, whereby he gets credit for everything he does during this project. If you'd like to check out the Clonlara School, which I personally find wonderful, visit: clonlara.org)
Anyhow, here are some problems that have come up as he has been trying to plan out his garden:
PROBLEM 1: BEST DIMENSIONS OF THE GARDEN -
Chris was on a budget, and we determined that, based on his budget (lots of arithmetic here, as you can imagine), he could afford, at most, 48 linear feet of chicken wire for fencing. With that in mind, he started to think about the dimensions for his garden. Then he said, and I do quote: "You can use the same amount of fencing and still have the same area for different gardens. Can't you?"
Oh boy! I couldn't have scripted that question any better. This question launched us into an exploration into the relationship between perimeter and area of rectangles. I asked Chris to test out several rectangular plots with perimeter of 48, and to see if their areas all come out the same.
Chris tested three rectangular plots with perimeter of 48 (20 x 4; 10 x 14; 12 x 12), Chris started to see the light: that area increases as the rectangle more and more approximates a square. As a follow-up problem, I asked Chris to calculate the area of his garden if he took his fencing and used it as the circumference of a circular garden (he was amazed when he came up with the answer - see this month's POTM below for the challenge stated formally.)
Classroom teachers: here is a problem that is worthy in its own right. As your students explore such a question, you might also ask them why they think a square maximizes the area of all rectangles with the same perimeter.
Homeschoolers: whether or not you are planning a garden, this would be an interesting problem for any student who has studied area and perimeter of rectangles. What's great about this problem is that the answer defies children's "common sense," and thereby engages their sense of wonder.
PROBLEM 2: TESTING THE SOIL -
Once Chris decided on the shape of his garden (10 x 14, only because it fits better with the contour of his land), we decided that we had better test the soil. To do this, we ordered a Garden Soil Test Kit out of the Edmund Scientific catalog (800/728.6999 or www.scientificsonline.com) [Maybe I should start charging for all these free ads, huh?]
The kit is very cool, and it allows you to test your soil for pH, and then for concentrations of nitrogen, phosphorous and potash. Doing the tests involves both chemistry and a lot of arithmetic. We found out that Chris' soil has good pH for vegetables (6.5), but that it is extremely weak in nitrogen, phosphorous and potassium.
Classroom teachers: there's no reason why, if your school allows for interdisciplinary projects, you couldn't have your children use such a soil test kit to evaluate the soil for a school garden.
Homeschoolers: here's a fun way to blend the studies of horticulture, chemistry and math. Not only that, you'll get better tasting vegetables and prettier flowers!
PROBLEM 3: HOW TO ENRICH THE SOIL & CALCULATING UNIT PRICES FOR SOIL ENHANCERS -
Armed with our soil-test information, we visited the local greenhouse. We were all set to purchase separate bags of nitrogen, phosphorous and potash to make our own customized blend of fertilizer for Chris' soil. But the salesman who waited on us warned us that this would be something of a waste, since Chris' soil had never been cultivated. Turns out that when dealing with virgin soil, you must first use mulch and compost to give it fiber, and peat moss to help your plants grow. Once your soil has a good fiber content, then you can also add fertilizer in the customized manner we'd been planning.
The salesman at this first greenhouse recommended that we use equal parts of mulch, compost and peat moss.
We did some comparison shopping to find the best prices on these three enhancers. To do this, Chris called up five different nurseries and made a chart with headings like the one below:
Store Product Cost Cubic Feet Cost / Cubic Foot
He found these best deals:
mushroom mulch: $1.67/1.25 cubic feet = $1.33/ cubic foot cotton compost: $2.90/2 cubic feet = $1.45 cubic foot peat moss: $9.97/5.5 cubic feet = $1.81/ cubic foot
Classroom teachers: you could have your own students do research on this in the same way that we did our research. Have your students present their information in a spreadsheet (a computer spreadsheet if you have access to computers).
Homeschoolers: You can do this sort of project just as we did it.
PROBLEM #4: FIGURING OUT WHAT WE COULD AFFORD -
Using the information we had, we set out to find out if we could afford to purchase equal quantities of the three soil enhancers.
Our budget for soil enhancers was $100, and we had previously calculated that we needed a total of 70 cubic feet of enhancers for Chris' 10 x 14 foot garden (70/140 = .5 cubic feet of enhancer for every square foot of garden space, a previous calculation we had made).
I asked Chris how to figure out whether or not we could afford a 1:1:1 ratio of enhancers, recommended by the salesman at the first greenhouse. To do this, Chris divided the number of total cubic feet needed by 3 (70/3 = 23.33 cubic feet) and then he did this calculation:
23.33(unit cost of mulch) + 23.33 (unit cost compost) + 23.33 (unit cost peat moss).
Factoring out the 23.33 and plugging in values, he got: 23.33(1.33 + 1.45 + 1.81) = $107.08. Pretty close to our $100 budget, but budgets are budgets. This led to the next question: could we still use 70 cubic feet of enrichers and stay within budget?
We spoke to more greenhouse people to find out where we should cut back, and most of those we spoke to said that when dealing with virgin soil, the least important ingredient is peat moss, so we decided to cut back on that. No problem, since that was the most expensive enhancer anyhow.
The math question then became: if we keep the two quantities of compost the same and decrease the peat moss, how much do we have to decrease it to hit our target of $100.
Chris set up an algebraic equation as follows:
let x = the amount of mushroom mulch in cubic feet
Since we want to use the same amounts of compost as mushroom mulch, x is also equal to the amount of compost.
Since all three enhancers must add up to 70 cubic feet, the amount of peat moss may be expressed as 70 - 2x
Using our unit prices, we can then come up with an equation to give us the information we need, namely:
(cost mushroom mulch) + (cost cotton compost) + (cost peat moss) = $100
Plugging in our values, we got:
$1.33x + $1.45x + $1.81(70 - 2x) = $100
Solving this, Chris got: x = 31.78, which we rounded to 32, meaning that to get the budget down to $100, we must use 32 cubic feet of the mushroom mulch and compost. That leaves us room for just 6 cubic feet of the peat moss. (70 - 32x2 = 6)
Classroom teachers:
You can give your students a problem like this, or let them set a budget, set a cubic foot amount of enhancers, and have them use their actual data to get the answer.
Homeschoolers: Once again, this sort of problem gives you a chance to use a real-life math. And it's more motivating, of course, if you actually use the information to create a garden.
That's all for now.
Happy gardening!
http://www.algebrawizard.com/nuzltrs/105.html#lesson
