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transcript
Solving Seventh-grade math problemS in the kitchen & in the garden
Making MatheMatics
Delicious
C h e z Pa n i s s e F o u n d at i o n
Cultivating a New Generation
Making MatheMatics
DeliciousSolving Seventh-grade math problemS Solving Seventh-grade math problemS
in the kitchen & in the gardenin the kitchen & in the garden
C h e z Pa n i s s e F o u n d at i o n
Cultivating a New Generation
� • m a k i n g m at h e m at i c s d e l i c i o u s | s e v e n t h g r a d e
Foreword
our mission at the Chez Panisse Foundation is to educate, nurture, and empower students to build a more sustainable future. our program, the edible schoolyard, brings this mission to life by involving students in growing, harvesting, cooking and enjoying simply-cooked, seasonal, organic meals. We lure students into the kitchen with delicious smells and flavors and find them excited by the simple pleasures of the garden—picking raspberries, digging up beds, or planting seeds.
“Learning by doing” is central to the way we teach at the edible schoolyard. in our kitchen and garden classes, students partici-pate fully in the cycle of producing organic and seasonal foods. they may bring kitchen and garden waste to the compost pile, for example, turn and tend the pile, spread the finished compost on garden beds before planting lettuce or tomatoes, then use the harvest from these plants in a delicious salad for sharing.
We also strive to bring the academic classroom to life, whether it’s through a social studies lesson on ancient grains or a science lesson on the composition and properties of soil. For the last two years we have also been exploring how to weave meaningful mathematics into our instruction. We do this because all students need mathematics skills to become socially responsible leaders and productive citizens and, in the short term, to enter college without need for remediation.
this book is not a comprehensive math curriculum. Rather, it offers a window onto our approach to teaching and learning. teachers may adapt these lessons according to the resources and concerns of their own classrooms, or simply use them for inspiration. our goal is to empower students to grapple with the intrinsic complexities of mathematics in a way that is purpose-ful and not devoid of common sense; with this book, we hope to provide a starting place.
Carina Wong Executive Director Chez Panisse Foundation
IntroductIon
When we began thinking about the importance of integrating kitchen and garden learning into the academic classroom, we did not have a mathematics book in mind. soon, however, teachers at the edible schoolyard began developing their own strategies for engaging students with mathematics. Making Mathematics Deli-cious is one product of the collective wisdom we have developed.
this book differs from many supplementary curriculum materials in its alignment with California mathematics standards for middle school.this table lists the mathematics content standards that inform our lessons:
Grade contentStrand Standard
Mathematicscontent
7 number Sense 7nS1.0
students know the properties of, and compute with, rational numbers expressed in a variety of forms.
7 number Sense 7nS2.0
students use exponents, powers, and roots and use expo-nents in working with fractions.
7 algebra & Functions 7aF1.0
students express quantitative relationships by using alge-braic terminology, expressions, equations, inequalities, and graphs.
7 algebra & Functions 7aF3.0
students graph and interpret linear and some non-linear functions.
7 measurement and geometry 7mg1.0
students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems.
7 measurement and geometry 7mg2.0
students compute the perimeter, area, and volume of common geometric objects and use the results to find mea-sures of less common objects. they know how perimeter, area, and volume are affected by changes of scale.
7 measurement and geometry 7mg2.0
students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures.
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the context for each assignment is drawn directly from the original edible schoolyard at Martin Luther King Jr. Middle school in Berkeley, California. however, middle school teachers from all regions will find these assignments relevant and useful for any mathematics classroom, with or without an adjoining school garden.
these mathematics assignments are what we call tasks. tasks are problem-based and set in a real-world context. they involve multiple steps and usually cannot be completed in one class period. nor can the tasks simply be assigned to the students as handouts. the tasks require conversation, experimentation, and at times collaboration. You may also notice that the tasks involve a lot of reading; this is because a task must require sense-making on the part of the student if it is to be a truly useful tool for learn-ing. each task is also designed to be accessible for all learners and to promote mathematical thinking over imitative computa-tion work.
When students make bread dough in the kitchen, for example, they must estimate to decide when it has doubled in volume. thus making bread provides an excellent opportunity for students to understand the relationship between concomitant increases in volume and linear dimensions. in the garden, students make potting soils to nurture plants through various stages of growth. the recipe for each type of soil is presented in a variety of standard and non-standard units because in the real world, gardeners often use cans, wheelbarrows, and spades to measure. this experience allows students to hone their quantita-tive literacy while also deepening their understanding of how gardeners work.
HowtHISbookISorGanIzed
this book includes five tasks for use with seventh-grade stu-dents. each task is introduced using handmade recipes, draw-ings, or images from the edible schoolyard. For the teacher, a set of notes is provided to explain underlying mathematical concepts and how to approach the lesson. the solution to each task is also included. Related tasks are outlined in booklets for seventh and eighth grades.
We published the three grades as a set so you could see how similar recipes or contexts can provide tasks of increasing diffi-culty. For example, the sixth-grade lesson using a structure in the edible schoolyard called the Ramada involves measuring angles and calculating area. at the eighth-grade level, the Ramada task involves constructing a scale model using measurements from the actual structure at the edible schoolyard.
We hope that these tasks will inspire you to look around and find the math in your kitchen, garden, or community.
MakInGMatHeMatIcSdelIcIouS•Grade7
probleMS&queStIonS ForStudentS
wHole-wHeateGGbread:relationshipbetweenchanges inVolumeandchangesinlineardimensions 8
GarlIcparMeSancrackerS:VolumeofaSphereandVolumeofarectangularprism 12
rHubarbJaM:linearFunctions anddirectVariation 16
edIbleScHoolyardSoIl: rate,proportionality,percentages, andnumberSense 20
tHetunnelIntHeedIbleScHoolyard:circumferenceandSurfacearea 23
teacHernoteS &SolutIonS
wHole-wHeat eGGbread 26
GarlIcparMeSan crackerS 30
rHubarbJaM 32
edIbleScHoolyardSoIl 35
tHetunnelIn tHeedIbleScHoolyard 38
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tHeMatHeMatIcSoF wHole-wHeateGGbread
estimating
the recipe for Whole–Wheat egg Bread says
that the dough should be left to rise until
doubled. this means that the dough is left to rest
until its volume has increased by a factor of 2.
1. Working in a group of two or three, talk about
how you might know if a ball of dough has
doubled in volume.
2. You might begin by estimating the diameter of
the ball of dough before it rises. This is shown
in the diagram below.
Then use this first
measure to estimate
the diameter of the
risen dough.
a. We know that the after-rising volume
needs to be twice the before-rising volume.
What will be the relationship between the
before- and after-rising diameter?
b. Will the diameter also increase by a factor
of 2?
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investigating increases in linear Measure and Volume of solids
3. The ball of dough is a sphere but since spheres
are difficult to make, start this investigation by
making cubes.
a. Use squared paper to create a set of cubes
with 1, 2, 3, 4, 5, and 6 centimeters per side.
b. Calculate the volume of each cube.
c. Create a table of data to show the length of
side and the corresponding volume.
d. Make a graph of your data. Record length
of side along the x-axis and volume along the
y-axis.
4. Use your data to justify each of the following
statements as true or false.
a. When you double the volume of a cube, the
length of side will always double.
b. When you double the length of side of a
cube, the volume will always be 8 times greater.
5. Use your data and make any needed
calculations to answer the following questions.
tHeMatHeMatIcSoF wHole-wHeateGGbread(cont )
a. When you double the volume of a cube, the
ratio of the volumes will be 1:2. What will be
the ratio of the corresponding lengths of side?
b. When you quadruple the volume of a cube,
the ratio of the volumes will be 1:4. What will
be the ratio of the corresponding lengths of side?
applying Your Findings
6. Can your findings apply to a ball of dough?
a. When you double the volume of a sphere, the
ratio of the volumes will be 1:2. What will be
the ratio of the corresponding radii?
b. Suppose that the estimated radius of a ball of
dough is 10 centimeters. What will be the radius
of the ball of dough after it doubles in volume?
c. Complete the table below to show a set of
before-and after-radii for balls of dough that
double in volume. What conclusions can you
draw from the data?
When a Ball of Dough Doubles in Volume
before-rising radius after-rising radius in centimeters in centimeters
4
5
6
7
1� • m a k i n g m at h e m at i c s d e l i c i o u s | s e v e n t h g r a d e
tHeMatHeMatIcSoFGarlIcparMeSancrackerS
1� • m a k i n g m at h e m at i c s d e l i c i o u s | s e v e n t h g r a d e
Measuring Dough
once the dough is prepared and gathered into a
ball, it approximates a sphere with a diameter of
3 inches.
1. What is the volume of this ball of dough?
2. This recipe tells us to divide the ball of dough
in half and roll each half separately. What is
the volume of each half?
tHeMatHeMatIcSoFGarlIc parMeSancrackerS(cont )
3. The recipe tells us to roll the half ball of dough
into a long, thin rectangular prism that is 1/16 inch thick, 1H inches wide, and an
unknown length x. What is the length of
the rectangular prism that is formed by rolling
half the dough, as shown in the following
diagram?
4. How many 1H-inch square Garlic Parmesan
Crackers can be cut from the whole ball of
dough?
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tHeMatHeMatIcS oFrHubarbJaM
increasing a Recipe
1. The recipe for Rhubarb Jam shows that for
every 3 cups of rhubarb, H cup of sugar is
necessary. Copy and complete this table to show
the amounts of rhubarb and the corresponding
amounts of sugar required when the recipe is
increased.
2. We can think of the number of cups of rhubarb
and the number of cups of sugar as two
variables.
Let x represent the number of cups of rhubarb.
Let y represent the number of cups of sugar.
a. Which of these two variables does it make
sense to call the independent variable?
Explain why.
b. Which of these two variables does it make
sense to call the dependent variable?
Explain why.
Quantities of Fruit and Sugar in Rhubarb Jam
number of cups numbers of cups of rhubarb of sugar
3 H
6
9
12
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3. Write a formula to express the number of cups
of sugar in terms of the number of cups of
rhubarb.
4. Draw a graph to show the relationship between
the number of cups of rhubarb and number
of cups of sugar. Record the number of cups of
rhubarb along the x-axis and the number of
cups of sugar along the y-axis.
5. Do the points form a line or a curve? Draw a
line or a curve to illustrate your answer.
6. What is the ratio of the number of cups of
sugar to the number of cups of rhubarb?
tHeMatHeMatIcS oFrHubarbJaM(cont )
7. What is the slope of the line?
8. What does the slope of the line represent in
terms of making Rhubarb Jam?
9. Does the line pass through the point (0,0)?
10. Does the number of cups of sugar needed to
make Rhubarb Jam vary directly with the
number of cups of rhubarb? Explain how
you know
� 0 • m a k i n g m at h e m at i c s d e l i c i o u s | s e v e n t h g r a d e
tHeMatHeMatIcSoF edIbleScHoolyardSoIl
graphing the components of soil
in the lesson on soil, you learned that an
understanding of soil is crucial to the knowledge
of life cycles and our food systems.
1. In this lesson you learned that one teaspoon of
rich soil contains 5 billion bacteria, 20 million
fungi, and 1 million protozoa.
Write the numbers, 5 billion bacteria, 20
million fungi, and 1 million protozoa in
scientific notation.
2. Look at the data below.
Composition of Healthy Soil
40% rock particles (clay, silt, sand)
10% organic material (decomposing matter in the form of sticks, leaves, roots, and the decomposers who break them down)
25% air (contains enough oxygen to enable plant roots and beneficial soil organisms to breathe)
25% water (enables plant roots and beneficial soil organisms to survive)
Edible Schoolyard Soil
comparing the components of soil
For soil to be healthy, it must contain a balance
of clay, silt, and sand because these materials have
very different properties. here is an example of a
healthy balance of clay, silt, and sand:
10% clay
60% silt
30% sand
3. What proportion of rock particles in healthy
soil is silt?
4. What proportion of rock particles in healthy
soil is clay?
5. What proportion of rock particles in healthy
soil is sand?
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Measuring Drainage Rates of clay, silt, and sand
in the edible schoolyard, students carried out
“drainage races” to explore differences in proper-
ties of clay, silt, and sand. students made soda bottle
funnels by cutting the bottom off each of three soda
bottles. they then covered the mouth of each funnel
with cheesecloth and filled it with either clay, silt,
or sand. Finally, students poured 500 milliliters of
water into each funnel and used a stopwatch to find
how long it took each funnel to drain.
the funnel containing sand drained in
2 seconds.
the funnel containing silt drained in
30 seconds.
the funnel containing clay drained in
3 minutes.
6. Find the drainage rate for sand, silt, and clay
in liters per second.
tHeMatHeMatIcSoF edIbleScHoolyardSoIl(cont )
tHeMatHeMatIcSoFtHetunnelIntHeedIbleScHoolyard
using Diagrams
the diagram below shows a picture view of the
tunnel in the edible schoolyard.
this diagram represents a front view of the tunnel.
The Tunnel in the Edible Schoolyard
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this diagram represents a side view of the tunnel.
1. How much wire mesh is needed to create this
tunnel?
tHeMatHeMatIcSoFtHetunnel IntHeedIbleScHoolyard(cont )
teacHernoteS&SolutIonS•Grade7
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tHeMatHeMatIcSoFwHole-wHeateGGbread—noteSandSolutIon
relationshipbetweenchangesinVolumeandchangesinlineardimensions
notes
in this task, students use rising bread dough to examine the relationship between increases in linear measure and the volume of solids. the purpose of this investigation is to find an easy way of discovering if a ball of dough has doubled in volume.
in most seventh-grade mathematics courses, students are expected to understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor. Making bread dough is a perfect context for students to experience this powerful concept because they get to see that when the volume increases by a certain scale factor, the linear measures increase by the cubed root of the scale factor.
solution
estimating
the recipe for Whole–Wheat egg Bread says that the dough should be left to rise until doubled. this means that the dough is left to rest until its volume has increased by a factor of 2.
1. Working in a group of two or three, talk about how you might tell if a ball of dough has doubled in volume.
answers will vary and should not be coached.
2. You might begin by estimating the diameter of the ball of dough before it rises. This is shown in the diagram below.
Then use this first measure to estimate the diameter of the risen dough.
a. We know that the after-rising volume needs to be twice the before-rising volume. What will be the rela-tionship between the before- and after-rising diameter?
answers will vary and should not be coached.
b. Will the diameter also increase by a factor of 2?
answers will vary and should not be coached.
investigating increases in linear Measure and Volume of solids
3. The ball of dough is a sphere but since spheres are dif-ficult to make, start this investigation by making cubes.
a. Use squared paper to create a set of cubes with 1, 2, 3, 4, 5, and 6 centimeters per side.
answers will vary and should not be coached.
b. Calculate the volume of each cube.
answers will vary and should not be coached.
c. Create a table of data to show the length of side and the corresponding volume.
d. Make a graph of your data. Record length of side along the x-axis and volume along the y-axis.
answers will vary and should not be coached.
length of side (cm) volume (cm2)
1 1
2 8
3 27
4 64
5 125
6 216
� � • m a k i n g m at h e m at i c s d e l i c i o u s | s e v e n t h g r a d e
4. Use your data to justify each of the following statements as true or false.
a. When you double the volume of a cube, the length of side will always double.
false
b. When you double the length of side of a cube, the volume will always be 8 times greater.
true
5. Use your data and make any needed calculations to answer the following questions.
a. When you double the volume of a cube, the ratio of the volumes will be 1:2. What will be the ratio of the corresponding lengths of side?
suppose that you have two cubes of volumes 8 and 16 cubic units, respectively. the ratio of the volumes will be 1:2.
the lengths of sides of these two cubes will be the cubed root of 8 and the cubed root of 16, respectively. that is 2: 16 or 2:2 2 or 1: 2 . thus, when the volumes of two cubes is in ratio 1:2, the ratio of the corresponding lengths of side will be 1: 2 .
b. When you quadruple the volume of a cube, the ratio of the volume will be 1:4. What will be the ratio of the corresponding length of side?
Following the same logic, the ratio of the corresponding lengths of side will be 1: 4 .
3√—— 3√
— 3√—
3√—
3√—
tHeMatHeMatIcSoFwHole-wHeateGGbread—noteSandSolutIon(cont )
applying Your Findings
6. Now check to see if your findings apply to a ball of dough—or a sphere.
a. When you double the volume of a sphere, the ratio of the volumes will be 1:2. What will be the ratio of the corresponding radii?
the ratio of the corresponding radii will be 1: 2 .
b. Suppose that the estimated radius of a ball of dough is 10 centimeters. What will be the radius of the ball of dough after it doubles in volume?
10 • 2
c. Complete the table below to show a set of before- and after-radii for balls of dough that double in volume.
7. In your own words, describe how you would expect the radius of a ball of dough to increase when that ball doubles in volume.
answers will vary and should not be coached.
When a Ball of Dough Doubles in Volume
before-rising radius after-rising radius in centimeters in centimeters
4 2 • 4 = 5.03
5 2 • 5 = 6.3
6 2 • 6 = 7.56
7 2 • 7 = 8.82
3√—
3√—
3√—
3√—
3√—
3√—
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tHeMatHeMatIcSoFGarlIcparMeSancrackerS—noteSandSolutIon
VolumeofaSphereandVolume ofarectangularprism
notes
in the context of making Garlic Parmesan Crackers, students examine and measure a series of geometric transformations. a ball of dough is rolled into a rectangular prism and then cut into a set of congruent rectangular prisms. although the shape is changed, the volume of the dough remains invariant under each transformation.
solution
Measuring Dough
once the dough is prepared and gathered into a ball, it approxi-mates a sphere with a diameter of 3 inches.
1. What is volume of this ball of dough?
volume of sphere = , so = 14.14 inches3
2. This recipe tells us to divide the ball of dough in ½ and roll each half separately. What is the volume of each half?
7.07 inches3
3. The recipe tells us to roll the half ball of dough into a long, thin rectangular prism that is 1/16 inch thick, 1½ inches wide, and an unknown length x. What is the length of the rectangular prism that is formed by rolling the dough, as shown in the following diagram?
4 πr3 — 3
4 x π x 153 — 3
4. What is the length of the rectangular prism that is formed by rolling half the dough as shown in the diagram?
volume of prism = length × breadth × height =
1 3 3 x = 3 3 x = 3 x = 3 x
Since volume of prism = volume of sphere,
7.05 inches3 = 3 x so x = 7.05 4 = 75.2 inches.
so the length of side x is 75.2 inches.
4. How many 1½-inch square Garlic Parmesan Crackers can be cut from the whole ball of dough?
50
1 — 2
1 — 16
24 — 16
24 — 256 1 — 16
3 — 32
3 — 32
3 — 32
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tHeMatHeMatIcSoFrHubarbJaM—noteSandSolutIon
linearFunctionsanddirectVariation
notes
in this task, students are asked to analyze the amount of sugar in a rhubarb jam recipe in terms of the amount of rhubarb. students will be able to see that when the recipe is increased, the amount of sugar is a function of the amount of rhubarb. Furthermore, students will be able to see that the function is a linear function, that the graph is a line, and that the relationship between sugar and rhubarb is a directly proportional one.
solution
increasing a Recipe
1. The recipe for Rhubarb Jam shows that for every 3 cups of rhubarb, ½ cup of sugar is necessary. Copy and complete this table to show the amounts of rhubarb and the corresponding amounts of sugar required when the recipe is increased.
2. We can think of the number of the cups of rhubarb and the number of cups of sugar as two variables.
Let x represent the number of cups of rhubarb.
Let y represent the number of cups of sugar.
a. Which of these two variables does it make sense to call the independent variable? Explain why.
it makes sense to call the cups of rhubarb the indepen-dent variable, because the amount of sugar that is added depends on the cups of rhubarb used and not vice versa.
Quantities of Fruit and Sugar in Rhubarb Jam
number of cups numbers of cups of rhubarb of sugar
3 H
6 1
9 1H
12 2
b. Which of these two variables does it make sense to call the dependent variable? Explain why.
it makes sense to call the amount of sugar the depen-dent variable, because the amount of sugar that is added depends on the cups of rhubarb used and not vice versa.
3. Write a formula to express the number of cups of sugar in terms of the number of cups of rhubarb.
6 cups rhubarb needs 1 cup sugar, so 1 cup rhubarb needs cup sugar. therefore, x = y.
4. Draw a graph to show the relationship between the number of cups of rhubarb and the number of cups of sugar. Record the number of cups of rhubarb along the x-axis and the number of cups of sugar along the y-axis.
answers will vary and should not be coached.
5. Do the points form a line or a curve? Draw a line or a curve to illustrate your answer.
the points form a line.
6. What is the ratio of the number of cups of sugar to the number of cups of rhubarb?
1:6
7. What is the slope of the line?
1 — 6
1 — 6
1 — 6
3 � • m a k i n g m at h e m at i c s d e l i c i o u s | s e v e n t h g r a d e
8. What does the slope of the line represent in terms of making Rhubarb Jam?
the slope of the line represents that factor by which the linear measures of sugar increases when the independent variable, rhubarb, increases.
9. Does the line pass through the point (0,0)?
yes
10. Does the number of cups of sugar needed to make Rhubarb Jam vary directly with the number of cups of rhubarb? Explain how you know.
Yes, the number of cups of sugar vary directly with the number of cups of rhubarb because the graph is a line that passes through (0,0).
tHeMatHeMatIcSoFrHubarbJaM—noteSandSolutIon(cont )
tHeMatHeMatIcSoFedIbleScHoolyardSoIl—noteSandSolutIon
rate,proportion,percentages,andnumberSense
notes
in the edible schoolyard, students study soil in a comprehen-sive and tangible way. this mathematics task allows students to discover the composition of healthy soil and compare properties of its components in mathematical terms.
solution
graphing the components of soil
in the lesson on soil, you learned that an understanding of soil is crucial to the knowledge of life cycles and our food systems.
1. One teaspoon of rich soil contains 5 billion bacteria, 20 million fungi, and 1 million protozoa.
Write these numbers in scientific notation.
5 billion = 5 × 109
1 million = 1 × 106
20 million = 2 × 107
2. Look at the data below.
Composition of Healthy Soil
• 40% rock particles (clay, silt, sand)
• 10 % organic material (decomposing matter in the form of sticks, leaves, roots and the decomposers who break them down)
• 25% air (contains enough oxygen to enable plant roots and beneficial soil organisms to breathe)
• 25% water (enables plant roots and beneficial soil organisms to survive)
3 6 • m a k i n g m at h e m at i c s d e l i c i o u s | s e v e n t h g r a d e
Display this information in a pie chart.
comparing the components of Rock Particles
For soil to be healthy it must contain a balance of clay, silt, and sand because these materials have very different properties. here is an example of a healthy balance of clay, silt, and sand:
10% clay
60% silt
30% sand
3. What proportion of rock particles in healthy soil is silt?
4. What proportion of rock particles in healthy soil is clay?
5. What proportion of rock particles in healthy soil is sand?
25% water
25% air
10 % organic material
40% rock particles
tHeMatHeMatIcSoFedIbleScHoolyardSoIl—noteSandSolutIon(cont )
3 — 5
3 — 10
1 — 10
Measuring the drainage rates of clay, silt, and sand
6. In the Edible Schoolyard, students carried out “drain-age races” to explore the differences in composition of clay, silt, and sand. Students made soda bottle funnels by cutting the bottom off each of three soda bottles. They then covered the mouth of each bottle with cheesecloth and filled it with either clay, silt, or sand. Finally, stu-dents poured 500 milliliters of water into each funnel and used a stopwatch to find how long it took each funnel to drain.
the funnel containing sand drained in 2 seconds.
the funnel containing silt drained in 30 seconds.
the funnel containing clay drained in 3 minutes.
Find the drainage rate for sand, silt, and clay in liters per second.
sand = 0.5l in 2 seconds = 0.25l or l per second
silt = 0.5l in 30 seconds = 0.017l or l per second
slay = 0.5l in 180 seconds = 0.003l or l per second
1 — 4
1 — 60
1 — 360
3 � • m a k i n g m at h e m at i c s d e l i c i o u s | s e v e n t h g r a d e
tHeMatHeMatIcSoFtHetunnel—noteSandSolutIon
circumferenceandSurfacearea
notes
the tunnel in the edible schoolyard is both aesthetically and mathematically inviting. the space that is carved out by the inside of the tunnel can be decomposed into a half cylinder that sits atop a rectangular prism. in this task, we ask students to cal-culate the surface area of the wire mesh that is used to construct the tunnel.
solution
using Diagrams
the diagram below shows a picture view of the tunnel in the edible schoolyard.
this diagram represents a front view of the tunnel.
this diagram represents a side view of the tunnel.
1. How much wire mesh is needed to create this tunnel?
the surface area of the tunnel can be found by calculat-ing the surface area of the two rectangular sides and the surface area of the curved roof, then adding these values to find the total mesh needed.
sa side = length × height = 27 × 6 = 162 feet2. as we have two sides, total is 324 feet2.
sa roof = length of arc × length of tunnel
circumference circle = πd = π × 6 = 18.84…
semicircle, arc = 9.42 …
so sa = 9.42 × 27 = 254.5 feet2.
the total surface area and mesh needed is 578.5 feet2.
aword oFGratItude
ann shannon developed these materials with support from staff at the edible schoolyard and teachers from Martin Luther King Jr. Middle school. special thanks to esther Cook for the delicious recipes and susie Walsh daloz for the garden lessons included here. our thanks also to the educational Foundation of america and Wendy ettinger for funding the development of these materials.
so many individuals and other foundations have supported our work at the edible schoolyard over the last year, including new-man’s own Foundation, the Compton Foundation, the Lattner Foundation, the zimmerman Foundation, the Charles and helen schwab Foundation, the Krehbil Family Foundation, the Martin
Family Foundation, and Mark and susie Buell.
about the chez Panisse Foundation
Founded by alice Waters in 1996, the Chez Panisse Founda-tion develops and supports educational programs that use food traditions to teach, nurture, and empower young people. the Foundation envisions a curriculum, integrated with the school lunch service, in which growing, cooking, and sharing food at the table gives students the knowledge and values to build a humane and sustainable future.
the edible schoolyard is a thriving one-acre garden and kitchen classroom for all 950 students at Martin Luther King Jr. Middle school. through the edible schoolyard, students experience all aspects of growing, cooking, and sharing food at the table. Garden classes introduce the origins of food, plant life cycles, community values, and the pleasures of work, while kitchen classes allow students to prepare and eat delicious, nutritious, seasonal dishes made from produce they have grown in the garden. the edible schoolyard is a program of the Chez Panisse Foundation.
For more information about our work and other publications, please visit our website at www.chezpanissefoundation.org.
All materials © the Chez Panisse Foundation, 2008
ISBN-13: 978-0-9820848-4-7 ISBN-10: 0-9820848-4-6
Interior illustrations by Celia Stevenson.
Copyediting by Ellen Goodenow. Design by Alvaro Villanueva.
C h e z Pa n i s s e F o u n d at i o n
Cultivating a New Generation