Common Core Garden Cluster Table of Contentsmsfarmtoschool.org/uploads/We_Dig_It_5th_Grade_Math...5th Grade Math School Garden Curriculum We Dig It! Common Core Garden Cluster Table

5th Grade Math School Garden Curriculum

We Dig It!

Common Core Garden Cluster Table of Contents Standards for Mathematical Practices

Lesson Plans/Evaluation Forms included for each lesson plan

1. Unit 1-Introduction to the Garden and Garden Map

2. Unit 2 – Square Unit Gardening

3. Unit 3 – Half of a Half of my Garden Plot

4. Unit 4 – Area and Perimeter of Leaves

5. Unit 5 – Bud, Flower and Fruit Data

6. Unit 6 – Plant Growth

7. Unit 7 – Cross Cut Snacks

8. Unit 8 – SNAP Challenge

Operations and Algebraic Thinking Completion Instructions and Receipt of Stipend

Standards for Mathematical Practices The Common Core State Standards for Mathematical Practice are integrated wherever possible in this

“School-to-Garden” curriculum. Below are a few examples of how these Practices may be integrated into tasks that students complete.

Mathematic Practices Explanations and Examples 1.) Make sense of problems and persevere in solving them

Mathematically proficient students in 5th grade should be familiar and comfortable working with integers, decimals, fractions and mixed numbers. These numbers will be encountered in the garden when tabulating crop harvest, measuring landscape features, utilizing the square-meter gardening method and when planting/ordering seeds.

2.) Reason abstractly and quantitatively

Students will be introduced to the garden as very much a “tool” to foster their learning. Their continuation of learning in the classroom, however, will be stimulated abstractly. For example, if a student is asked to find the area of a raised bed in the garden, they will do so with a meter stick. If back in the classroom, a student would take given measurements and utilize the same algorithm as they did in the garden.

3.) Construct viable arguments and critique the reasoning of others

A school garden provided the perfect opportunity for critiquing the reasoning of others, as there is a communal need for cooperation. When projects or activities in the garden are constructed around the pursuit of an appropriate method (i.e., “we can’t move onto step 2 unless everyone has done step 1 correctly”) then there exists an obvious incentive for the sharing of information.

4.) Model with mathematics

Students will have ample exposure to real geometric shapes and figures. The use of a square-meter gardening method creates a natural coordinate plane and contextualizes the modeling of fractions and partial areas.

5.) Use appropriate tools strategically

Math “tools” in the garden will come very much in the form of algorithm short-cuts and an improved sense of numeracy and rounding.

6.) Attend to precision

So much math that takes place in gardening is done mentally and results in financially significant decisions—attention to detail is of the utmost importance when trying to limit waste.

7.) Look for and make use of structure

Students will recognize mathematical “shortcuts” used in the garden, such as unit squares for determining volume and area. Students will also be able to identify patterns and proofs for different geometric and mathematic processes in the garden.

8.) Look for and express regularity in repeated reasoning

Many gardening practices require redundant calculations—such as area—in order to determine yield, watering, coverage etc.,. The constant practice of these calculations will help to reinforce patterns and objective practice.

SCHOOL GARDEN LESSON PLAN EVALUATION

The Garden Curriculum lesson plans are part of a Farm to

School Initiative for Delta Fresh Foods.

In order to make these lessons more beneficial to teachers and

learners, please provide us you’re your honest feedback. Thank

you!

NAME OF LESSON PLAN: _________________________________________

1. Lesson Plan Format: Were all necessary components included in the lesson? Yes___ No___ If No, please list what should be added. _____________________________________________

______________________________________________________________________________

2. Was the lesson line clear, easy to follow? Yes___ No ___ If not, why & please list any suggestions: _____________________________________________ ______________________________________________________________________________

3. Was the length of the lessons right for the time allotted? Too long _____ Too short ____ About Right _____

4. When did you implement the lessons? 1st time instruction of objective or Enrichment During subject-‐area time_____ Enrichment_____ After school ______

5. Please list any obstacles (resources, additional time/effort, etc.) that made implementing these

lessons difficult?

6. How relevant were the activities to the objectives listed? Somewhat ______ Not really _______ Very ________

7. Did students respond positively to these lessons? Somewhat _____ Not really _______ Very ________

8. Did you use the lesson plan in conjunction with a school garden at your site? If so, what changes or improvements in your garden site are needed to enrich the learning experience? ____________________________________________________________________

______________________________________________________________________________ ______________________________________________________________________________

(Please attach a separate page with other specific comments, additions or corrections)

Math Unit 1 Introduction to the Garden and Garden Maps

This lesson will provide students with a detailed map of their school garden, one that will be useful for all lessons held in the garden and in the classroom. Students will also be introduced to the metric layout of the garden and useful units of measurement. A major goal for this lesson—and ultimately this unit—is for students to become familiar and comfortable using the metric system. Standards: 5.NBT.1 Recognize that in a multi-‐digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.3 Read, write and compare decimals to the thousandths place. 5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols to record results of comparisons. 5.NBT.4 Use place value understandings to round decimals to any place. Objectives: SWBAT identify the meter as the base metric unit for measurement of length SWBAT express non-‐integer measurements as decimals up to the thousandths place SWBAT create a detailed and scaled map of the school garden for use in further lessons Materials Graphing paper (¼’’ x ¼’’) Pencil and Eraser Student checklist of various structures to measure Meter stick Enough string/twine to measure the longest side of your school garden Something hard to write on Key Points: Knowledge • A garden is an area of land where plants are grown, it is a geometric shape. • Some important garden vocabulary words are:

§ Bed § Perimeter § Soil § Mulch/Gravel § Square meter

• The garden is an extension of our classroom, it is a place for learning. We can use the garden to learn math and see why math is important in the real world

• A well organized garden requires sharp math skills. Gardeners and farmers must perform accurate measurements and calculations in order to reduce costs and maximize profits.

• A well detailed map allows us to remember parts of the garden once we’re back in the classroom.

Skills • Teamwork is essential when making large measurements. In order to work

cooperatively and attain accurate results, students will need to communicate respectfully and effectively with one and other.

Essential Questions How do we measure length? How are the (raised)-‐beds organized and measured? How big is our garden? How much growing space is there? Introduction to New Material (10 min) Introduce students to the garden. Point out certain features like (raised)-‐beds, gravel/mulched open-‐space, garden perimeter, compost area etc.,. Take a moment and point out what direction is North, what direction is South and the directions East and West. Then use a meter stick to try and measure the height of a student volunteer. In all likelihood you’ll have a student who is 1.X meters tall, which requires you to use a decimal. For practicality purposes, round to the hundredths place (centimeters). Demonstrate again, with the same student, how you might use a piece of string to first measure the student and then measure the string with the meter stick. Guided Practice (25 min) Students are free to measure about the garden, using the checklist of structures for completion. The checklist should go from largest structure (perimeter) to smallest, this way students have an idea of where to start with their maps. Mapping the perimeter using string will require multiple students. If time is up and students have not completed all measurements, have them collaborate with others to get the ones they missed. Remind students that they need to measure not just the macro features, but also the distance of one object to another. For example, how far are the raised bed from the perimeter. Independent Practice (15 min) Once all measurements are taken, maps can either be drawn in the garden or back in the classroom. Instruct students to start by first mapping out the perimeter and using an appropriate scale for the size of your garden (eg., 1 meter in the garden equals 1 box on graph paper, or ¼’’). Addendum: To be done perfectly, this lesson would most likely take closer to 90 minutes. You could easily split this into two days, doing just measurements on day one and mapping on day two. Some classes may not be at a level ready to map abstractly and so you could provide a crude map of all garden features and have students simply find measurements listed. This lesson provides a great opportunity to review rounding. Conclusion: Administer Student Exit Slip

Name: Introduction to the Garden Today you are going to create a map of our school garden. It is important that you make this as detailed as possible so that you may use it to help remind you where everything is. 1.) First, circle the unit you are going to measure in: in m cm ft yd 2.) Determine what direction is North (your teacher should help you with this) and then decide what directions are South, East and West. 3.) Now, decide what major structures you want to map out and measure. What pieces of the garden do you think are important? List them here: -‐ Ex. Garden Beds -‐ (8.0 ft x 3.5 ft) -‐ -‐ -‐ -‐ -‐ -‐ -‐ -‐ Remember to use appropriate rounding skills! Your teacher will tell you what value

place you should round to.

Instructor notes: You’ll need to decide on a scale for students to use (e.g., 1 square on the grid equals 1 meter in the garden).

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Name: Introduction to the Garden Exit Slip

1.) What unit did you use when measuring the garden today?

2.) What was the largest feature you measured in the garden? What were it’s dimensions? Which side is the longest side?

3.) What was the smallest feature you measured in the garden? What were it’s dimensions? Which side is the shortest side?

4.) How would you round 4.46 yds if you were rounding to the tens place?

5.) How many millimeters are in one centimeter?

6.) How many times larger is 50 meters compared to 50 centimeters?

7.) What has a larger area, a 2 x 3 ft section of dirt or a 2 x 3 yd section of dirt?

8.) What was the southern most feature in the garden?

Math Unit 2 Square Unit Gardening

This lesson will provide students with a hands-‐on measurement of area and volume as well as introduce students to coordinate planes. With some beforehand preparation, fall planting can be performed in the garden using the established coordinates. This lesson requires that a square meter lattice network already be implemented in the gardening beds. Standards: 5.NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fractions side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas. 5.NF.5a Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication 5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers called its coordinates. Understand that the first number indicates how far to travel from the origin in the directions on one axis and the second umber indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-‐axis and x-‐coordinates, y-‐axis and y-‐coordinate). Objectives: SWBAT determine area of a gardening bed by counting the number of square meters in the bed SWBAT determine the area of a gardening bed by multiplying the side lengths SWBAT students will be able to compare the relative areas of gardening beds (>, <) based on one side measurement alone SWBAT identify a given region on a coordinate plane Materials Student Worksheet and planting assignment Maps from Week 1 Pencil and Eraser Something hard to write on Key Points Knowledge

• Square unit gardening is an intensive, yet effective method of growing many different fruits and vegetables

• Plants grow best in certain groups or concentrations, so gardeners often use a square unit to keep track of what needs to be planted next to what

• Some important garden vocabulary words are: § Square meter § Concentration § Coordinate § X-‐axis, Y-‐axis

Skills

• Planting seeds and seedlings needs to be done gently and with care. Students/teachers need to keep track of what is planted where to ensure proper care of the growing plants.

Essential Questions Why divide a bed into square units? What purpose does this serve?’ How might we determine the area of a bed if we didn’t have a meter stick? How might we compare the relative area of one gardening bed to another without a meter stick? Introduction to New Material (10 min) Reacquaint students with the garden and share the day’s objectives. Square meters should already be measured out and lattices strung above the beds and labeled from 1 à 10. Explain that this is a square meter gardening system and how it is used to foster intensively planted gardens. Show how you can use the labeled axes in the beds to locate a particular square-‐unit. Then demonstrate how you would look at a planting assignment and properly plant a seed or seedling. Guided Practice (20 min) The student worksheet should guide students towards calculating the area of every bed in the garden. It should also include a section that has students evaluate the relative size of one bed to another (i.e., Bed A is [<.>,=] Bed B). Independent Practice (20 min) Have students then transpose the same coordinate lines that are in all the beds onto their maps from Week 1. Students should then color in or label where their planting assignment is on their maps. Once maps are complete, allow students to proceed in planting their respective seeds/seedlings in their assigned areas. It would be a good idea to not allow students to actually plant until they properly identify their planting location on their maps. Addendum: This lesson packs a lot of material into just one gardening assignment, planting. As with Week 1, this lesson could easily be expanded to cover a 90 min period or two days. This lesson relies on students already having been introduced to coordinate system nomenclature as well as area formulas. It might be a good idea to have a large data-‐board displaying all coordinate planes in the garden.

Name: Square Gardening Worksheet Use this worksheet to help guide you in the planting activity today. Remember to use your garden map from “Introduction to the Garden” to help you remember where different things are in the garden and what some of their dimensions are. What is your planting assignment today? What gardening bed are you planting in? What are the dimensions of your gardening bed? Remember to include units. What coordinates were you assigned to plant in?: x: y: Label the Origin (0,0) and x-‐axis and y-‐axis. Number the coordinate as they already are in the gardening bed.

Now, indicate where different types of plants are being planted in your garden.

Instructor Notes: The student worksheet will need to be adjusted to fit the dimensions of beds in your individual garden. A large coordinate plane where examples can be shown would be beneficial. Try to have multiple students working in the same bed so that they can plot multiple points. If this is not feasible you include multiple coordinate grids on the student worksheet. Student Exit Slip Name:

1.) What were the dimensions of the garden bed you planted in? Remember to include units.

2.) John planted carrots at point (2,3). How many units did John move along the x-‐axis?

3.) Suzy planted okra at point (1,4). How many units up the y-‐axis did Suzy have to move?

4.) Micah planted broccoli at (1, 5), lettuce at (2, 4), eggplant at (3, 5) and radishes at (3, 4). Graph these points and label them. The bottom left-‐hand corner is the origin.

5.) What has a larger area, a 2 x 3 ft. bed or a 3 x 4 ft. bed?

6.) What can you say about a 4 x 8 ft bed and an 8 x 4 ft bed?

Math Unit 3 Half of a Half of My Garden Plot

This lesson will provide students with a physical example of working with fractions in the garden. Students can perform this skill when doing any sort of activity in raised beds be it planting, weeding, watering or harvesting. Standards: 5.NBT.5 Fluently multiply multi-‐digit whole numbers using the standard algorithm 5.NF.3 Interpret a fraction as division of the numerator by the denominator. 5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers 5.MD.1 Convert among different-‐sized standard measurement units within a given system Objectives: SWBAT divide a rectangular prism into half and calculate the side lengths SWBAT multiply multi-‐digit numbers to calculate area SWBAT determine the appropriate metric scale for different sized fractions in the garden Materials Graphing paper (¼’’ x ¼’’) Pencil and Eraser Meter stick and enough string/twine to measure the longest side of a raised bed Nail/Pushpins/Tape—to secure string/twine across the bed Large tongue depressors Something hard to write on Scissors Key Points: Knowledge • A raised bed is used to grow all different types of plants and vegetables • Some important garden vocabulary words are:

§ Raised bed § Lattice/Square-‐unit § Square meter/foot § Midpoint

• Plants need individual space to grow, if they’re too close they have to compete for nutrients and water

• Dividing a bed into smaller fractions is a great way to help plant seed/seedlings • WHY: Fractions help gardeners decide how to divvy up their beds Skills • Making measurements in the garden using the desired unit of measurement • Working together to make large measurements • Communicating with peers to help form lattice structures over the beds

Essential Questions How do we measure length? How are the (raised)-‐beds organized and measured? How much space does each type of plant need to grow Introduction to New Material (10 min) Set up a mock garden bed using string and sticks on a large flat area—make it the same size as the beds the students will be using. Explain the reason for dividing the bed into small single-‐plant spaces and why this is important. Using volunteers, use a meter stick to determine the midpoint of one of the sides of the bed—have another student volunteer do the same on the opposite side length. String the two midpoints together and repeat on the opposite side. Then repeat with one quadrant and again with quadrants until you reach the smallest square area needed for a single plant; you should end with a square unit roughly 1’ x 1’. Be sure to demonstrate tying off string and using tongue depressors as stakes in the bed to help elevate the lattice structure. If you are pairing this lesson with a specific gardening activity, be sure to demonstrate that as well (e.g., weeding, planting, thinning). Guided Practice (35 min) Students should be able to work through this exercise without the guidance of a worksheet, however, the demonstration should be left as an example. Students are to work in small groups, dividing each half into another half until they reach a square unit containing a single plant. For guidance, leave the mock garden bed lattice structure in tact so that students may reference it for an example. Students should then measure the area of that unit using the area formula and appropriate units. This can be done at various times of the season, the activity just needs to be adjusted for plant growth. If doing this activity prior to planting, students should be given a final square area to end with. Independent Practice (5 min) Have students record their finds and sketch the resulting lattice structure. More time can be allocated to yield more specific measurement-‐based illustrations. Math worksheets with various fraction problems can also accompany students as they work through this exercise. Example: How many 0.5 m x 0.5 m square units are there in the planting bed? How many have something growing in them? How could you express this as a fraction? If 20 of the 40 squares have plants growing in them, what is a simplified fraction I can use to explain how much of the bed is planted? If you plant 3 squares worth of peas and 1 square worth of cucumbers, what fraction expresses the ratio of cucumbers to peas in that area? Closure (5 min)

Have students critique the garden beds of their peers. Ask if they recognize or see a pattern? Do they see anything that was done incorrectly? How might they do it differently next time? Addendum: A good idea is to pair this exercise with a certain garden task, such as weeding, in order to expand on standard practice. Say you’re discussing the importance of weeding that week, this activity could then be done to the point of isolating individual plants and then having students record weed numbers per unit are. When done correctly, this activity provides a perfect lattice/coordinate-‐plane for data collection (e.g., weeds, plants, fruits, water, insects etc.,). Encourage students to use different metric prefixes to build on NBT standards and remember that this can be done in non-‐rectangular beds if measured appropriately. Student Exit Ticket Name: Half of a Half Activity

1.) What were the dimensions of your garden bed? Based on those dimensions, what area did you determine for your garden bed?

2.) After you divided your bed in half, what happened to the area of one side of the garden?

3.) Victoria is weeding in a 4 x 8 foot gardening bed. If she divides the garden in half along the 8 ft side, what are the new dimensions? What is the are of one half of the garden?

4.) How many times do you need to divide a garden in half before you get 8 equal pieces?

5.) Jason divided his garden bed into 16 equal parts. He then harvested ¼ lb of tomatoes from each part. How many pounds of tomatoes total did Jason harvest?

Math Unit 4 Area and Perimeter of Leaves

This lesson provides students with experience measuring perimeter and area in two different ways. Students will apply these skills when measuring a variety of leaves in the garden. Students can also compare and analyze the two different types of measurement. Standards: 5.G.2 Represent real world and mathematical problems by graphing points 5.MD.1 Convert among different-‐sized standard measurement units within a given system 5.OA.2 Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them Objectives: SWBAT determine the perimeter of an irregular shape using a piece of string SWBAT determine the area of an irregular shape using a grid system SWBAT perform multi-‐digit multiplication Materials Graphing paper (1cm x 1 cm) Pencil and Eraser 30-‐centimeter piece of string Something to work on Scissors Ruler with centimeters Key Points: Knowledge • Perimeter is the distance around a closed shape • Area is the space inside a closed shape • Some important vocabulary words are:

§ Area § Perimeter § Centimeter

• Area is a very important measurement used in the garden; it’s used to measure just about everything from garden sized to leaf sized

• Perimeter is also important, especially when ordering garden materials • Irregular shapes don’t have simple equations for area and perimeter because they

don’t have equal sides Skills • Gathering a variety of leaves to measure • Constructing data tables for keeping track of area and perimeter data • Critiquing peer work and calculations

Essential Questions How do we measure perimeter? How do we measure area? How might these measurements be important for gardeners to know? Why can’t I multiply base times height to determine the area of a leaf? Introduction to New Material (10 min) Be sure that there are adequate sized leaves in your garden—if there is not, you may want to try and find other samples or buy some. Instruct students to only pick the bottom leaves off of live plants so as not to hamper photosynthetic needs. Ask students what the outer line of the leaf is (perimeter) and what the inner part of the leaf shape is (area). Demonstrate for students how to measure perimeter using a piece of string to first measure the perimeter of the leaf and then measuring said length against a ruler or meter stick. Then demonstrate how tracing leaf over a piece of grid paper transposes the leaf shape. Have a volunteer then count the number of enclosed whole units. Explain that a good estimation is one that also includes half of the partial units. Guided Practice (30 min) Have students pick leaves of their choice, perhaps encouraging them to gather an assortment from different plants or different parts of the same plant. Have students then measure perimeter and area as demonstrated. Students should record finding in a journal or on scratch paper. For guidance, keep a worked example of the steps for determining perimeter and area. Independent Practice (10 min) Have students compare calculations and encourage them to check each others work. Is your partner calculating area correctly? Did they round to the nearest unit as directed? Closing (5 min) The end result of this activity is great for display if the leaves and calculations are secured to a piece of cardstock or poster board. Administer Student Exit Ticket. Addendum: This lesson can be expanded to investigate trends in perimeter and area. Generally speaking, plants suitable for growing in less than full light will have larger leaves than those needing full light. Why do students think this is?

Name: Area and Perimeter of Leaves

1.) What is the equation for perimeter? How do you determine perimeter if your object doesn’t have a base or height?

2.) A rectangular garden bed has a base of 3 ft and a length of 8 ft. Write an expression that could be evaluated to determine perimeter.

3.) Paul is measuring the perimeter of a leaf and creates the following expression: 8 + 4 +5 + 4 +2

What can be said about two sides of the leaf?

4.) A leaf with a perimeter of 12.3 cm would have a perimeter of mm

5.) When measuring a perfectly rectangular garden bed, how could you write an expression using parentheses to simply your math? Give an example.

Math Unit 5 Bud, Flower and Fruit Data1

Students follow an established algorithm counting the number of stems on a developing plant in order to estimate the number of flowers, buds and fruits that will be produced. This activity can be expanded over multiple dates in order to compare data as plants grow. Standards: 5.OA.1 Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols 5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms Objectives: SWBAT estimate future fruit production of a single plant by counting the number of buds SWBAT use parentheses and possibly brackets to perform multi-‐step multiplication estimation problems SWBAT construct data plots showing the number of identified plant parts Materials Graphing paper (1cm x 1 cm) Pencil and Eraser Data Table Flower study steps Ruler Key Points: Knowledge • Estimation is an important skill by which we make educated guesses about

statistical outcomes • Different parts of a developing flower can give us a good idea of how much fruit the

plant will produce • Some important vocabulary words are:

§ Bud § Flower § Fruit

• Flowers are very important in the garden not just because they look nice but because they attract pollinators like bees

• Estimating is a great tool to have when you need to count a large number of things Skills • Identifying different parts of growing plant • Counting different parts of a plant • Analyzing plant data for mean

1 Adapted from Math in the Garden: Hands-‐On Activities That Bring Math to Life. University of California Botanical Garden and Lawrence Hall of Science. National Gardening Association, 2006.

Essential Questions How can we formulate a good guess as to how much fruit a plant will yield? What’s the importance of flowers? What is an average? How do you calculate it? Introduction to New Material (10 min) Use a part of your school garden with well-‐defined, good-‐sized fruit. Choose one plant to demonstrate on and point out the different part (flower, bud, fruit). Show students how they should count and fill in their tables with the numbers of various parts. Explain why a farmer might look at one plant to estimate the yield of all his plants. Example: Count how many fruit/vegetables are growing in a 1 m x 1 m unit square. How many unit squares are growing that exact same type of fruit/vegetable? What two numbers could you multiply to get an idea of how many total fruit/vegetables are in the garden? Would this number be exact or an estimation? Guided Practice (20 min) Prior to entering the garden, provide students with a rough outline of data you are looking for. They should be recording the type of plant, number of flowers, number of buds, number of fruits, total stem growth (flowers+buds+fruit) and numbers of stems. Have students find the average fruit yield per unit area and predict what they might harvest later in the season. Depending on math content progress, students might be supplied with a useful equation for determining average. The guiding element to this part of the activity rests in the students being assigned a particular part or species to count, plan ahead accordingly based on what is available in the garden. Example: Have students calculate average two different ways. First, have students count the number of fruit/vegetables in a unit square and multiply by the number of unit squares with that particular crop (as done above). Then have students pick the square they think has the most fruit/vegetables (of one varietal) and a the square with the least. Add those two numbers together and divide by two. How does this compare to the average found when multiplying? Which one do students think is more accurate? Independent Practice (20 min) Students should consult with peers to compile further data. Once a student completes her count for one plant, she could ask a peer for a count on the same species but different plants. Have students compare averages across the same plant varietals and against different types of crops. Conclusion (5 min) Have students compare and record data for the entire garden. Calculate class averages and pass out Student Exit Ticket. Addendum: This lesson can easily be expanded to cover two periods if the first day is spent in the garden and the second doing data analysis. Worked examples of averages and concentrations should be provided if appropriate. This lesson can also be expanded to include the graphing of data.

Name: Bud, Flower and Fruit

1.) What part of the plant were you tasked with counting? What does this part of the plant do?

2.) Evaluate the expression 3 (9+1)

3.) Write an expression to represent the sum of three garden beds with 12, 8 and 11 fruits respectively.

4.) How many different types of fruits did you count?

5.) Write a single expression for the following total harvest: -‐ 4 lettuce beds: 1 with 10 plants, 2 with 8 plants and 1 with 4 plants -‐ 8 tomato plants: 4 with 8 fruit, 4 with 10 fruit -‐ 3 zucchini plants: all three with 4 fruits each

6.) Ms. Smith’s class harvested 20 pounds of produce their first month in the

garden, 30 pounds the second month and 40 pounds in the third month. How much produce do you anticipate Ms. Smith’s class harvesting next month?

7.) Mr. Boyer’s class planted 80 seeds and then harvested 20 plants that fall. They then doubled the number of seeds planted in the spring. How many plants do you expect Mr. Boyer’s class to harvest after the spring planting?

Math Unit 6 Plant Growth

This activity can be formatted to either one class period or as a course during the growing season. In this activity, students track the growth of a particular plant and measure its progress using a unified system of measurement. * If using the metric system, this lesson can be a good practice of tens-‐based exponents. Standards: 5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point. 5.NBT.4 Use place value understanding to round decimals to any place. 5.MD.1 Convert among different-‐sized standard measurement units within a given measurement system Objectives: SWBAT take measurements to a stated degree of precision SWBAT measure an object with both metric and imperial units SWBAT move a decimal to the left or right to change metric unit measurement Materials 1 to 2 meters of string Pencil and Eraser Ruler and/or meter stick Data worksheet or blank paper for recording measurements Key Points: Knowledge • There are multiple ways of expressing the measurement of length • The metric system is based on units of ten • Some important vocabulary words are:

§ Meter, centimeter, millimeter § Yard, foot, inch § Precision

• Plants grow and change throughout the season, they do this at different rates during different times of year

Skills • Selecting an appropriate unit of measurement • Working with a partner to measure large lengths and communicating with math

fluently • Identifying trends in growth data • Plant drawings Essential Questions How do we know what unit of measurement is correct/appropriate? When do plants grow the most? When do they grow the least? How do we express a measurement taken in metric as imperial and vice versus?

Introduction to New Material (10 min) Select a large plant to first demonstrate on (sunflowers are perfect if available). Start by pointing out different features for measurement and explain how students should first sketch the plant and then measure and record measurements on their drawings. Guided Practice (10 min) Demonstrate for students how to round to the most defined unit. For example, if a stem measures 35.45 centimeters, on a meter stick it will most likely look like 35.4, but you can round the ten-‐thousandth to 5. Also discuss with students the different systems of measurement (imperial and metric) and decide on using just one for the day. Independent Practice (30 min) Encourage students to pick their favorite plants to measure and draw. Have students first sketch the plant and then measure various parts using the string and meter stick. Have students practice rounding by giving them a specific place of precision that they must round to. Later, in the classroom, have students pair and share their work. This would be interesting if students used different units of measure and had to then convert to the other so as to allow collaboration and comparison. Conclusion (5 min) If using activity over the duration of a growing season, have students save work for later measurements. Assess activity objectives with Student Exit Ticket. Addendum: Worksheets practicing various math standards could certainly accompany this activity, instructing students to manipulate their measurements any number of ways. This exercise emphasizes the above standards best when done over an entire growing system as the plant growth is rapid enough to demonstrate the powers of ten in the metric system (e.g., a seedling first measured in millimeters can then be measured in centimeters and eventually decimeters and possibly even meters).

Name: Plant Growth

1.) What plant did you measure today? What is one observation you made about your plant?

2.) How tall was your plant? How wide was your plant? What was the largest part of your plant?

3.) What unit did you use when making your measurements? Why did you choose to use this unit?

4.) Whitney measured the stalk of her sunflower to be 3.45 centimeters. How many millimeters is this?

5.) Two months later, Whitney’s sunflower is 1.8 meters high. How many centimeters is this?

6.) What is larger, a 2.45 decimeter tomato plant or a 145 millimeter bean plant?

Math Unit 7 Cross Cut Snacks

In this activity students are encouraged to try and sample new fruits and vegetables. Students will first be exploring geometric shapes and patterns in fruit/vegetable structure and then eating their creations. Standards: 5.G.3 Understand that attributes belonging to a category of two-‐dimensional figures also belong to all subcategories of that category 5.G.4 Classify two-‐dimensional figures in a hierarchy based on properties Objectives: SWBAT identify geometric shapes based on attributes SWBAT group together similar shapes SWBAT predict internal geometric shapes based on external observations Materials Paper plates Journal Pencil and eraser, colored pencils Illustrations or examples of geometric shapes Plastic cutlery or kid-‐safe knives Key Points: Knowledge • Geometric shapes are found all over the garden; some are natural, others are

man-‐made • Some important vocabulary words are:

§ Sphere, hemisphere § Cylinder, circle, oval § Half-‐circle § Square, rectangle § Polygon

• External shapes can help predict internal shapes Skills • Shape identification • Fruit/Vegetable selection and identification • Safe knife handling • Drawing various geometric shapes Essential Questions How do we group together similar shapes and figures? Why is it important to try new foods? How did your prediction of inner geometry shape out?

Introduction to New Material (10 min) Depending on desires for safety, either go ahead and pre-‐slice all fruit or plan on demonstrating safe cutting techniques. First, go through various shape examples with students, pointing out major features like faces, plane and angles. Ask volunteers to name and point to examples of shapes they recognize in the garden. With a sample, identify the outer shape, predict the inner geometric shape, cut open and discuss your findings. Show for students how to record their findings (how many triangles they’ve eaten, how many squares etc.,.) and model positive eating behavior. Guided Practice (10 min) Students should work in pairs to investigate various shapes in the garden. A data board listing all possible shapes and allowing for students to record the number of shapes they encounter is a good idea. Independent Practice (30 min) Students work around the garden trying new fruits and recording their findings. Collaboratively, students should be answering questions like: “What shapes are we using?” “How do shapes change depending on how you are looking at them or how you cut them? “ What new foods did we try?” Conclusion (5 min) Have student volunteers share their journal entries with the class. Hand out Student Exit Ticket Assessment. Addendum: Pattern exercises can also stem from this lesson. Have students construct patterns with geometric shapes and then have partners either mirror or modify. Students can also construct complex shapes from simpler shapes, for example a rhombus out of two triangles. Data analysis can also take place if class data is compiled on eating preferences. Look for the fruits most people liked, most people didn’t like, fractions of the class that liked certain things and not others etc.,.

Name: Cross Cut Snacks Activity

1.) What was your favorite snack today? Why was this your favorite?

2.) What was your least favorite snack? What was it your least favorite?

3.) What is an example of a fruit with a circular cross-‐section?

4.) What is an example of a fruit with two different shapes based on which way you cut it?

5.) What shape that you saw in this activity had the most sides?

6.) What was the simplest shape you saw in the garden?

7.) Sarah designed a pattern out of crops she harvested in the garden. In her pattern she had cross-‐sections of squash, tomatoes, cucumbers and raspberries. Draw a pattern using these possible crops that follows the pattern simplest shape à most complex shape.

Math Unit 8 Project: SNAP Challenge

In this activity students work on multi-‐digit number manipulation while investigating the Supplemental Nutrition Assistance Program (SNAP). Students are challenged to create a healthy diet on a limited budget and must perform math operations in order to calculate their nutritional needs verses financial means. Standards: 5.NBT.6 Find whole-‐number quotients of numbers with up to four-‐digit dividends and low-‐digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. 5.NBT.7 Add, subtract, multiply and divide decimals to hundredths using concrete models or drawings and strategies based on place value, properties of operation and/or the relationship between addition and subtraction Objectives: SWBAT catalog what they eat in an average day and perform necessary operations to calculate average nutrient intake SWBAT analyze daily intake to determine what can be given up SWBAT reformulate a diet based on only $4 per day Materials Paper Pencil and eraser Colored Pencils Nutrient Information table (see, Teaching the Food System website at Johns Hopkins Center for a Sustainable Future teacher resources) Key Points: Knowledge • Many foods are more healthy for you than others because of the nutrients they

have in them • Unfortunately, most food that is not healthy for you is also the cheapest • When you evaluate foods based on nutrient content per dollar, it becomes more

obvious that it’s better to buy the good stuff and avoid the bad stuff • Being able to divide multi-‐digit numbers quickly in your head using rounding

and place value strategies is a valuable tool to be able to use when buying groceries

Skills • Healthy Eating • Food Budgeting Essential Questions

Why is it important to budget for healthy eating? Why is are some foods healthier than others? How do you determine nutrition per dollar? Introduction to New Material (10 min) Discuss with students the SNAP program and why some people try to demonstrate how hard it is to subsist under this program by “SNAP dieting” for short periods of time. Ask volunteers to explain how they might determine if one food is healthier than another. Then introduce the ANDI scoring system and go through various examples, both nutritious and non-‐nutritious ones. Be sure to discuss what serving size is and how the values for nutrient density and cost are expressed in uniform serving sizes. Share with students what a healthy diet looks like and what sort of ANDI score they should be shooting for. Guided Practice (10 min) First, start by showing students how you would record a weekly diet. Ask for volunteers to share a typical daily diet and keep track of this on a white board or chalkboard. Then walk through the steps of calculating the relative nutritional benefit of a food item by dividing the ANDI score by the dollar amount per serving. Use integers or decimals depending on where you are in your math curriculum. A standard algorithm for guidance should be shown. Independent Practice (30 min) Students should work independently or in small groups to first write out an average weekly diet, that is, what they would like to eat. Students then calculate the total cost of that diet using the given prices. Students should also calculate the ANDI score of their desired diet. Have students then compare their diets with peers and find the average for the class. Students should then try and design a diet that falls under the SNAP benefit guidelines. This will require them to recalculate their old diets using multiplication and division or design a completely new diet following the same steps as before. Conclusion (5 min) Have students reflect on what they learned in this activity. Do they think they could live very comfortably this way? Pass out Student Exit Ticket. Addendum: It is critical that this lesson be adapted for whatever level of math proficiency your students are at. A completely worked example of the steps would be beneficial. This lesson also has a lot of potential to be manipulated to utilize different iterations of numbers, meaning decimals, fractions, integers…whichever you’re trying to practice.

Name: SNAP Challenge Activity

1.) What is food insecurity?

2.) What is generally cheaper, healthy food or unhealthy food?

3.) If Jenny has $1,040 to spend on food for an entire year, how many dollars can Jenny spend per week? (There are 52 weeks in one year).

4.) John needs help deciding how to eat healthy with just $5. Based on the following ANDI scores, what would you buy to maximize John’s nutrition? Explain your choice(s).

-‐ $5 dollar hamburger (40 ANDI points) -‐ $3 turkey sandwich (25 ANDI points) -‐ $1 carrot sticks ( 20 ANDI points) -‐ $2 soda (1 ANDI point) -‐ $1 juice (5 ANDI points)

5.) About how many times healthier is kale (ANDI score of 1000) compared to a cheeseburger (ANDI score of 50)? Explain your reasoning.

Operations and Algebraic Thinking 5.OA Common Core Garden Cluster: Write and interpret numerical expression In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: parentheses, brackets, braces, numerical expressions, calculate, lattice, estimate Common Core Standard

In Practice1 What should a student be able to know and do? What does this look like in the garden?

Garden Examples

5.OA.1 Use parentheses, brackets or braces in numerical expressions and evaluate expressions with these symbols

The order of operations is introduced in third grade and is continued in fourth. In upper levels of mathematics, evaluate means to substitute for a variable and simplify the expression. However, at this level, students are to only simplify the expressions because there are no variables. Example: In order to evaluate the total area of all her raised beds, a gardener creates the following expression: 2{ 3[ 4+5(70-‐60) +6]} Students should already have experience working first with parentheses, then brackets and finally braces. This standard is one that will be routinely used in the garden to calculate area and counting the numbers of things (seeds, plants, fruits etc.,). Many activities can be formatted to highlight this standard in any area where repetition of actions takes place. Of course students are not expected to come up with these equations on their own but could, according to the standards, evaluate already created expressions.

• Seed/fruit estimation

• Peer constructed math problems

• Crop yield with number models

• Crop dot patterns with number models

1 Adopted from “5th Grade Mathematics: Unpacked Content.” Instructional Support Tools For Achieving New Standards. North Carolina Department of Public Instruction. 2012.

5.OA.2 Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them

Expressions are a series of numbers and symbols (+,-‐, x, ÷) without an equals sign. Equations result when two expressions are set equal to each other (1+2 = 3+0). This standard calls for students to verbally describe the relationship between expressions without actually calculating them. This standard calls for students to apply their reasoning of the four operations as well as place value while describing the relationship between numbers. The standard does not include the use of variables, only numbers and signs for operations. Now while the standard does not allow the use of variables, it does allow the use of units, such as peas and carrots or plants and seeds. Examples: How many tomatoes are on two bushes if each plant has 8 fruit? (8 x 2) What is the total area of beds A, B and C (AA+AB+AC) Show me how many 5 gallons buckets of mulch you need to move 20 gallons of mulch (20 ÷ 5) *Both 5.OA.1 and 5.OA.2 rely heavily on material that should be first introduced in the classroom. 5.OA.2 builds on basic arithmetic, which students will have 3+ years of experience with by the time they reach fifth grade. Thus, in the garden, this standard will almost always exist in everyday practice, but won’t ever be explicitly taught.

• Estimation activities

• Garden measurement (multi-‐step)

• Garden scavenger hunt with algebraic steps

• Crop/Fruit yield calculation

• Simple unit conversions

• Square-‐unit garden planning

Operations and Algebraic Thinking 5.OA Common Core Cluster Garden Cluster: Analyze patterns and relationships In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: numerical patterns, rules, ordered pairs, coordinate plane, linear, change over time Common Core Standard


Garden Examples

5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns and graph the ordered pairs on a coordinate plane.

This standard extends the work from fourth grade, where students generate numerical patterns when they are given one rule. In fifth grade, students are given two rules and generate two numerical patterns. The graphs that are created should be line graphs to represent the pattern. Students could generate graphs depicting plant growth over time, water absorption throughout the day, plant shadow movement across the ground during the day etc.,. Any activity whereby students create a table and then graph results should meet this standard. Whether it’s crop harvest per student/class/school or rainfall during the year or numbers of worms in the compost bin during different seasons, these can all be demonstrated graphically. Example: Mr. S’s 1st period class picked 10 lbs of produce on Monday, 12 lbs on Tuesday and 16 lbs on Thursday. First enter this information into a data chart and then create a line graph showing their harvest yields for the week. How much did they most likely harvest on Wednesday?

• Data tables and line graph creation

• Pattern analysis—seed plots, flower petals, leaf structure

• Planting patterns

• Harvest and yield data analysis


Number and Operations in base Ten 5.NBT Common Core Cluster Garden Cluster: Understand the place value system In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: place value, decimal, decimal point (.), patterns, multiply (x), divide (÷), tenths (0.X), thousands (X000), greater than (>), less than (<), equal to (=), compare/comparison, round Common Core Standard


Garden Examples

5.NBT.1 Recognize that in a multi-‐digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Students extend their understanding of the base-‐ten system to the relationship between adjacent places, how numbers compare, and how numbers round for decimals to thousandths. This standard calls for students to reason about the magnitude of numbers. This standard extends the understanding of decimals as fractions and the expression and use of rational numbers. Students will be exposed to this recurring practice when using the metric system in the garden as well as when utilizing the square meter gardening method. Routine measuring in the garden will also practice this standard. Example: Arrange a squared-‐off planter bed to have four rows and label them ones, tens, hundreds and thousands. Students receive four different seed varietals and instructions on what varietals can be planted in what density—for example, radishes—16 per square unit, beets—9 per square unit, cucumbers—8 per square unit and celery—1 per square unit. Students then attempt to plant as many different “numbers” across the bed as they can (i.e., 16981, 8291, 9128 etc.,)

• Measuring • Garden-‐

based worksheets

• Place-‐row planting

• Dilutions


5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-‐number exponents to denote powers of 10.

New to fifth grade math is the use of whole number exponents to denote powers of 10. Students understand why multiplying by a power of 10 shifts the digits of a whole number or decimal that many places to the left. The use of tens based exponents is of course the basis of the metric system, even if it is not taught expressly so. Although scientific notation would not be appropriate for this grade level, factors of ten could be used to show simple metric conversions (e.g., 1 meter = 1 x 102 centimeters = 100 cm). This practice will also come into play when calculating dilutions of concentrations of soil and fertilizer. Example: Any sort of metric system conversion in the garden will practice this skill. Having students measure compost amounts in different beds would be a great example of this. Say one bed is to receive 500 grams of compost/fertilizer and another bed is to receive 6 hectograms. Which one is more? How many “places” are their numbers different? How many factors of 10 is this?

• Seed/plant counting worksheets

• Size or magnitude calculation

• Large-‐scale farm calculations

• Hectare analysis

• Garden planning

5.NBT.3 Read, write and compare decimals to the thousandths. a. Read and write decimals to thousandths using base-‐ten numerals, number names and expanded form.

b. Compare two decimals to thousandths based on meanings of the digits in each place using >, = and < symbols to record the results of

This standard references expanded form of decimals with fractions included. Students should build on their work from fourth grade, where they worked with both decimals and fractions interchangeably. Students connect their prior experiences with using decimal notation for fractions and addition of fractions with denominators of 10 and 100. They use concrete models and number lines to extend this understanding of decimals to the thousandths. Models in the garden my include square-‐unit beds, coordinate planes, units of volume and mass etc., This investigation leads them to understanding equivalence of decimals (0.8 = 0.80 = 0.800). Example: Have students use the numbers of plants or seedlings in a raised bed to create decimals of varying degrees. For example, a student, reading across a bed, might see 4 radishes, 1 lettuce and 5 onions. They could express this as 4.15, 0.415, 514. etc.,. A game could very easily be constructed with part b to compare student numbers. Comparing decimals builds on work from fourth grade. Students need to understand the size of decimal numbers and relate them to common benchmarks such as 0, 0.5 (0.50 and 0.500) and 1. This can pretty easily be accomplished by asking students to compare their findings in the garden to stated measurements or peer measurements/calculations.

• Garden size comparisons

• Scaling • Metric

conversion and analysis

• Measuring quizzes

• Planter bed number comparison

• Planting numbers

comparisons. 5.NBT.4 Use place value understanding to round decimals to any place.

This standard refers to rounding. Student should go beyond simply applying an algorithm or procedure for rounding. The expectation is that students have a deep understanding of place value and number sense and can explain and reason about the answers they get when they round. Students should experience using a number line to support their work with rounding. Again, with routine measurements in the garden, rounding will become commonplace. Before any lesson or activity, a rounding expectation should be set. For example, if measuring distance of garden features, students should round to the nearest whole meter or decimeter. If measuring length in a gardening bed, centimeters. If measuring plant features and anatomy, to the nearest whole millimeter or express in centimeters with a decimal. Example: Analyze the vegetable varietals in a raised bed by counting the number of fruits present in every square unit. Find the average yield per square unit and round to the nearest tens place. Now compare your findings with those of your peers. Where are carrots growing the best? Where are they growing the worst? What are some differences that may be accounting for this? Note: All of these standards should be routinely practiced and emphasized, there shouldn’t be a single lesson in particular that extolls one of these any more than another. Rounding is an inherent part of measurement and measuring is inherent to best practices in the garden.

• Counting in the garden

• Crop yield • Hand

measuring • Plant

anatomy and measuring

• Mass measuring

• Garden bed building

• Area, perimeter and volume calculations

Numbers and Operations in Base Ten 5.NBT Common Core Cluster Garden Cluster: Perform operations with multi-‐digit whole numbers and with decimals to the hundredths place. In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: multiplication/multiply, division/divide, decimal, decimal point, tenths, hundredths, products, quotients, dividends, rectangular arrays, area models, addition/add, subtraction/subtract, (properties)-‐rules about how numbers work, reasoning Common Core Standard


Garden Examples

5.NBT.5 Fluently multiply multi-‐digit whole numbers using the standard algorithm.

In fifth grade, students fluently compute products of whole numbers using the standard algorithm. Underlying this algorithm are the properties of operations and the base-‐ten units and applying the distributive property to find the quotient place by place, starting from the highest place. (Division can also be viewed as finding an unknown factor: the dividend is the product, the divisor is the known factor and the quotient is the unknown factor). Students continue their fourth grade work on division of up to four digits and two-‐digit divisors. Estimation becomes relevant when extending to two-‐digit divisors. Even if students round appropriately, the resulting estimate may need to be adjusted.

• Finding area of square gardening units

• Watering calculations

• Fertilizer and compost dilution calculations


5.NBT.5 Cont.

Computation algorithm. A set of predefined steps applicable to a class of problems that gives the correct result in every case when the step are carried out correctly. Computation strategy. Purposeful manipulations that may be chosen for specific problems, may not have a fixed order and may be aimed at converting one problem into another. In the garden this looks almost exclusively like guided practice and independent practice. There are obvious instances where these operations will need to be performed, but initial instruction of these standards should take place in the classroom. Students will practice dividing numbers whenever working in and around the garden, whether its in counting the numbers of plants per unit area or dividing parts of a whole. As with other standards, practice of these operations can easily be tailored to the garden, with worksheets using garden attributes as units to help students acquire fluency and numeracy. Example: Estimate the crop yield of bed X based on the number of fruit on one plant. If the tomato plant has 24 fruits and there are 11 plants in the bed, how many fruits can you expect to harvest? You can do this with seeds, fertilizer, leaves…pretty much anything growing in the garden or being done in multiples.

• Peer

designed algorithm practice—using crop numbers in the gardening beds or geometric values found in the garden

5.NBT.6 Find whole-‐number quotients of numbers with up to four-‐digit dividends and low-‐digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain the calculations by using equations, rectangular arrays and/or area models

This standard references various strategies for division. Division problems can include remainders. Even though this standard leans more towards computation, the connection to story contexts is critical; this is easily adopted in the garden setting Make sure students are exposed to problems where the divisor is the number of groups (plant yields) and where the divisor is the size of the groups (square-‐unit garden areas). In fourth grade, student experiences with division were limited to dividing by one-‐digit divisors. This standard extends student’s prior experiences with strategies, illustrations and explanations. When the two-‐digit divisor is a “familiar” number, a student might decompose the dividend using place value. Example: There are 1,243 seeds that need to be stored for the winter in packages of 12 each. How many packages will be created? What should be done with leftover seeds? Students could then be directed to solve in one of two different ways, either by standard algorithm or place value decomposition. This could be further illustrated using a latticed gardening bed, with a known number of seeds per row. Different rows could represent different place values and students could support their initial division answers by multiplying back through the rows, using them as area models.

• Peer derived

division problems in the garden

• Yield per unit are calculations

• Garden construction calculations

5.NBT.7 Add, subtract, multiply and divide decimals to hundredths using concrete models or drawings and strategies based on place value, properties of operation and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used

Because of the uniformity of the structure of the base-‐ten system, students use the same place value understanding for adding and subtracting decimals that they used for adding and subtracting whole numbers. Like base-‐ten units must be added and subtracted, so students need to attend to aligning the corresponding places correctly (this also aligns the decimal points). It can help to put 0s in places so that all numbers show the same number of places to the right of the decimal point. Although whole numbers are not usually written with a decimal point, but that a decimal point with 0s on its right can be inserted (e.g., 16 can also be written as 16.0 or 16.00). The process of composing and decomposing a base-‐ten unit is the same for decimals as for whole numbers and the same methods of recording numerical work can be used with decimals as with whole numbers. For example, students can write digits representing new units below on the addition or subtraction line and they can decompose units wherever needed before subtracting. The use and manipulation of non-‐whole numbers in the garden will help students to practice meeting this standard. Finding the area of various features can help to illustrate the result of multiplying tenths by tenths and calculating volume can take this all the way to the thousandths place. Example: Find the average yield of all the X plants. First you will need to add up all the masses from each individual plant, rounded to the tenths place and then you will divide that number by the total number of plants.

• Pretty

much any of activities mentioned in the about NBT standards can be approached from a real number point of view

Numbers and Operations—Fractions 5.NF Common Core Garden Cluster: Use equivalent fractions as a strategy to add and subtract fractions In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: fraction, equivalent, addition/add, sum, subtraction/subtract, difference, unlike denominator, numerator, benchmark fraction, estimate, reasonableness, mixed numbers Common Core Standard


Garden Examples

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b +c/d = (ad+ bc)/bd)

This builds on work from fourth grade where students add fractions with like denominators. In fifth grade, the example provided in the standard 2/3 +3/4 has students find a common denominator by finding the product of both denominators. This process should come after students have used visual fraction models (area models, number lines etc.) to build understanding before moving into the standard algorithm. This is best exemplified in the garden with the lattice structure of the square-‐unit gardening method. Lattices can be specifically constructed to demonstrate a multitude of fractions and provide visual aid; planting in the beds can be expressed in fractions. The use of these visual fraction models allows students to use reasonableness to find a common denominator prior to using the algorithm. For example, when adding ¼ of a bed with 1/8 of a bed, fifth grade students should apply their understanding of equivalent fractions and their ability to rewrite fractions in an equivalent form to find common denominators (solve for 3/8).

• Garden planning

• Planting • Soil mixes • Fertilizer

dilutions • Adding and

subtracting crop types and harvest amounts

• Garden feature measuring (imperial units)


5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

This standard refers to number sense, which means students’ understanding of fractions as numbers that lie between whole numbers on a number line. Number sense in fractions also includes moving between decimals and fraction to find equivalents, also being able to use reasoning such as 7/8 is greater than ¾ because 7/8 is missing only 1/8 and ¾ is missing ¼ so 7/8 is closer to a whole. Also, students should use benchmark fractions to estimate and examine the reasonableness of their answers. Example: Students need to mix two different types of soil. One recipe calls for ¾ potting soil and the other 2/3, the rest is compost. How much potting soil do they need to fill two beds? How much compost will they need.

• Garden derived word problems

Numbers and Operations—Fractions 5.NF Common Core Garden Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: fraction, numerator, denominator, operations, multiplication/multiply, division/divide, mixed numbers, product, quotient, partition, equal parts, equivalent, factor, unit fraction, area, side lengths, fractional side lengths, scaling, comparing

Common Core Standard


Garden Examples

5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers, e.g., by using visual fraction models or equations to represent the problem.

Fifth grade students should connect fractions with division, understanding that 5 ÷ 3 = 5/3. Students should explain this by working with their understanding of division as equal sharing. Students should also create story contexts to represent problems involving division of whole numbers. Students need ample experiences to explore the concept that a fraction is a way to represent the division of two quantities. Example: Have students model different fractions in the garden using strings to set up lattice structures just as they normally would to plan in the square-‐unit gardening method. For example, to model 3/8, a student might square off 3 pea plants out of a group of 8. Now this could be made more exciting if made into a competition where there was a list of known fractions the students had to search for in the garden.

• Square-‐unit garden planting

• Group planting

• Plant thinning


5.NF.4 Apply and extend previous understanding of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) x q as parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas.

Students need to develop a fundamental understanding that the multiplication of a fraction by a whole number could be represented as repeated addition of a unit fraction (e.g., 2 x (1/4) = 1/4 +1/4 This standard references both the multiplication of a fraction by a whole number and the multiplication of two fractions. Visual fraction models (area models, tape diagrams, number lines) should be used and created by students during their work with this standard. Example: This can be represented by multiplying given coefficients, like requisite amount of watering, times fractions found in the garden—e.g., if every bed gets 8 gallons of water, how much water does ¼ of the bed receive? This standard extends students’ work with area. In third grade students determine the area of rectangles and composite rectangles. In fourth grade students continue this work. The fifth grade standard calls students to continue the process of covering (with tiles). Grids, as implemented in the garden beds, can be used to support this work. Example: What is the area of a planting unit that measures ¾ meters by 2 meters? Find the area covered by all the pea plants, all the carrot plants, all the cucumbers etc.,. What fractions did you encounter when doing this?

• Plant nutrient calculations

• Watering calculations

• Crop coverage estimation

• Area calculations

• Yield estimation

5.NF.5 Interpret multiplication as scaling (resizing) by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated operation b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1.

This standard calls for students to examine the magnitude of products in terms of the relationship between two types of problems. This extends the work with 5.OA.1. Example: This can be practice when estimating area without measuring. Say a student needs to determine the area of a bed and compare it to another bed, they could compare one side length to another without determining the product. This standard asks students to examine how numbers change when we multiply by fractions. Students should have ample opportunities to examine both cases in the standard: a) when multiplying by a fraction greater than 1, the number increases and b) when multiplying by a fraction less than one, the number decreases. This standard should be explored and discussed while students are working with 5.NF.4. Example: Students will observe this whenever multiplying by a coefficient by a fraction in the garden. This happens when calculating fertilizer/compost/water concentration for a particular area, crop yield per unit are or when building various garden features.

• Plant watering

• Compost managing

• Fertilizer dilutions

• Crop yield

5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., using visual fraction models or equations to represent the problem

This standard builds on all of the work done in this cluster. Students should be given ample opportunities to use various strategies to solve word problems in the garden involving the multiplication of a fraction by a mixed number. This standard could include fraction by a fraction, fraction by a mixed number or mixed number by a mixed number. This is easily accomplished using fraction found in the beds, be it plants, fruits, seeds etc., or various features found in the garden. Problems can be either real-‐life and relevant to the gardening experience, or hypothetical and creative.

• Peer created story problems using garden features

• Scavenger hunts through the garden using fraction problems found around the garden

5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.* a. Interpret division of a unit fraction by a non-‐zero whole number and compute such quotients * Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. Keep in mind that division by a fraction is not a requirement at this grade level. 5.NF.7a Students do the above but in a story context.

This is the first time students are dividing with fractions. In fourth grade, students divided whole numbers and multiplied a whole number by a fraction. The concept unit fraction is a fraction that has a one in the denominator. For example, the fraction 3/5 is 3 copies of the unit fraction 1/5. 1/5 + 1/5 + 1/5 = 3/5 Example: Knowing the number of groups/shares and finding how many/much in each group to share. Have a student group decide how many of a particular harvest fruit they can get based on the number of students and the yield expressed as a fraction. Say a group of 3 students harvests 1/3 of a bed of carrots, what fraction of the bed does each student get to harvest? Example: The above can be done in the classroom as story problems.

• Crop distribution

• Group activities division and sharing

• General garden measuring

5.NF.7b Interpret division of a whole number by a unit fraction and compute such quotients. 5.NF.7c Solve real world problems involving division of unit fractions.

This standard calls for students to create a story contexts and visual fraction models for division situations where a whole number divided by a unit fraction. Example: Have students plan out a garden bed, including a schematic detailing fractions of different seeds planted. Then have students carry fractions through to the harvest and calculate yield. This extends student work from other standards in 5.NF.7. Students should continue to use visual fraction models and reasoning to solve these real-‐world problems. Example: Calculating percent yield or crops yielded per fractional unit in a bed.

• Seed planting

• Garden planning

• Harvest and yield calculations

Measurement and Data 5.MD Common Core Garden Cluster: Convert like measurement units within a given measurement system In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: Conversion/convert, metric and customary measurement. From previous grades: relative size, liquid volume, mass, length, kilometer (km), meter (m), centimeter (cm), kilogram (kg), gram (g), liter (L), milliliter (mL), inch (in), yard (yd), mile (mi), ounce (oz), pound (lb), cup (c), pint (pt), quart (qt), gallon (gal), hour, minute, second Common Core Standard


Garden Examples

5.MD.1 Convert among different-‐sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m) and use these conversions in solving multi-‐step, real world problems.

Calls for students to convert measurements within the same system of measurement in the context of multi-‐step, real-‐world problems. Both customary and standard measurement systems are included; students worked with both metric and customary units of length in second grade. Students should explore how the base-‐ten system supports conversions within the metric system. This is an excellent opportunity to reinforce notions of place value for whole numbers and decimals and connection between fractions and decimals (e.g., 2 ½ meters can be expressed as 2.5 meters or 250 centimeters). This standard is by and large the most practiced in the garden setting. Any sort of measurement opportunity should be taken advantage of.

• Any measuring in the garden

• Garden construction

• Plant anatomy lessons

• Crop harvest

• Plant care


Measurement and Data 5.MD Common Core Garden Cluster: Represent and interpret data In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: line plot, length, mass, liquid volume Common Core Standard


Garden Examples

5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, ⅛). Use operations on fractions for this grade to solve problems involving information presented in line plots.

This standard provides a context for students to work with fractions by measuring objects to one-‐eighth of a unit. This includes length, mass and liquid volume. Students are making a line plot of this data and then adding and subtracting fractions based on data in the line plot. Example: Have students go through the garden measuring various leaf widths and rounding their answers to the nearest 1/8 in. While doing this, students should keep track of their measurements in a chart displaying where they rounded to, displaying it on a line plot.

• Harvest analysis

• Sunlight tracking data

• Watering data

• Class garden data


Measurement and Data 5.MD Common Core Garden Cluster: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: measurement, attribute, volume, solid figure, right rectangular prism, unit, unit cube, gap, overlap, cubic units (cubic cm, cubic in., cubic ft., nonstandard cubic units), multiplication, addition, edge lengths, height, area of base Common Core Standard


Garden Examples

5.MD.3 Recognize volumes as an attribute of solid figures and understand concepts of volume measurement. a. A cube with a side length of 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume and can be used to measure volume.

These standards represent the first time that students begin exploring the concept of volume. The concept of volume should be extended from area with the idea that students are covering an area (the bottom of a cube) with a layer of unit cubes and then adding layers of unit cubes on top of the bottom layer. Example: Using the square-‐unit grid pattern in a garden, start to calculate the volume of some of the beds. The lattice may have to be reevaluated to compensate for a smaller unit (feet rather than meters), but it’s essentially the same as all other measurement standards thus far.

• Raised bed volume calculations

• Fruit volume

• Lattice formation in three-‐dimensions


b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume n 5.MD.4 Measure volumes by counting unit cubes, using cubic centimeters, cubic inches, cubic feet and improvised units. 5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-‐number side lengths by packing it with unit cubes, and show that the volume is the same as would be found

Example: Do a volume investigation into the volume of irregular objects, such as fruits. Have students place a known amount of sand in a pot, measure the fill level and then bury the object. Record the new level to calculate total volume of the object. As students develop their understanding of volume they will understand that a 1-‐unit by 1-‐unit by 1-‐unit cube is the standard unit for measuring volume. This cubic unit is written with an exponent of 3 ( e.g., in3, cm3, m3). Students connect this notation to their understanding of powers of 10 in our place value system; this build on 5.NBT.2. Models of cubic inches, centimeter, feet and meters in the garden are plentiful and helpful in developing an image of a cubic unit. The major emphasis for measurement in fifth grade is volume. Volume introduces a third dimension and thus a significant challenge to students’ spatial structuring, but also complexity in the nature of the materials. Practicing this standard in the garden alleviates some of this abstractness by using objects the student will have grown familiar with by that point. Example: To illustrate the equivalency of 1 milliliter and 1 cm3, have students build a 10 cm x 10 cm x 10 cm cube and pour 1 liter of water into it. What other 1000 ml structures can they create? Is there anything with irregular dimension that they can build and prove it’s volume? What about determining the volume of a watering can using a known measure of volume.

• Watering

volumes • Fruit

volumes • Raised bed

volumes • Liquid

versus dry volumes

by multiplying the height by the area of the base. Represent threefold whole-‐number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-‐number edge lengths in the context of solving real world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-‐overlapping right rectangular prisms by adding the volumes of the non-‐overlapping parts, applying this technique to solve real world problems.

*Note: The unit structure for liquid measurement may be psychologically one dimensional for some students. This will be accomplished in the garden on a more macro scale, using plant beds. Students should construct square units, based on whatever unit is being used in the garden bed lattice structure and first estimate or crudely measure the gardening beds with said units. Then have groups of students measure the dimensions of the bed and calculate volume using the standard rectangular equation. This can be scaled up or down based on unit. Have students determine the volume of a shed in meters, a barn in meters, a classroom, a box etc.,. Students also need to be able to construct and deconstruct rectangular prisms and determine their joint volumes. This can be practiced similar to how the garden maps were created when looking at area and perimeter in two dimensions. Have students draw determine volume independently and draw schematics including measurements. Then do this in three dimensions and show how some side lengths become additive, others subtractive. Example: Have students design their own garden after experiencing their school garden for a while. What structures will they have in their garden? What will the volume of said structures be? What volume of

• Planter box

measuring • Square-‐unit

volume calculations

• Soil volume • Fertilizer

volume • Water

volume • Crop and

harvest volume calculation

construction materials will they need? What volume of produce do they hope to harvest?

Geometry 5.G Common Core Garden Cluster: Graph on the coordinate plane to solve real-‐world and mathematical problems In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: coordinate system, coordinate plane, first quadrant, points, lines, axis/axes, x-‐axis, y-‐axis, horizontal, vertical intersection of lines, origin, ordered pairs, coordinates, x-‐coordinate, y-‐coordinate Common Core Standard


Garden Examples

5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that

5.G.1 and 5.G.2 deal with only the first quadrant, thus only positive numbers. Once introduced in the classroom, a lattice structure can be constructed over a raised bed to serve as a coordinate plane; it’s important that each string is numbered, not each space. A standard procedure should also be established for identifying what side length is the x-‐axis and which one is the y-‐axis. Although students can often locate a point, these understandings are beyond simple skills. For example, students often fail to distinguish between two different ways of viewing the point (2,3), as either directions or distances. An standard procedure for determining points in a garden must be enforced.

• Coordinate planting

• Coordinate harvesting

• Coordinate watering

• Tracing in the garden

• Coordinate plane design

• Locations in the


the first number indicates how far to travel from the origin in the direction of one axis and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-‐axis and x-‐coordinate, y-‐axis and y-‐coordinate. 5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.

Example: Have students plant seed assignments based on coordinate shapes. For example, plant carrot seeds in the square-‐unit outlined by the points (2,4,),(3,4),(2,5),(3,5). This can be done with watering, harvesting or any other task which must be done in the garden so long as the coordinate plane is in place. As far as graphing goes, this can be emphasized during harvest times. Placing bushels on a coordinate plane based on yield can help to graphically show the magnitude. Students should then graph this data on graph paper or self-‐made graphs.

garden • Directions

in the garden

• Locating unit squares

• Scavenger hunts

Geometry 5.G Common Core Garden Cluster: Classify two-‐dimensional figures into categories based on their properties. In the garden, students will practice becoming mathematically proficient by engaging in discussion using standard-‐appropriate vocabulary. In this cluster, this includes: attribute, category, subcategory, hierarchy, (properties)-‐rules about how numbers work, two dimensional From Previous grades: polygon, rhombus/rhombi, rectangle, square, triangle, quadrilateral, pentagon, hexagon, cube, trapezoid, half/quarter circle, circle, kite Common Core Standard


Garden Examples

5.G.3 Understand that attributes belonging to a category of two-‐dimensional figures also belong to all subcategories of that category.

This standard calls for students to reason about the attributes (properties) of shapes. Students should have experiences discussing the property of shapes and reasoning. The notion of congruence (“same size and shame shape”) may be part of classroom conversation but the concepts of congruence and similarity do not appear until middle school. Example: What are some different shape types found in the garden? What sort of parallelograms can be found in the garden? What angle is found in all of the raised beds?

• Garden shapes

• Plant shapes

• Shapes in the coordinate plane

• Symmetry in the garden


5.G.4 Classify two-‐dimensional figures in a hierarchy based on properties.

This standard builds on what was introduced in fourth grade. Figures from previous grades include: polygon, rhombus/rhombi, rectangle, square, triangle, quadrilateral, pentagon, hexagon, cube, trapezoid, half/quarter circle, circle, kite. A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-‐length sides that are beside (adjacent to) each other. In the garden this looks like geometric shape chart activities, plant dissections, triangles in the garden, angle searches, planting in geometric patterns and basic garden construction. Example: Use your hierarchy of geometric shapes to find one example of every shape in the garden. Be creative, some plants may need to be investigated closely to find these shapes.

• Plant

shapes • Garden

structures • Fruit

shapes • Angles in

the garden and beds

• Trellises

Common Core Garden Cluster Table of Contentsmsfarmtoschool.org/uploads/We_Dig_It_5th_Grade_Math...5th Grade Math School Garden Curriculum We Dig It! Common Core Garden Cluster Table

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