SLED Implementation Plan
Your Name(s):
Jo Goodrich
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Grade Level:
6th Grade Math
School:
Taylor Middle School
Total time (hours or class sessions):
Two – 47 minute class sessions
Unit BIG IDEAS:
Understand the mathematics of surface area and
volume and how size and shape may affect
properties.
Understand mathematical concept of ratio ( S/V in
units of 1/cm) of the surface area and (S in cm²) to
the volume (V in cm³) for each rectangular prism.
Understand that geometry can be used to model
and design solutions to real-world
problems/situations.
Understand that measurement is used to quantify
attributes of objects in order to solve a problem.
Key vocabulary:
ratio, formulas, surface area, volume, measurementmetric, three-dimensional, squared, cubic, design
process
Unit prior to and following this unit:
Prior: Using proportions (equivalent ratios) to solve
problems.
Following: Define, identify, draw, and measure
types of angles: vertical, adjacent, complementary,
and supplementary.
Estimated starting date in the school year:
Third 9 weeks grading period (Jan.)
Unit Objectives:
By the end of this unit, students will be able to:
- Create a rectangular prism with an accurate measurement to solve a problem.
- Compute surface area and volume using correct unit labeling and measure.
- Identify the change in surface area and/or volume as the prism becomes smaller.
- Using knowledge gained of surface area and volume, design a successful prototype
- Engineering Design Process will facilitate interactive and productive student learning
Core Indiana Academic Standard to be addressed:
6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. (Formulas)
6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical
problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand,
any number in a specified set.
6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes
of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by
multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right
rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical
SLED Summer Institute 2011
problems.
6.SP.5 Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its
units of measurement.
Standard Indicator(s) to be addressed:
6.1.6 Use models to represent ratios.
6.2.6 Interpret and use ratios to show the relative sizes of two quantities. Use the notations:
a/b, a to b, a:b.
6.3.2 Write and use formulas with up to three variables to solve problems.
6.3.5 Use variables in expressions describing geometric quantities.(Find surface area of 3-D objects of
rectangular solids.
6.5.1 Select and apply appropriate standard units and tools to measure length, area, volume, weight, time,
temperature, and the size of angles.
6.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying
missing information, sequencing and prioritizing information, and observing patterns.
6.7.5 Express solutions clearly and logically by using the appropriate mathematical terms and notation.
Support solutions with evidence in both verbal and symbolic work.
6.7.9 Make precise calculations and check the validity of the results in the context of the problem.
6.7.10 Decide whether a solution is reasonable in the context of the original situation.
Process Standards:
- Build new mathematical knowledge through problem solving
- Identify a need or problem to be solved
- Select and apply a solution to the need or problem
- Adapt a variety of appropriate strategies to solve the need or problem
- Monitor and reflect on the problem solving process
- Present evidence by using mathematical representations (e.g., graphs, data tables, model)
Materials and Resources (available in school and/or will need to get):
Exploration Activity:
Teacher: large kitchen knife, spatula, metric ruler, measuring cup, 8 envelopes Knox unflavored gelatin per
class, 6 packages Jello, wax paper squares to work on per group per class
Students: plastic knives (10), metric ruler, graph paper, design notebooks
Design Activity: cardboard pieces (10” x 12”), craft sticks, colored duct tape, masking tape, glue, markers,
straws, pipe cleaners, graph paper, construction paper, material, string, scissors, design
notebooks
Overview of Lesson Activities:
INTRODUCTION: This lesson and included activities introduce students to the mathematical concepts of
ratio, surface area, volume, rectangular prism, and the Engineering Design Process. Through ratio calculations
SLED Summer Institute 2011
of surface area to volume, students will learn of the need for exact measurement and design. This knowledge
will be applied during an engineering design project that will challenge students to solve a problem, examine
multiple solution approaches, and create a usable model.
DAY 1
Pre-Preparation: Make rectangular prism Jell-O blocks: 8x8x2 cm.(one per group per class) For 30 students
you will need to prepare 2 sheet pans of Jell-O blocks.
Recipe for one sheet pan (makes 6 blocks).
1) Combine 4 envelopes (1/4 oz.) of Knox unflavored gelatin with 3 paaackages (3 oz.) of Jell-O
flavored gelatin in a mixing bowl and stir together. (Color blocks differently for each class)
2) Add 4 cups boiling water and stir until dissolved.
3) Spray 8x12 pan lightly with cooking oil spray.
4) Pour in gelatin until firm (overnight). Firm gelatin should be 2 cm. thickness.
5) Cut gelatin into six 8cm. x 8cm. x 2cm.
6) Using a spatula, carefully remove a block for each group to use.
Introduce Vocabulary: Surface area, volume, 3-dimensional, squared, cubed, formulas, and metric
Have students create in their design notebooks and share with their group a KWL chart for each vocabulary
word as they should have some knowledge of these words.
EXPLORATION ACTIVITY:
Ask: Why would surface area be important to know? (dimensions must match between an object and
model.)
How do you measure surface area? Formula: 2(l x w) + 2(l x w) + 2(l x w)
top & bottom both long sides
both ends
How do you measure volume? Formula: l x w x ht
2) Display a box as each face is recognized as a rectangle and the formula is applied.
3) Give a handout to each group of a chart to be pasted in their design journals.
3) Have each group measure using centimeter scale all 6 faces of the Jell-O block and record their findings in
their table.
4) Instruct students to calculate the volume (cm³) and total surface area (cm²).
5) Have students share and discuss computations to reach an agreed value.
Predict: What will happen to the surface area and volume when each block is cut in half?
(surface area will increase because you are adding 2 faces at fresh cut. Volume will remain the same
when you add
both back together)
6) Calculate the surface area and volume with each cut into new halves until they have a 1 x 1 x 1.
Ask: What is a ratio? (comparison of two values by division)
7) Instruct students to now compute the ratio of surface area/volume, labeling correctly, and completing the
chart
8) Guide students to put the results on a graph with x-axis labeled volume and y-axis labeled ratio S/V.
9) Discuss results: Ratio will decrease quickly as the size of prism decreases.
SLED Summer Institute 2011
10) Display on screen the table and complete with each groups data. Discuss differences.
11) Have students write a reflection in their notebook as to what surprise them, what learned, and how this
could be used in real life.
(When will I use surface area and volume?)
REVIEW ACTIVITY:
1) Students will review the multi-tab foldable in their design notebook on the steps of the engineering design
process.
2) Have students share what they wrote in their notebooks about real-life situations to use surface area and
volume.
DAY 2
ENGINEERING DESIGN PROCESS:
1) Display the Design Process flow chart on the screen and review any step that is needed.
2) Pass out the Design Activity: Calculator Cracks
Taylor Middle School 6th grade math teacher, Mrs. Goodrich, has stressed out for the last time over dropped
calculators off of desk with an end result of “CRRAAACCKK!!” She is pleading with you, 6th grade math
student, to design a calculator holder that will sit on the desk and safely contain the calculator in-between uses.
You will follow the steps of the design process as you use your knowledge of measurement, surface area, and
volume.
CRITERIA:
A. Your end model must completely hold the calculator in an upright position.
B. Each of the five steps must be recorded in your notebook with notes on procedure.
C. Answers to the questions at each step must be included.
D. Include a detailed and labeled diagram of the model you want to create using the supplied materials only.
E. Group share time will be provided for exchange of ideas.
F. A re-design session will be provided if you feel changes should be made. At that time, a new diagram
must be drawn.
G. Provide a creative way to display the measurement and data of your end product. Included must be the
dimensions of volume, surface area, and ratio of surface area to volume.
H. The project will conclude with a poster that you design to market your container and all of the wonderful
attributes of your design.
3) Read the task and identify the problem individually. Then as a group, discuss each question from the 1st
step of the process and answer in your design notebook.
Problem: How can classroom calculators remain safely on the desk when not in use?
Setting: Taylor Middle School
User/Client: Students/ Mrs. Goodrich
4) Continue working through the steps of the design process writing individual thoughts and group discussions
for each of the remaining four steps in your design notebook.
Constraints: Time…work quickly and carefully. Do not waste materials. Once you return to your desk with
materials, you will not be allowed to go back to the table.
SLED Summer Institute 2011
Materials: cardboard pieces (10” x 12”), craft sticks, colored duct tape, masking tape, glue, markers,
straws, pipe cleaners, graph paper, construction paper, material, string, scissors, design
Assessment:
FORMATIVE ASSESSMENT:
- Informal check-off list of group performance/participation, on-task behavior, process notebook entries
SUMMATIVE ASSESSMENT:
- Rubric to assess all steps of process performed in notebook
- Percentage grade of mathematical computation and measurement in tables
- Points totaled on foldable & KWL chart
- Rubric to assess model design
- Ten points for neatness/creativity
SLED Summer Institute 2011