The math standards addressed in our class project of finding ways to reuse the discarded food from school lunches will include many that are not at the first grade level. The first grade standards are:
Operations and Algebraic Thinking:
1.1: Represent and solve problems involving addition and subtraction.
1.7: Work with addition and subtraction equations.
Number and Operations in Base Ten:
2: Understand that the two digits of a two-digit number represent amounts of tens and ones.
4: Use Place Value understanding and properties of operations to add and subtract.
Add within 100 (probably up to 1000 or 10000, not first grade level) including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 using concrete models or drawings and strategies based on place value.
Measurement and Data:
Measure lengths to the nearest inch.
Mathematical Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7 Look for and express regularity in repeated reasoning.
Reflection from class:
I have not made a cross section before, or don't remember having done so. The YouTube was helpful. This activity had me wishing I had the map in my hands. I am so old school in some ways, I like to hold things, manipulate them. My cross section turned out to be correct so I look forward to redoing it and making it look nice for the due date. I would love to find an online link that could take my data and make a great looking visual. I guess I will need to spend some time looking on line. I am thankful that Chip gave us lots of time to do this as I would have been frustrated to have less time and not finish. This was a great example of how I probably need to give my students more time when learning something new. It is a fine line of enough time to finish versus enough time to lose focus and be off task, at least in first grade!
Wednesday, March 12, 2014
Heather D Math Standards and Reflection
I feel that my project will cover many math standards for second grade. But here are some, that I know it will focus on.
Numbers and Operation in Base Ten
Use place value understanding and properties of operations to add and subtract.
2.NBT.5 Fluently add and subtract using number up to 100. (I imagine we will go past 100)
2.NBT.6 Ad up to four two-digit numbers using strategies based on place value and properties of operations.
2.NBT.7 Add and subtract using numbers up to 1000.
Measurement and Data
Measure and estimate lengths in standard units.
2.MD.4 Measure to compare lengths of two objects, expressing the difference in terms of a standard length unit.
Relate addition and subtraction to length.
2.MD.5 Solve addition and subtraction word problems using numbers up to 100 involving length that are given in the same units.
Work with time and money.
2.MD.8 Solve word problems involving dollar bills and coins using the $ and ¢ symbols.
Geometry
Reason with shapes and their attributes.
2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Class Reflection
This was the first time I had ever drawn a cross section of a topo map. I really enjoyed it. THe biggest issue with it was making are that the horizontal and vertical scale were the same - or at least similar. The reason to make sure this happens is because it warps the look of the terrain if the scales are not the same. I did want to use my graph from class for my assignment, but have decided that t is not very polished, so I need to make it look much better. I will have to figure how to do that.
My children and I had fun in the world after class. I am not sure we found all of your ore, but it was hard because Abby found some lapis and then mined them quickly, but for some reason, i could not actually see her. She was invisible to me much of the time. If we do it again, I would probably try it again using the schematic.
I have also been thinking that this week would be a great week to do an extra credit lesson. Hmmm which one that is in my brain shall I do. I have been thinking about doing place value with numbers using different blocks for 100s, 10s, and 1s, or maybe area with rectangles (I actually just realized that this was a standard for 2nd grade - although it doesn't say area.) Maybe even something using number patterns. We shall see. Or maybe even a Sudoku.
Numbers and Operation in Base Ten
Use place value understanding and properties of operations to add and subtract.
2.NBT.5 Fluently add and subtract using number up to 100. (I imagine we will go past 100)
2.NBT.6 Ad up to four two-digit numbers using strategies based on place value and properties of operations.
2.NBT.7 Add and subtract using numbers up to 1000.
Measurement and Data
Measure and estimate lengths in standard units.
2.MD.4 Measure to compare lengths of two objects, expressing the difference in terms of a standard length unit.
Relate addition and subtraction to length.
2.MD.5 Solve addition and subtraction word problems using numbers up to 100 involving length that are given in the same units.
Work with time and money.
2.MD.8 Solve word problems involving dollar bills and coins using the $ and ¢ symbols.
Geometry
Reason with shapes and their attributes.
2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
Class Reflection
This was the first time I had ever drawn a cross section of a topo map. I really enjoyed it. THe biggest issue with it was making are that the horizontal and vertical scale were the same - or at least similar. The reason to make sure this happens is because it warps the look of the terrain if the scales are not the same. I did want to use my graph from class for my assignment, but have decided that t is not very polished, so I need to make it look much better. I will have to figure how to do that.
My children and I had fun in the world after class. I am not sure we found all of your ore, but it was hard because Abby found some lapis and then mined them quickly, but for some reason, i could not actually see her. She was invisible to me much of the time. If we do it again, I would probably try it again using the schematic.
I have also been thinking that this week would be a great week to do an extra credit lesson. Hmmm which one that is in my brain shall I do. I have been thinking about doing place value with numbers using different blocks for 100s, 10s, and 1s, or maybe area with rectangles (I actually just realized that this was a standard for 2nd grade - although it doesn't say area.) Maybe even something using number patterns. We shall see. Or maybe even a Sudoku.
Blog Post March 12, 2014
Math Standards for Playground Project with Minecraft
I went ahead and listed the mathematical practices that I hope to focus on as well which are the same across the grade levels. Then I highlited the standards my 6th grader(s) and my 4th grader(s) will focus on. My friend's children would like to join in the fun, so if I can work it out I will have two fourth graders and two sixth graders working on the project. We will begin tomorrow with the project timeline; we are heading over to the golf course to take a look around and draw some sketches.
Math:
Mathematical Practices:
- Make sense of problems and persevere in solving them.
- Model with mathematics
- Use appropriate tools strategically
Geometry
6.G Solve real-world and mathematical problems involving
area, surface area, and volume.
Expressions
and Equations
6.EE Apply and extend previous understandings of arithmetic
to algebraic expressions.
Operations
and Algebraic Thinking (4th grade)
- Use the four operations with whole numbers to solve problems
- Generate and analyze patterns.
Number and
Operations in Base Ten
4.NBT Use place value understanding and properties of
operations to perform multi-digit arithmetic.
Geometry
4.G Draw and identify lines and angles, and classify shapes
by properties of their lines and angles.
Class:
Class was challenging for me on Monday. I have never made a topographic map before. I am a little nervous about constructing one for the assignment due after spring break. I am hoping with a little more practice I can figure it out. Also, I thought it might be interesting to construct a topographic map for the golf course the students and I will be looking at. I am excited to look at this as an option for a part of their project. It may be useful if we are going to construct a world in Minecraft for them to build a playground in. It may just be me making a world or they may use one already constructed. I would like to try to construct something for them, though I am still learning how to use Minecraft.
Joel had so much fun playing with the class. I worked on dinner and watched him play around. He really enjoys talking with teachers. :)
Finally, I am excited to meet up with Chris and Colin tomorrow to create something for Joel and Ben to work on together. How cool!
Tuesday, March 11, 2014
This week's class was fun. I learned quite a bit. Mapping was fun, but I was very frustrated with the vertical line in the cross section mapping. I got the A-B line, but figuring out the vertical line accurately stumped me (even after class). Luckily, I have Chip as my math instructor in the 608 class and he was able to clarify for me. I am not confused anymore and look forward to completing the assignment. Now, I need to figure out how to best represent the monster lobe, highway and pipeline. I was bummed that I missed the TNT fun after class, I had a meeting I needed to attend. My son keeps asking me when he can get online and create his maze for all of you. I wasn't sure where you wanted him to create it. I may just have him place it somewhere around our homes. It's so funny that my son is so excited about my college course.
Below I just re-posting my project timeline, with the standards in bold.
Project
Timeline:
·
Introduce the project – creating a vessel on
Minecraft. Give all of the guidelines
and scoring grid.
·
Do research on large water vessels on the
internet, and through books. Discover
what you need to include in creating a vessel that is functional and practical.
Measurement
and Data 4.MD.1. Know relative sizes of measurement units within one system
of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement,
express measurements in a larger unit in terms of a smaller unit.
·
Create blue prints to show what will be on the
vessel, and keep in mind that each block is 1 meter^3.
Geometry
4.G.1. Draw points, lines, line segments, rays, angles (right, acute,
obtuse), and perpendicular, parallel, and intersecting line segments. Identify these in two-dimensional (plane)
figures.
·
Calculate the amount of materials needed to
complete the vessel. Types of blocks,
amenities, etc…
Number and
Operations in Base Ten 4.NBT.4. Fluently add and subtract multi-digit whole
numbers using any algorithm. Verify the
reasonableness of the results.
·
Create the vessel on Minecraft.
Understand
decimal notation for fractions, and compare decimal fractions. 4.nf.7. Compare two decimals to
hundredths by reasoning about their size.
Recognize that comparisons are valid only when the two decimals refer to
the same whole. Record the results of
comparisons with the symbols >, =, or <, and justify the conclusions
(e.g., by using a visual model).
Extensions:
·
Create a model representation of the vessel so
we can see both inside and outside.
Measurement and Data 4.MD.1. Apply
the area and perimeter formulas for rectangles in real-world and mathematical
problems.
·
Create an actual vessel that can be placed in
water and propel itself forward, using the same guidelines as the Minecraft
blue prints to test if it will float.
Geometry 4.G.2. Classify figures
based on the presence or absence of parallel or perpendicular lines, or the
presence or absence of angles of a specified size.
Math Standards and Reflection
Measurement and Data:
3rd grade:
3.MD.2: Estimate and measure liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve and create one-step word problems involving masses or volumes that are given in the same units.
3.MD.3-Select and appropriate unit of English, metric, or non-standard measurement to estimate time, length, weight, or temperature.
4th grade:
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement.
4.MD.1-Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a small unit. Record measurement equivalents in a two-column table.
This class was a great refresher in topographic maps. Once I watched the video I was reminded what it was we were exactly doing it has been several years since I have worked with them. Like many I had a bit of struggle figuring out how to do the scale correctly. I wasn't fully understanding how the vertical scale was created. I'm still not sure I could explain how to get it or what my students would need to do. I think this will be a fun activity for my students and spring break gives me time to explain to my students what a topographic map is. The one thing I struggle with this class and the lesson we have to teach is how to make the relevant students' lives, managing to teach them while not veering completely away from the curriculum we have. Since my students back knowledge to many things is limited there has to pre-teaching involved for them to even do the activity. Again I look forward to teaching the lesson and glad I have an extended period of time to teach my students about topographic maps.
3rd grade:
3.MD.2: Estimate and measure liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve and create one-step word problems involving masses or volumes that are given in the same units.
3.MD.3-Select and appropriate unit of English, metric, or non-standard measurement to estimate time, length, weight, or temperature.
4th grade:
4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement.
4.MD.1-Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a small unit. Record measurement equivalents in a two-column table.
This class was a great refresher in topographic maps. Once I watched the video I was reminded what it was we were exactly doing it has been several years since I have worked with them. Like many I had a bit of struggle figuring out how to do the scale correctly. I wasn't fully understanding how the vertical scale was created. I'm still not sure I could explain how to get it or what my students would need to do. I think this will be a fun activity for my students and spring break gives me time to explain to my students what a topographic map is. The one thing I struggle with this class and the lesson we have to teach is how to make the relevant students' lives, managing to teach them while not veering completely away from the curriculum we have. Since my students back knowledge to many things is limited there has to pre-teaching involved for them to even do the activity. Again I look forward to teaching the lesson and glad I have an extended period of time to teach my students about topographic maps.
Math Standards for STEM Project
My project consists of having students construct a hydroelectric dam using Minecraft. I am basing the project on a dam engineering lesson from tryengineering.org. The lesson plan relies heavily on NGSS standards and is not math specific. However, I do know that real-world construction of dams involves understanding area, surface area, and volume. I also know that a real-world engineer will consider the force of the water on the dam as well.
This lesson addresses geometry standards such as:
Alaska Standard 7.G.6 Solve real life and mathematical problems involving angle measure, area, surface area, and volume and Alaska Standard 6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems.
This lesson addresses geometry standards such as:
Alaska Standard 7.G.6 Solve real life and mathematical problems involving angle measure, area, surface area, and volume and Alaska Standard 6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems.
I also know that the physics behind force requires the use of calculus found in Alaska Standard F-1F.7. Analyze functions using different representations.
I found an article entitled: AP Calculus BC Project:The Dam Problem:Constructing a Dam across the River http://www.ms.uky.edu/~droyster/APCalculus/Dam%20Problem.pdf very helpful in identifying the higher level mathematics used in construction a dam.
Timeline with Standards
Students will keep a
log of their day-to-day adventures in Minecraft.
1. Explore Minecraft and crafting in Minecraft (1 ½ hours)
Standard(s):
·
Technology. Using a computer program.
References:
Assignment:
·
Explore Minecraft,
collect items on your journey.
·
Spend time digging
downward in Minecraft. Go down at least
six blocks deep.
·
Build a 3 x 3 crafting
table.
·
Craft at least two
items with your 3 x 3 table.
Log Prompt:
·
What did you discover
in your explorations in Minecraft?
·
What did you find when
you dug downward in Minecraft.
·
What did you collect
during your explorations?
·
What did you craft?
·
What else would you
like to know about Minecraft?
2. Learn about
building materials available in Minecraft. Build a house in Minecraft. (1 ½ hours)
Standard(s):
·
Science. Properties of building materials.
·
Technology. Using a computer program.
Reference:
Assignment:
·
Study the
"real-life" properties of five of the building materials that are
available in Minecraft.
Log Prompt:
·
What are the five
building materials that you chose?
·
Briefly describe the
“real-life” properties of each of these materials.
3. Build a
house (2 hours)
Standard(s):
·
Engineering. Drawing “blueprints”
and building a house.
·
Technology. Using a computer program.
·
Mathematics:
o
6.RP.2. Understand the
concept of a unit rate (a/b associated with a ratio a:b with b ≠ 0,
and use rate language in the context of a ratio relationship) and
apply it to solve real-world problems (e.g., unit pricing, constant
speed).
o
6.RP.3. Use ratio and
rate reasoning to solve real-world and mathematical problems (e.g., by
reasoning about tables of equivalent ratios, tape diagrams, double number
line diagrams, or equations). Use
ratio reasoning to convert measurement units between given measurement
systems (e.g., convert kilometers to miles); manipulate and transform
units appropriately when multiplying or dividing quantities.
o
7.RP.1. Compute unit
rates associated with ratios of fractions, including ratios of lengths, areas
and other quantities measured in like or different units.
o
7.G.1. Solve problems
involving scale drawings of geometric figures, including computing
actual lengths and areas from a scale drawing and reproducing a scale
drawing at a different scale.
Assignment: Build a house in Minecraft.
·
Draw a “blueprint” of
your house. Indicate measurements of
each wall and roof. When measuring
surface area, each block is 1 meter x 1 meter.
·
Build the house in
Minecraft.
·
Convert the
measurement of your house from squared meters to squared feet using conversion
fractions.
Log Prompt:
·
Place the “blueprint”
of your house in the log. Indicate the
measurements on drawing.
·
Show all the steps of
your conversion from squared meters to squared feet using conversion
fractions.
·
What materials did you
use to build your house?
·
Did you have to craft
materials? If so, what did you
craft? Write the materials that you
needed for crafting those items.
·
Where did you build
your house? Was there a special reason
you choose this site?
4. The Monster Lobe (1 ½ hour)
Standard(s):
·
Engineering. Study to gain information for creating a
plan.
Assignment: Read at least two articles regarding the
Monster Lobe.
Log Prompt:
·
Which articles did you
choose? Briefly summarize the
information from these articles.
·
Look up one item
mentioned from one of the article and find more information on this item. List the citation for this item.
·
State the problem that
the Monster Lobe is potentially going to cause?
·
How might you solve
the Monster Lobe problem?
5. Planning Session (2 hours)
Standard(s):
·
Mathematics:
o
7.G.1. Solve problems
involving scale drawings of geometric figures, including computing
actual lengths and areas from a scale drawing and reproducing a scale
drawing at a different scale.
Assignment:
·
In Minecraft, find the
Monster Lobe.
·
In a group, be sure
everyone has found the Monster Lobe.
·
Draw a map of where
the Monster Lobe is in relationship to your house.
·
With a group, come up
with some ideas as to how solve the Monster Lobe problem. Come up with at least three ideas, these
ideas will destroy, redirect, or some other solution.
Log Prompt:
·
Draw a map of where
the Monster Lobe is in relationship to your house.
·
List your three
ideas. Briefly describe how you might
implement these ideas.
6. Planning (1 ½ hours)
Standard(s):
·
Engineering. Creating plan.
·
Mathematics:
o
7.NS.3. Solve
real-world and mathematical problems involving the four operations
with rational numbers. (Computations with rational numbers extend the
rules for manipulating fractions to complex fractions.)
o
7.EE.3. Solve
multi-step real-life and mathematical problems posed with positive and
negative rational numbers in any form and assess the reasonableness of
answers using mental computation and estimation strategies.
Assignment:
·
With your group,
decide which plan you will pursue.
·
Make an
outline/timeline for your project.
·
Decide which materials
you will need to complete your project.
Log Prompt:
·
Describe the plan you
are going to use.
·
Write down your
outline/timeline.
·
What materials are you
planning to use? Why are you using
these materials?
7. Execute plans
(1 ½ hour)
Standard(s):
·
Engineering. Implement plan.
·
Technology. Using computer program.
·
Mathematics:
o
7.NS.3. Solve
real-world and mathematical problems involving the four operations
with rational numbers. (Computations with rational numbers extend the
rules for manipulating fractions to complex fractions.)
o
7.EE.3. Solve
multi-step real-life and mathematical problems posed with positive and
negative rational numbers in any form and assess the reasonableness of
answers using mental computation and estimation strategies.
Assignment:
·
In a group, using
Minecraft, implement your plan.
Log
Prompt:
·
Describe how your plan
went? Did you execute the plan the way
that you had planned? Did anything
change from your original plan? What
changed?
8. Analyze/Extension (1 hour)
Standard(s):
·
Engineering. Analyzing plan.
Assignment/Log Prompt:
·
Do you think your plan
would work in “real-life.”
·
Consider the
following, what if there was a “debris flow,” similar to the Monster Lobe, was
heading towards Palmer. Pretend that the
“debris flow” has appeared on Lazy Mountain and is working its way down the
mountain towards the Matanuska River.
Given this course, the “debris flow” continue traveling into the
Palmer. Would your solution to the
Monster Lobe work in this situation? What might work and what might not
work?
It was interesting and frustrating trying to construct the topology map. Hopefully my assignment will go better.
It was interesting and frustrating trying to construct the topology map. Hopefully my assignment will go better.
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