Author: oursland

What does common sovereignty mean? (MP3 Math Reasoning)

oursland Common Core State Standards Mathematics, Improve Mathematical Thinking, Mathematics History, Picture Problems

Integrated Mathematics and Social Studies Lesson
th-2The United State Constitution protects tribal sovereignty by Indian Nations but the Indian Nations are not completely sovereign. To understand the interplay between Tribal, Federal, State, and local governments on the Tribal sovereignty read the attached HS_US_L2_Supremacy_Commerce_Clauses_Boldt.

Fishing rights were among the rights protected by treaties for many of the tribes in Northwestern Washington. In 1974 the Boldt decision reaffirmed the “usual and custom” fishing grounds and rights of the treaty tribal (native) people of coastal Washington State.  The Boldt decision was the result of much conflict for many years leading up to the 1970’s, to understand this conflict read the attached HS_US_L1_Constitution_Boldt_Article_Activity.

In the Boldt decision, Judge Boldt considered the interaction between individual rights, tribal rights, and the common good [non-tribal people]. A part of the decision was that treaty Indians were entitled to 50 percent of the fish that came to the “usual and accustomed places” because an 1854 treaty used the language “in common with.” The Boldt decision is attached Boldt_Decision.

The ramification of this decision is still very much apart of fishing today in Northwest Washington.  To understand some of the present views read the following  Seattle PI article and history lesson.  In present day legal decisions and ecological activities cooperation is needed to ensure that the number of salmon is increased.

As a math lesson uses your knowledge of Venn diagrams to identify the region of the Venn diagram you feel a current legal or ecological issue should reside. Each student needs to identify at least two issues from one of the three documents and one of personal interested. Write your issue on a posted note and place the note in the region on the Venn diagram you feel this issue should reside. After all students have place three posted notes on their Venn diagram the students will get into groups of four to discuss their claims. The teacher will take notes during the group discussion period and discuss the placement of one issue from each group.  Rubric for the lesson in on the attached worksheet. Venn Diagram Boldt Decision – Impact Issues between individual

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Pictures Can Give Math Lessons a Context for Learning

oursland Common Core State Standards Mathematics, HS Algebra, Picture Problems

When a math teacher begins a lesson by discussing the learning target she or he needs some type of reference that engages the students.  Something more than reminding them of the worksheet they completed yesterday.  One method for making a learning target more interesting and relevant is a picture, diagram, or video from the internet.

Examples of different ways pictures can be used to engage students in learning math:significateddigits

Humor, can be used when teaching student the mathematical practice of attend to precision.

MP-Attend to precision

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Math diagram with color, many times it is quicker to use an internet diagram with color, rather than to draw the figure.

slope

A-CED. Creating Equations

 

 

 

 

Photograph, show different names for mathematical terms.  In this ad grade is used to refer to slope.grade

A-CED. Creating Equations

 

A.CED-Using Pictures to Give Context to Math Lessons

oursland HS Algebra, HS Modeling, Picture Problems

Many students ask, “When am I ever going to use this math?” and many more are thinking the question.  To make our math lessons more relevant and interesting, math teachers need to give lessons real-world contexts.  Using pictures, images, and videos from the internet is a easy way to give math lessons a context outside of the math classroom.

Example: When teaching equations of circles on a coordinate plane, pictures can be used to give a real-world context.

A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scale.

In many real-world examples, a problem is mathematized by laying a coordinate axis over the real-world figure or picture.  In the 3 examples below, if a coordinate axis over -lays the figures, circle equations can be used to gain information or solve real-world problems:

1. A sports reference, marking the javelin sector on a football field;Javelin sector

 

2. An art reference, making an art design using circles; andCircle Design

 

 

3. Science or nature reference, using circles to study tree rings.
th

Walk This Way – An activity that can be adapted for grades 5-11

oursland HS Algebra, HS Functions, HS Modeling, ML Expressions & Equations, ML Functions, ML Modeling, Technology Teaching Issues

The Walk This Way activity uses a Motion Detector from Vernier and TI Calculators to connect student movement to graphical representations.

Notice each of the standards and cluster from the CCSS-Math.   

5.OA.B.3 Identify relationships between corresponding terms.

6.EE.C.9 Represent and analyze quantitative relationships between dependent and independent variables.

7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about quantitites.

8.F.B. Use functions to model relationships between quantities.

F-IF.A. Understand the concept of a function and use function notation.

A-CED.A. Create equations that describe numbers or relationships.

F-LE.B. Interpret expressions for functions in terms of the situation they model.

The Walk this Way activity includes both Lesson Guidelines and Student Handout.  Walk This Way – Lesson Guidelines

This activity engages students in modeling discourse – Student make and test predictions about graphical models of their classmates movement.

Screen Shot 2015-10-28 at 4.37.33 PMStudents work in groups of four: a. one person walks, b. another operates the calculator, c. another draws the graph on the calculator, and d. the graph of the peers walk, and the final person gives and writes the walking directions.  On the next walk the students switch tasks, so that everyone performs all tasks.

Students perform three different processes of modeling: Part 1. Physically walk from a graph given by the calculator (seen above); Part 2. Physically walk from a graph given on the work sheet (first two activities below); and Part 3. Draw and test a graph when given a walking story (final activity shown).

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Equipments Required

product.md-btd._hero.001.590.332TI- 83 or 84 calculator with Easy Data app (usually comes with the calculator)

Motion Detector from Vernier

7.SP.C The Great Race

oursland ML Statistics & Probability, Technology Teaching Issues

Imagination your students comCompass2Campusparing a simulation of rolling two dice with horse racing.  In the attached worksheet student choose from a list of 12 horses. They are told that the number associated with their horse corresponds to the sums from rolling two dice.

 CCSS.Math 7.SP.C. Investigate chance processes and develop, use, and evaluate probability models.

ProbSim
figure 1

The powerful aspect of this activity is using the TI calculator app Prob Sim to simulate rolling two dice.  In figure 1, you can see how the students find the app Prob Sim.

 In figure 2, notice that the simulation shows a picture of the two dices as well as records the sum on a histogram.

Rolldicesimulator
figure 2
ManyRollsDice
figure 3

 

 

In figure 3, 50 rolls at once can be used to reveal the pattern of probabilities that occur with a large number of rolls.

The worksheet, “The Great Race”, guides the students through individual or pair sampling to whole class horse racing with when 50 rolls at a time are recorded.  Students like to cheer for their horse when 400 to 500 samples are recorded on the histogram.  Finally the worksheet guides the students through organizing the 36 equally likely outcomes and discussing how the frequency of different sums influenced the chance of different horses winning.

The Great Race

 

Creating SBAC Performance Classroom Assessments

oursland Assessment of CCSS-Math

Using interesting question stems is the best way to engage your students in communicating and thinking about math.  These questions stems can be designed to model the item stems of the SBAC item stems.  A good question stems requires students to decide what the question is asking and figure out what information they will need to answer that question.  After students have decided on the data needed, they can collect and analyze the data.  Since the data and solution are personal to them, it is easier to get the students to write about their modeling process or defend their solution.  Here are some resources for good ideas connected to the CCSS.

Smarter Balanced Digital Library

Dan Meyers Three-Act Math Tasks

Illustrative Mathematics

MARS

 

 

Carnegie Learning Online: Will It Work?

oursland Algebra Teaching Issues, Technology Teaching Issues, Uncategorized

Using on-line learning to supplement in-class instruction is becoming very common.  There are many program systems, in the attached study a mathematics teacher studied the impact of  the system she was given to use, Carnegie Learning Online Program/Cognitive Tutor Algebra I.  The study is interesting and reveals that how an on-line system is implemented with different populations of students is as important as the design of the software.

Carnegie Learning On-line Study

F.BF-Great Algebra Modeling Activity that uses Geogebra

oursland Algebra Teaching Issues, Common Core State Standards Mathematics, HS Functions, HS Modeling, Technology Teaching Issues, Uncategorized

Pizza 01

The article Pizza, Pizza, Pizza: Using Technology to Teach Mathematical Modeling walks readers through using the formative assessment process to teach mathematical modeling. A worksheet, small group discussion, and whole group discussion are used to support the diverse needs of students when building math models. In this activity students understand the problem by discussing needed information to solve the problem in small groups and then recording this information on their worksheets. The teacher prompts students to share their assumptions and knowledge about the problem in a whole class discussion. The teacher then uses student answers, to ask others students, how this information could be used to build a geometric model. The teacher uses the students’ ideas about a geometric model to create the Geogebra model. Finally, students are prompted to use the Geogebra model to solve the pizza problem.

This resource includes the article Pizza Pizza PIzza Article which explains how to teach the modeling activity and the worksheet Pizza Pizza Pizza which was used in the modeling lesson. Teachers should read the article and use the Pizza, Pizza, Pizza worksheet or adapt this idea of using Geogebra to create their own lesson and worksheet.

N.RN-Using the iPad for Peer Review with Rational Exponents

oursland Common Core State Standards Mathematics, HS Number and Quantity, Technology Teaching Issues, Uncategorized

Attached is an article explaining how the MyScript Calculator ipad app can be used to check open-ended student responses. Student can show mathematical understanding by writing a math expression or equation of their choosing with their finger and see if the app interprets their notation and solution as intended. Teachers can use this app as a teaching tool by requiring students to suggest a math problem with a worked solution that they feel demonstrates their mastery of a learning target and have the app check their work. The MyScript Calculator can be used to check both the correctness of their notation and solution.

The teacher can use this app for whole class instruction can use this resource by putting the iPad under a document camera or by using screen share software. Teachers can also using this resource for small groups or individual students by giving an iPad to each group or individual. Internet access is not needed because the MyScript Calculator app does not use the internet when operating.

Article and Worksheet Rational Exponents with MyScript Calculator App

Rational Exponents Worksheet

Using MyScript Calculator ipad App to teach CCSS Rational Exponents

oursland Assessment of CCSS-Math, HS Number and Quantity, Technology Teaching Issues

I had a lot of fun playing with the free ipad app MyScript Calculator. This app allows the user to write a mathematical statement or equation with their finger on the tablet; the app then translates the handwriting into math typescript; and finally the app evaluates the math statement. A math statement will be evaluated by producing an equation, with an equal sign and correct value to make the new equation correct. If you want to create an equation with a placeholder variable, create an equation with an empty parentheses for the variable. In both cases the users’ input is in black and the ipad response is in gray.

I have an example of how a teacher could use this app in the class to enhance teaching of the CCSS MATH. To teach the following CCSS Math:
CCSS.Math.Content.HSN-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power) to the power of 3 = 5, so (5^1/3)^3 must equal 5.
The following math activity illustrates how technology can be used to provide feedback to students in an open-ended modeling activity. To meet this standard students must be able to explain how properties of integer exponents can be applied to make sense of rational exponents. Ideally students should be able to express math statement using correct math syntax and explain the evaluation of the math statement using properties of exponents.

Math Activity:
Each student would be given a worksheet that would be used to write down three examples that use at least one rational exponent to model the following integer exponent properties (a to power of m) to the power of n , a power of m multipled by a to the power of n, and a to the power of m divided by a to the the power of n. Student will work in pairs with an ipad to write and explain 2 original rational exponent examples for each property. The teacher would model the process by saying, “to model (am)n an exponent of an exponent, chose (43)1/3 that this would equal 4 because the exponents are multiplied resulting in 41, this also shows that the inverse operation of 4 to the 3rd power is the cube root of 4. Then students have your partner check your work and their understanding of your example by writing it with your finger on the ipad using MyScript Calculator. power outside a power If there is a discrepancy work it out, if you cannot raise your hand I will come to help. You are not allowed to try out your example on the ipad before you write it down, we learn from our what doesn’t work as much as what works.”
Reason for using the ipad:
I know the students will want to play with the ipads so I will let them each try writing math statement for 5 minutes before I give them the activity. For this activity the ipad acts as peer assessment for the both the person suggesting the model example and the partner writing the example in math syntax.