Math Sites

Bill Reed has posted some sites Google+ that are resources for Math instruction.

You can get to his post by clicking here.

Here is a part of what the post includes. If you want to see the whole list, click on the link above.

Best Practices Weekly

Mrs. Harvey shared this site with me today. It is all about Best Practices, and has some great suggestions for Math and ELa.

I took the time to watch the first Math video, about estimation. Even though it focuses on elementary students, the thinking behind the presentation is solid, that when teaching a strategy such as estimation in multiplication, if we want the students to comprehend the concept, it means more than just telling them how to do something, it involves multiple solutions and rich discussion of the thought process of each solution.

Think about the Standards of Mathematical Practice and how many apply in such instruction.

1. Make sense of problems and persevere in solving them. Estimation begs the very questions, "Does my answer make sense?" While many a students goal is to simply provide an answer, our desire should be that students come up with a reasonable answer.
2. Reason abstractly and quantitatively. We want our students to think about numbers in a variety of ways. Multiplication can be a rather abstract concept to many students, even as time goes on. Presenting multiplication as "times" (abstract) and "groups of" (quantitative) helps students make stronger connections to the processes involved.
3. Construct viable arguments and critique the reasoning of others. Did you see in the video the way he presented 2 thought processes and discussed their reasoning?
4. Model with mathematics. Manipulatives, drawings, diagrams, that promote the understanding. An area model is especially appropriate for multiplication.
5. Use appropriate tools strategically.
6. Attend to precision. Notice that this is paired with #1 in the diagram above. It's not just about getting an answer, it's about getting the best answer.
7. Look for and make use of structure. Patterns!
8. Look for and express regularity in repeated reasoning. More patterns. Critical thinking!

Using Google in the Classroom

Link to the post

Interactive Graphing

Great site that allows you to graph points and lines.

http://www.mathsisfun.com/data/cartesian-coordinates-interactive.html

Here is one for quadratics...

http://www.mathwarehouse.com/quadratic/parabola/interactive-parabola.php

Here is an on-line graphing calculator.

https://www.desmos.com/calculator

Here is one that does lines, connect points, and scatter plots.

http://www.shodor.org/interactivate/activities/OrderedSimplePlot/

UPDATE: 4/17/2015

Here is an app that you can add to Chromebook. Go to the Chromebook Apps Store and search "Graph.tk." This app allows you to enter the formula, and it creates the graph.

Math Game Sites

This is from Bill Reed at the DOE...

Adapted Mind site

Extended Response Resources

Extended response (Applied Skills) starts nest week. Here are some resources for practice.

Please be aware: These are Common Core resources. Check your standards before using. You may need to adjust a grade level up or down depending on your grades standards for that strand.

Milwaukee Mathematics Partnership. Multiple problems with scoring rubrics.

Morgan County Schools - TN. Includes possible solution paths, assessment questions to ask, as well as some possible student misconceptions.

Louisiana Believes - 6th Grade - 7th Grade - 8th Grade

State of Washington. Released items and scoring rubrics.

Northwest Illinois Mathematics and Science. 

Illinois State Board of Education - Released items

If you have others that we might not already be aware of, please share in the comments section.

Teaching Fractions

Even though this video presents information regarding the instruction of fractions at a 3rd grade level, it is important for understanding a conceptual piece that is often missing in the student's understanding of fractions. That piece is seeing fractions as actual numbers on a number line.



So if students are missing this conceptual piece, perhaps we need to find ways (and the time) to provide that instruction in the classroom.

To read the article this was attached to (Approach to Fractions Seen as Key Shift n Common Standards), click here.

New Whiteboard App - Show Me

Now that Educreations has decided to charge for its services (to the tune of about $100/year), I am switching to Show Me. Show me is similar to Educreations, and is a free app with unlimited storage. Educreations still has a free version, but many of the previously free features (such as unlimited storage) are now only available in the paid version.

Below is a first attempt at using Show Me. As you can see, it looks similar to Educreations.


While Show Me does not have as many features as Educreations, it appears to be a solid app. I like that I can import PDFs or other formats as a background, and can have several pages set up ahead and scroll through them as needed. I also like that I can explore topics and find things that I might be able to use in the classroom.

Here is an example of a video found on their site that teaches about solving 1 and 2 step equations. These can be embedded on a site as below, or you can link to them.


Thanks, Show Me!

Instructional Guidance from the DOE

This is a very important document from the DOE. It takes each current Indiana College and Career Readiness Standard and lets you know how important that standard is for the coming ISTEP test.

6th Grade: (Page 6)

7th Grade: (Page 7)

8th Grade: (Page 8)

See the entire document here.

8th Grade Math - 1A

Here are the standards for 8th Grade - 1A

8.NS.1 Give examples of rational and irrational numbers and explain the difference between them. Understand that every number has a decimal expansion; for rational numbers, show that the decimal expansion terminates or repeats, and convert a decimal expansion that repeats into a rational number.

8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, plot them approximately on a number line, and estimate the value of expressions involving irrational numbers. (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.)

8.NS.3 Given a numeric expression with common rational number bases and integer exponents, apply the properties of exponents to generate equivalent expressions.

8.NS.4: Use square root symbols to represent solutions to equations of the form x^2 = p, where p is a positive rational number.

Have an idea or question? Use the comment button to share.

7th Grade Math - 1A

Here are the standards for 7th Grade - 1A

7.C.5  Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.

• Bar models are great for solving rate and ratio problems.

7.C.8  Solve real-world problems with rational numbers by using one or two operations.

7.AF.9  Identify real-world and other mathematical situations that involve proportional relationships. Write equations and draw graphs to represent proportional relationships and recognize that these situations are described by a linear function in the for y = mx,  where the unit rate, m, is the slope of the line.

7.GM.3  Solve real-world and other mathematical problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. Create a scale drawing by using proportional relationships.

7.GM.2  Identify and describe similarity relationships of polygons including the angle-angle criterion for similar triangles, and solve problems involving similarity.

Have an idea or question? Use the comment button to share.

6th Grade Math - 1A

Here are the standards for 6th Grade 1A:

6.NS.1: Understand that positive and negative numbers are used to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge).  Use positive and negative numbers to represent and compare quantities in real-world contexts, explaining the meaning of 0 in each situation.

• Idea: Number line activity. Prepare numbers on post-its and have the students place the numbers on a number line. Remember, it is the mathematical discussion that takes place that provides learning and understanding. Allow mistakes, and use them to promote discussion.
• Idea: Place numbers on construction paper from -10 to +10. Have students take turns do problems by coming up to the line and physically moving. Example. 3 - 7 = x. Student goes to the number 3 and moves 7 spaces to the left to arrive at an answer of x = -4. Students at seats could have a smaller number line copied and follow along with their fingers. Adding movement activates more of the brain, increasing retention!

6.NS.2: Understand the integer number system.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself (e.g., –(–3) = 3), and that 0 is its own opposite. 

6.NS.8: Interpret, model, and use ratios to show the relative sizes of two quantities.  Describe how a ratio shows the relationship between two quantities.  Use the following notations: a/b, a to b, a:b.

• Idea: Bar models are great for solving ratio and showing the relationship between quantities.

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Algebra Tiles

Here is a link to a site showing various uses for Algebra Tiles.

Here is another link.

NCTM Pinterest Board

Did you know that the NCTM (National Council of Teachers of Mathematics) has a Pinterest board for Middle School Math lessons? Neither did I, until today. Here is the link.

Resources

Denise Harvey found this one...

Click here to go to the site!

And this one was found by Natalie Ramsey...

Click Here to go to Coloring Squared

Thanks for sharing, Ladies!

Cycle 4A (6th Grade Math)

Link to PDF copy.