POW: Train Problems

This week you may choose one of two problems to complete for the Problem of the Week.

You can download the handout here.

Due Monday, December 7.

Check Up Quiz corrections, ACE 3.3

Today we talked about the past Problem of the Week, Measuring Area in both the English and Metric systems. We also discussed some of the common mistakes made on the Check Up Quiz they took on November 18. Finally, we began work on Problem 3.3, on pages 42-43 of the handout packet, which we will continue tomorrow. MaryBeth, our learning specialist, helped several people on test corrections. Class notes for 7A are available here, and for 7B are available here.

Please look at the problems marked with arrows on the quiz, and try again. You may use your notes, math book, and help from others. Please make your corrections in colored pencil! I will not accept corrections made in regular pencil.

Due tomorrow, Tuesday, December 1.

For the ACE 3.3 homework, please choose one of the options below on the
handout, which you can download here.

Option 1
Problems 7-18

Option 2
Problems 8, 11-14, 16, 18, 32, 38-41

Due Wednesday, December 2.

ACE 3.2 More rep-tiles

Today we studied problem 3.2 on pages 40-41 of the handout (which can be downloaded here), and worked with triangles to find out if they were rep-tiles. We found out that indeed triangles can tile to create similar triangles, either by putting smaller triangles together or subdividing triangles into similar smaller triangles.

The perimeter increases with the scale factor, so if the scale factor is 1.6, the perimeter will be 1.6x the original. And if the scale factor is 0.5, the perimeter will be 0.5 of the original.

We also found out that the area of a new similar figure is equal to the square of the scale factor times the area of the original figure. So if the scale factor is 1.6, and the area of the original figure is 3 square units, then the new image will have an area equal to 1.6 x 1.6 x 3 square units. And if the scale factor is 0.5, the new image will have an area equal to 0.5 x 0.5 x 3 square units.

Class notes can be downloaded here.

For homework, please choose one of the options below on the handout, which can be downloaded here.

Option 1
Problems 4-6 and 26-27

Option 2
Problems 4-5, 26-27, 34, and 37 (an interesting example of a fractal)

Due Monday, November 30. Do the homework tonight to have a math-homework free vacation. And don't forget the POW is also due Monday, November 30.

Have a great break!

No new homework

Today, Wednesday, Josephine subbed for me because I was on a field trip at the Exploratorium with the sixth graders. Students took a Check Up Quiz on the concepts we have covered thus far in Stretching and Shrinking, and those who finished early did an art project featuring tesselations.

There is no new homework, but ACE 3.1 is due tomorrow, Thursday, 11/19.

ACE 3.1 Rep-tiles

Today we talked about rep-tiles, figures you can use to make larger, similar versions of the original. Rep-tiles are a subset of tesselations, since not all shapes will tile to make a similar, larger version of the original shape. We answered the questions in problem 3.1, which is in the handout you can download here. Class notes are available here.

Tomorrow I will be absent for a sixth grade field trip. You will have a quiz on all the geometry concepts we have covered thus far. You will also have an opportunity to make tesselations if you finish the quiz early.

Homework for Thursday is to choose one of the options below to complete in the homework handout, that you can download here.

Option 1
Problems 1-3 on pages 44-45

Option 2
Problems 1-2 and 22-24 on pages 44-47

Be sure to write out your thinking completely.

Due Thursday, November 19.

POW: Measuring Area in English vs. Metric Systems

This week you may choose one of two options to complete for the Problem of the Week. Option 2 is not more challenging than Option 1. In fact, metric measurements tend to be friendlier numbers.

You can download the handout here. Because of Thanksgiving vacation, the POW is not due until 2 weeks from now.

Due Monday, November 30.

Math Reflections 2

Today, Monday, we discussed the POW, Presentation Perplexers, and we acted out a room full of liars and truth-tellers to solve a logic puzzle. We also discussed two important terms in geometry, "similar" and "scale factor."

Polygons are similar if:

· their corresponding angles are equal
· the scale factor between their corresponding sides is the same

The scale factor is the ratio of the side of one polygon to the side of second similar polygon. It tells how many times longer (or shorter) the sides of the image are than the sides of the original figure. Class notes may be downloaded here.

We discussed the Math Reflections 2 handout, which can be downloaded here. If you did not finish answering questions 1-4, please complete them for tomorrow.

Due tomorrow, Tuesday, November 17.

ACE 2.2

On Thursday we discussed how adding or subtracting numbers to the x and y coordinates, or multiplying x and/or y coordinates affects a figure. We did this by looking at different hats in Problem 2.2 in the packet I previously gave out. Classnotes can be downloaded here. They drew the hats using the handouts you can download here (Mug hat graph and table, Four graphs, Enlarged graph).

For homework, please answer questions on the handout, which you can download here. Choose one of the options below.

Option 1
3, 4, 16, 17

Option 2
4, 16, 17, 32

Be sure to write out your thinking completely.

Due Monday, November 16.
Remember, the POW: Presentation Perplexers is also due Monday!

7A & 7B: ACE 2.1 Drawing Wumps, 7B: 2.2 Wump Hats

Today we continued drawing figures on a coordinate grid using algebraic rules for transforming another figure in both 7A and 7B. We compared the computer game character named Mug Wump to Zug, Lug, Bug, and Glug, and decided whether they were members of the same family. Family members (Mug, Bug, Zug) are geometrically similar, which means that their corresponding angles are the same and their sides are increased or decreased by multiplying by the same scale factor. Impostors (Lug, Glug) are not similar, because their corresponding angles are not equal, and for example they are 3 times taller but not any wider, or 3 times wider but not any taller.

Classnotes are available here. The handout packet students received for the next few days is available here.

For the ACE 2.1 homework at the end of the handout packet above, please choose one of the options below to complete:

Option 1
1, 2, 14

Option 2
1, 2, 29

Due tomorrow, Thursday, November 12.

Students in the 7B class began looking at problem 2.2 in the handout packet above, drawing hats for Mug Wump that use rules that multiply by different scale factors or add a number to the x and/or y coordinate. Classnotes can be downloaded here. They drew the hats using the handouts you can download here (Mug hat graph and table, Four graphs, Enlarged graph). We will finish working on this problem tomorrow.

Problem 2.1: Drawing Similar Figures

Today we learned how to read the intersection points of a coordinate grid by playing the Four in a Row game. Then we started learning how to draw figures on a coordinate grid using algebraic rules for transforming another figure. The original figure is a computer game character named Mug Wump, and we started drawing Zug, Lug, Bug, and Glug using the points for Mug.

Classnotes are available here. The handout packet students received for the next few days is available here.

There is no new homework, but the POW is due Monday, 11/16, and if students want to get a head start on the homework for this Thursday, they may start ACE 2.1 in their handout packet.

POW: Performance Perplexers

Please complete 2 of the 3 questions from the Problem of the Week, Performance Perplexers, and show your thinking and write about how you solved the problem. You can download a copy of the handout here.

Due Monday, November 16.

ACE 1.2: Stretching a Figure

Today we used a rubber band stretcher to make similar figures, in problem 1.2, on pages 7-9 of the handout which you can download here. We made the figures on handouts, which can be downloaded in right- or left-handed versions here (right labsheet, left labsheet). We discussed corresponding angles and sides using the original figure and the image that we created with the stretcher, and defined corresponding and image. The notes from today's class are available here.

For homework, please choose one of the options below to complete. You can download the ACE homework in right- and left-handed versions here (right-handed, left-handed).

Option 1
3-4, 13, and 22

Option 2
4, 13, and 22-23

Due tomorrow, Tuesday, November 10.

ACE 1.1: Similarity, Perimeter, & Area

This week we reviewed perimeter and area formulas for rectangles, triangles, parallelograms, and circles. We also discussed similarity, and solved a problem in which a picture of a person with magazines of known size allow us to determine the size of the person in real life. Similarity in geometry means objects that are the same shape but different sizes.

Notes from class for this week are available to download here.

All students should have received a letter describing this new geometry unit to give to their parents. The letter is available to download here.

The assignment is complete the ACE 1.1 homework problems 1-2 and 8-12 on the handout, which can be downloaded here.

Due Monday, November 9.

Area & Perimeter

In class today we worked on area and perimeter, by discussing the design of bumper car courts. After looking at rectangles, we worked with triangles. There is no new homework, but several people still need to turn in their self- and peer-assessments of their business planning projects. You can download the rubric forms here if you have not yet completed this.

We are hoping that our sick students return soon so that we can finish the final business plan presentations!

7A & 7B: Business Planning Project; 7B: Parent Letter

The 7A and 7B classes presented their business plans today, except for a few groups with students absent because of illness. The projects were varied in nature, with creative ideas ranging from cafes, shoes, electric guitars, cupcakes, and make-your-own t-shirts. Students who presented should complete their self- and peer-assessments of their project; a copy of the rubric, which you received October 26, is available to download here in case you lost it.

The 7B class began looking at what happens when one enlarges or reduces an image, and what "similarity" means in geometry. We began a new unit, and students received a letter describing the unit that they should give to their parents. The letter is also available to download here.

Both should be complete by tomorrow, Wednesday, November 4.