Help for Connected Mathematics 2 at home

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**Help is available for the work in each session in the current units in sixth, seventh, and eighth grades! Click below for the grade you need:

Sixth Seventh Eighth

**Quick Time videos with explanations of major concepts/skills from each grade are new to this site! (9/20/07) This list will grow continually.

To download Quick Time for PC (free), click here. To download Quick Time for Mac (free), click here. You may need to check the system requirements for your computer. We are working on ensuring as much accessibility to the videos as possible.

Coordinate grids – 1 min., 46 sec. (identifying and graphing points)

Basic connections between fractions and decimals (grade 6) – 5 min., 53 sec.

If you are a student working on homework or a parent helping your child, use the questions below to guide you:

∑ What is this problem asking you to do?

∑ How might you get started?

∑ What do you know so far?

∑ Does this remind you of other problems? How did you solve those?

∑ How can you organize the information?

∑ Would drawing a picture or diagram help?

∑ What would happen if ( )?

∑ How does this relate to ( )?

∑ Can you think of anything you worked on at school that connects to the problem?

∑ You said you do not get it. What part of the assignment is confusing to you?

∑ How can I help you (without giving you the solution)?

∑ How do you know your method and answer make sense?

∑ Has the question been answered?

∑ Can you explain it in a different way?

Finally, if you are unsure about how to complete an assignment after a reasonable amount of time, write at least two specific questions that you have about parts of the problem, and the teacher will help with these questions on the following day. Students, not parents, are responsible for these assignments. However, do not allow the homework to become a source of great stress or anxiety. Follow the suggestions on this page as best you can, and then ask your teacher the questions you had about the assignment.

Final thoughts about homework:

You will see fewer problems in homework than you are used to seeing. This is because the program is aiming for a much deeper understanding of mathematics, so students are expected to spend their homework time thinking about fewer problems. It is often not immediately obvious how to solve the problems (which makes them real problems), and there are usually several possible methods of solution. Often assignments require several solution attempts, the refining of strategies, and a picture or diagram showing the problem and solution. When students find ways to clearly explain a strategy, they must articulate – and therefore further clarify – key mathematical ideas.

Other general suggestions and ideas

First, be positive about your opportunities to learn! We all struggle when we learn new things, and a good struggle is a sign that you are learning, not that you will not learn.

Second, if you are a parent, it is important to be aware of the thinking and reasoning of your child:

∑ Listen to how your child makes sense of the math he/she is working on in school. Let the focus of your interaction be your interest in his/her ideas. Try to display a positive attitude about mathematics, even if you found it difficult or unpleasant as a student.

∑ It is OK to say that you never learned it this way but that you are interested in learning about math in this new way. The strategies that you use to solve problems are valid, but they may not be strategies your child is developmentally ready to learn and understand.

∑ It is OK not to entirely understand what is expected in homework your child brings home. On this page (below) are questions that you can ask your child to draw out what was discussed in class and what your child might do to approach the problems.

∑ Be aware that it takes time and work to learn a concept. Struggle does not indicate failure or inability – it is the best precursor to real learning. Encourage your child not to give up!

∑ You may find that you understand more of the math than you think at first. You may also find that you will learn from helping your child with assignments.

∑ Ask your child to explain his/her strategy to you – let him/her teach you.

Third, if you are a student OR parent: keep in mind these criteria for mathematical thinking for students (Greenwood, 1993):

1. Everything you do in mathematics should make sense to you.

2. Whenever you get stuck, you should be able to use what you know to get yourself unstuck.

3. You should be able to identify errors in answers, in the use of materials, and in thinking.

4. Whenever you do a computation, you should be use a minimum of counting. [That is, since counting is inefficient, students should be able to do the computation with a more efficient strategy.]

5. You should be able to perform calculations with a minimum of rote pencil-paper computations. [That is, the more students can do mentally, the better.]

6. When the strategy you are using is not working, you should be willing to try another strategy instead of giving up.

7. You should be able to extend, or change, a problem situation by posing additional conditions or questions. [This is especially helpful for challenging students who need the extra challenge.]

How can students become more comfortable with writing to express solutions?

One easy way to start to get thoughts on paper is to use verbal prompts, such as I think the answer is ( ). I think this because ( ). Another way to use prompts could be, First I did ( ); then I did ( ); next I did ( ); last I did ( ). I know my method of solution makes sense because ( ). Leave the work for 15 minutes, then return to it and read it aloud to see if it makes sense. This gives you a way to check the work. The thinking of students is valued by each teacher. It is true that many students will find the process of writing in math very difficult at first, but it is a valuable skill to learn for life and for our state tests, including the Ohio Graduation Test.

In 1989, the National Council of Teachers of Mathematics wrote:

Children learn language through verbal communication; it is important, therefore, to provide opportunities for them to talk mathematics. Writing about mathematics, such as describing how a problem was solved, also helps students clarify their thinking and develop deeper understanding. Opportunities to explain, conjecture, and defend ideas orally and in writing can stimulate deeper understandings of concepts and principles. Writing and talking about their thinking gives the teacher valuable information from which to make instructional decisions.

Teachers learn a great deal about each student through his/her writing – much more than the teacher would have learned from scoring a page of 20 problems. This helps the teacher to work with each student much more effectively than would have possible in the past.

Articles available (PDF versions):

Helping Your Children Learn Math (Plano Independent School District; Plano, TX)

Tips Parents Can Use to Help Their Children (Wherry, 1997)

Click the link in this line for a PDF version of an excellent article called Parents Can Help Children Learn Mathematics from Involving Families in School Mathematics (NCTM, 2000). This article includes dozens of great suggestions for fun activities involving math.

Click here to download Adobe Acrobat Reader (free) in order to read these PDF documents.

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