Introducing Make It Real Learning workbooks

I have recently had the pleasure to add Make It Real Learning workbooks to my site. These books contain real-life math activities with real-life data, companies, and situations. They are written by Frank Wilson.

Arithmetic I



Fractions, Percents, and Decimals I



Linear Functions I


Calculus I



Periodic and Piecewise Functions I

Some examples of the topics included in these activities are: cell phone plans, autism, population growth, cooking, borrowing money, credit cards, life spans, population growth, and music downloads. But there are many more, more than I can list here.

As students work through the problems, they can use the math skills and concepts they have learned in their math curriculum (such as the concept of average or graphing), and apply those to a situation from real life.

Each activity-lesson in the book contains several questions about the situation, starting with basics and going into more in-depth evaluations, and should be adequate for one-two complete class periods.

Why does that benefit you, the teacher? It will motivate the students far more than dull, boring word problems from the textbook. It will show students how mathematics is truly USEFUL. Also:

• The problems are written by an experienced math teacher (Frank Wilson)


• The problems are matched to the learning objectives of the National Council of Teachers of Mathematics (NCTM). This means that the concepts and skills required to complete the problems ARE found in typical middle and high school mathematics curriculum. You can simply replace some of the problems in your textbook with these real-life scenarios.
  
  
• These activities are excellent to be used in a small-group setting.
  
  
• Typically, the activities contain challenging parts and therefore allow students to practice real problem solving - not just apply knowledge from textbook examples to other almost identical problems.
  
  
• Gifted students can enjoy the challenge of solving all the questions on their own.

All books include complete solutions to all activities and problems. Please note that Make It Real Learning workbooks do not contain the instruction or explanations of the concepts.

List of available books:

Arithmetic I - for grades 3-6
Fractions, Percents, and Decimals I - for grades 4-8
Fractions, Percents, and Decimals II - for grades 6-11
Sets, Probability, and Statistics I - for grades 6-10

Linear Functions I - for algebra 1 and algebra 2
Linear Functions II - for algebra 1 and algebra 2
Quadratic Functions I - for algebra 1 and algebra 2

Exponential and Logarithmic Functions I
- for algebra 2/precalculus
Periodic and Piecewise Functions I
- for algebra 2/precalculus
Polynomial, Power, Logistic, and Rational Functions I
- for algebra 2/precalculus
Calculus I - for grade 12

Alcumus

Alcumus is a brand new online math program - currently free - by the Art of Problem Solving folks. This program is specifically designed to provide a challenging enrichment program for gifted math students.

Alcumus interacts with the student and adapts to his or her level. Currently, the program contains over 1100 problems with fully worked-out solutions and over 60 video lessons.

Anyone can join - whether you are just interested in exploring math a little further, or you have student who is training for some math contest, etc.

However, currently one can only join the program as part of a registered class. If you are a single person, this can be a problem. Fortunately, Denise at Let's Play Math has set up a class which is open to all interested homeschoolers and self-directed learners. Please click here to find out more about joining Alcumus as part of Denise's class. Otherwise, if you have a class, just go straight to Alcumus and join there.

Math enrichment problems at MathNotations

Today I want to highlight a blog called Math Notations by Dave Marain that specializes in math enrichment problems such as various type challenges and investigations. And they are quite good!


For example, recently Dave posted a geometry problem, and even gave the answer in his post, but he asked the readers to find DIFFERENT ways to solve the problem.

I encourage you to go see the problem and see how many different ways you can find to solve it!

That is exactly what we can ask students too - especially if you have many students and some of them solve the original problem in no time. You can use the same problem as a basis for further investigations for them.

His blog has "labels" in the sidebar, which makes it easy to find problems on a particular topic or concept.

Performing well below grade level

I am leading a training next week on how to introduce grade level concepts/standards when the students are performing well below grade level, and I am sure that math is going to be an issue. Any suggestions?

These are my 2 cents on teaching under-performing students.

Let's imagine we have an 8th grader performing on 3rd grade perhaps.

I would dismiss for starters geometry and measuring topics, and concentrate on this train of topics, in THIS ORDER:

addition
subtraction
multiplication
division
fractions
decimals.

... the goal being to cover the basic arithmetic up to pre-algebra.

Think of mathematics as a building. You need to have the foundation building blocks before you can go forward.

Maybe the child stopped understanding the math on 2nd grade or 3rd. We need to find the exact point after which he has not understood everything.

You can gauge this by the way by asking the child simple questions such as,

• I give you an addition 8 + 2 = 10, you give me a subtraction sentence (1st grade knowledge).


• How much do you need to add to 600 to make a thousand? (2nd grade place value)


• Draw a picture of 4 x 3 (3rd grade knowledge)


• There are 293 flowers and 145 are red. How many are not red - how do you find that? (using subtraction in finding parts)


• Draw a picture of 20 : 4. (division concept, 3rd grade)

etc.

So for such imaginary 8th grader, I'd make up a separate curriculum that goes through addition, subtraction, multiplication, division, fractions and decimals, in this order.

A teenager can go through those topics in 1 year, and understand it all, if he wants to. Obviously you'd want to show the student the train of topics too so they know what's coming next. You'd want to motivate them that hey, in one year I can learn all this basic math. You'd want to show them how the basic topics lead to the next ones.

Addition: you'd start at adding single-digit numbers, then memorizing addition facts, then 2-digit addition, then multi-digit addition.

If the student does NOT know addition facts, then spend a week practicing them! But not in random order. Like I do in my books (Addition 1 and Subtraction 1) you need to put those facts into contexts, study them in systematic, logical fashion such as sums of 5, sums of 6, etc. (using fact families). Or, adding to 9, adding to 8, etc.

Not knowing the addition facts makes the student SLOOOOOWWWW in doing simple addition problems, and makes it hard to get into subtraction or multiplication. So it is important, even if he's on 8th grade, and it is 1st grade stuff.

On to subtraction. Cover the three situations where subtraction is used, even if it is 1st grade stuff. Cover multi-digit subtraction. Shouldn't take many weeks.

Then multiplication concept. Times tables. Multi-digit. Absolutely remember to show what principles 23 x 38 is based on (multiplying in parts). Spend several weeks here.

And so on.

In a school year's time, it absolutely is possible to cover the basic arithmetic if the student is a teenager. I just would cover it all, including 1st grade topics, to make sure to catch those points where the student "dropped" off.

Any comments anyone?

Maria Miller

Developing positive attitude

What are the incentives needed in order to develop a positive attitude in children and other students towards mathematics?

I don't think special incentives is the main factor in developing a positive attitude towards mathematics.

I feel it is sufficient to get a few of the basics right, and then that alone will take care of most of it, and then students will like math just fine.

Disliking math is not something that is inherent in us or in our kids. Little kids don't dislike math or numbers. They're just fine with them! This "I hate math" or "I don't like math" attitude seems to develop during school years.

Now, I also don't think that children are disliking reasoning, because they're happy to do puzzles and play games where you have to think.

And, students' negative attitude towards math also is NOT due to (school) math being difficult. The math we learn in school is not difficult. You don't have to be a math whiz to understand it.

If you can learn to read and to use computer software, surely you can learn basic math. It's not that complex.

So... here are the two main factors that I feel contribute most to what attitude children develop towards math:

1) The teacher's attitude.

If you love math and are enthusiastic about it, it is seen in your teaching, and your attitude will be somewhat contagious.

It's true the other way around as well: if you don't like math, yet you teach it, students will sense your attitude. (I've written about the teacher's attitude in this article.)


2) How the math is being taught.

Children can end up not liking math when it is taught in such a way that they don't understand it. And, when they don't understand math, then they don't like studying it.

When they don't understand it, then they don't like studying more of it.

The teacher obviously can influence A LOT how the math is taught, but curriculum or the book also plays a role.

So, if we as teachers can get these two basic things straightened out, our students should learn to like math... or at least not hate it.

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See also:
Four habits of highly effective math teaching

Is your math curriculum coherent?

How to motivate and prevent math anxiety