Introduction to Decimals

Pamela has delays in many areas, including math. Her abstract thinking skills and ability to reason really did not emerge until she turned thirteen. While her sequential skills are an asset in learning operations and math routines, her literal thinking and aphasia make word problems the most challenging. We have been using Making Math Meaningful since she was twelve, and she has completed Level 1 through Level 4. She is near the end of Level 5, having completed place value, addition/subtraction (to the trillions), multiplication/division of three- and four-digit numbers, and addition/subtraction/multiplication/division with fractions.

Today was her first lesson in the link between decimals and fractions. Pamela has worked with decimals in the past whenever we have worked on money. Last year, she worked her way through one of those cheap workbooks sold at Wal-Mart that covered the concepts of telling time and counting money. She has added and subtracted decimals, but has never seen the connection between decimals and fractions until today.

The introduction to decimals played right into the money work we did last year. The author usually starts on a concrete level for new concepts and introduced tenths with dimes. The book has her make a table comparing ways to express the value of seven dimes. Pamela has an eagle eye for patterns and caught onto this activity right away:

7 dimes = 70 cents or 70¢ = 7 (1/10) = 7/10 = .7 = seven tenths or point seven

She found the next page equally easy. The author showed icons for three whole apples and four slices. A key indicated that one whole apple equaled one and a slice equaled one tenth. Pamela filled out another chart that showed and sailed through it because the chart played up to her ability to recognize patterns:

3(1) + 4(1/10) = 3 + 4/10 = 3 4/10 = 3.4 plus a column heading for the ones place and tenths place.

By the end of this school year, Pamela should get three quarters of the way through Level 6 (we school year round). Then I plan to start her on Math-U-See Zeta and then Pre-Algebra. I am not sure if she can make it through high school math, but I am willing to teach as long as she continues to be willing to learn. She enjoys math now. I have a master's degree in operations research (fancy-smancy word for statistics), so I can create extra material when she needs more practice in higher-level mathematics.