Rachel McAnallen, also known as Ms. Math, challenges students and teachers to look beyond the way that mathematical operations are regularly taught.
"Mathematics is a language to be spoken,
an art to be seen,
a music to be heard,
and a dance to be performed." - Ms. Math
Place Value vs. Face Value
Flashing a one dollar bill, a ten dollar bill and an eye-catching one hundred dollar bill to represent place value, Ms. Math demonstrates how we often name the digits instead of numbers. The number 592 is written beneath the monetary place value markers.
Rachel (pointing to the left-most digit in $592): "What's this number?"
Teacher: It's a 5.
Rachel (waving the $100 bill and the $1 bill): You've changed this hundred dollar bill into a one-dollar bill! This number is five hundred, but we've all been taught to say that it's a five. The digit is a five, but the number is 500.
And so begins Rachel's lesson on place value vs. face value, showing teachers how confusion can result when the value of numbers are not clearly expressed. You can read about a whole lesson built around this idea in the article Place Value vs Face Value.
Algebraic Addition!
Rachel challenges students to solve mathematical problems in a variety of different ways, which opens up students' minds and perceptions of numbers. For example, when asked to add the numbers 24, 17 and 33, students may set up a column addition problem such as the one below. The person might add the first column to get 14, write down the 4, then put a small 1 up above the left column.
1 1
24 24 24
17 17 17
+33 +33 +33
4 74
Rachel asks a student for a favorite number, then helps the students to do the same addition problem in terms of that number. This process is illustrated below, in terms of 10, 7 and 12. Students are then challenged to do the same problem in terms of other numbers. Can you find 4 different ways to solve this problem? How creative can you get when choosing the number and working through the mathematics?
24 = 2(10) + 4 24 = 3(7) + 3 24 = 2(12) + 0
17 = 1(10) + 7 17 = 2(7) + 3 17 = 1(12) + 5
33 = 3(10) + 3 33 = 4(7) + 5 33 = 2(12) + 9
6(10) + 14 9(7) + 11 5(12) + 14
6(10) + 1(10) + 4 9(7) + 1(7) + 4 = 5(12) + 1(12) + 2
7(10) + 4 = 74 10(7) + 4 = 74 6(12) + 2 = 74
You can find out more about this method, by reading the article Algebraic Addition!
Rachel McAnallen, Ms. Math, has written a number of articles that illustrate her creative ways of teaching mathematics. In these lessons, students develop better number sense and become comfortable with representing numbers and mathematical problems in a variety of ways. Check them out!
Pigs in the Pen! (One-to-One Correspondence & Parts of a Whole)
Place Value vs Face Value
Algebraic Addition!
Subtraction is Shopping!
Multiplication!
Fair Share (A Rational Approach to Division!)
Wonderful Word Problems!
For more information about Ms. Math, go to her website, www.zoidandcompany.com
an art to be seen,
a music to be heard,
and a dance to be performed." - Ms. Math
Place Value vs. Face Value
Flashing a one dollar bill, a ten dollar bill and an eye-catching one hundred dollar bill to represent place value, Ms. Math demonstrates how we often name the digits instead of numbers. The number 592 is written beneath the monetary place value markers.
Rachel (pointing to the left-most digit in $592): "What's this number?"
Teacher: It's a 5.
Rachel (waving the $100 bill and the $1 bill): You've changed this hundred dollar bill into a one-dollar bill! This number is five hundred, but we've all been taught to say that it's a five. The digit is a five, but the number is 500.
And so begins Rachel's lesson on place value vs. face value, showing teachers how confusion can result when the value of numbers are not clearly expressed. You can read about a whole lesson built around this idea in the article Place Value vs Face Value.
Algebraic Addition!
Rachel challenges students to solve mathematical problems in a variety of different ways, which opens up students' minds and perceptions of numbers. For example, when asked to add the numbers 24, 17 and 33, students may set up a column addition problem such as the one below. The person might add the first column to get 14, write down the 4, then put a small 1 up above the left column.
1 1
24 24 24
17 17 17
+33 +33 +33
4 74
Rachel asks a student for a favorite number, then helps the students to do the same addition problem in terms of that number. This process is illustrated below, in terms of 10, 7 and 12. Students are then challenged to do the same problem in terms of other numbers. Can you find 4 different ways to solve this problem? How creative can you get when choosing the number and working through the mathematics?
24 = 2(10) + 4 24 = 3(7) + 3 24 = 2(12) + 0
17 = 1(10) + 7 17 = 2(7) + 3 17 = 1(12) + 5
33 = 3(10) + 3 33 = 4(7) + 5 33 = 2(12) + 9
6(10) + 14 9(7) + 11 5(12) + 14
6(10) + 1(10) + 4 9(7) + 1(7) + 4 = 5(12) + 1(12) + 2
7(10) + 4 = 74 10(7) + 4 = 74 6(12) + 2 = 74
You can find out more about this method, by reading the article Algebraic Addition!
Rachel McAnallen, Ms. Math, has written a number of articles that illustrate her creative ways of teaching mathematics. In these lessons, students develop better number sense and become comfortable with representing numbers and mathematical problems in a variety of ways. Check them out!
Pigs in the Pen! (One-to-One Correspondence & Parts of a Whole)
Place Value vs Face Value
Algebraic Addition!
Subtraction is Shopping!
Multiplication!
Fair Share (A Rational Approach to Division!)
Wonderful Word Problems!
For more information about Ms. Math, go to her website, www.zoidandcompany.com