Standards and Backwards Mapping

The subject and level I am teaching is eight grade mathematics at the International School of Hilversum in The Netherlands.

The last Teach Now activity, Activity 1, included a standard for one branch of mathematics as written by the International Baccalaureate Organization (IBO) for the Middle Years Program (MYP). The standard is written as follows:

Students are expected to have an understanding of number concepts and to develop the skills of calculation and estimation. Students should understand that the use of numbers to express patterns and to describe real-life situations goes back to humankind’s earliest beginnings, and that mathematics has multicultural roots. 
(Mathematics subject guide, IBO MYP)

To backward-map this standard, we start with the standard itself. I want my students to learn calculating and number concepts, but they need to do this in a global, cross-cultural context. They should not only understand numbers, but understand where they come from and be able to express this.  As the lessons and activities for this unit are created, backwards mapping will ensure that these end goals are met. In other words, every single activity planned is going to end up mapping back to the end goal.

I am starting this activity with the first unit of a school year in hopes that it becomes my regular planning procedure for the following units in the curriculum. This standard will be the first of several used in a unit that covers previous knowlegde and introduction to new concepts. It will probably take about five lessons to introduce, discuss, formatively assess and finally summatively assess the students.

Estimation is a valuable and necessary tool/skill that’s used in virtually all branches of math. Students need to become accustom to the idea of rounding off a non-integer numeral and replacing the value with a shorter one in order to keep calculations manageable. This skill is also relevant when using irrational numbers since a natural terminus to the decimal doesn’t exist. In that case the irrational number can be replaced by fractional rounding to give estimation.

One proficiency the students will have at the end of the unit is rounding off to the nearest whole number. They will learn whether or not a number being rounded needs to be rounded up in value to make it slightly larger or rounded down to make it slightly smaller. They will learn about rounding decimals as well as to which decimal place a number should be. They will also learn how to round larger numbers in order to perform multiplication between multiple digit digits. Finally, the students will learn how to round to a significant number to help in estimation of larger numbers as well.

Learning assessments will include

- An investigation to find patterns in reoccurring decimals when they are converted to fractions. In the assessment they will come to realize that even though a decimal number has no terminus, it can still be rational if it’s repeating itself consistently;

- A written exam testing knowledge and understanding of the theory in an applied way through questions and answers;

- A written assignment using estimation and rounding off in real life situations and explaining the relevance to the technique in context.

Learning experiences for the students will include detailed class discussions and informal question and answer sessions. This is where we will take part in activities such as the Around the World Game for extra cultural and global context.

Individual learning experiences are constructed using online reference tools such as iMaths, coolmaths.com, and khanacademy.org, whereby the goal of reaching certain levels of proficiency can be set within formative assessments.

Students will use their calculators for understanding world currency exchanges and finding equivalencies between them. They will find the best exchanges for currencies in their top five travel destinations in order to determine where they would get the best ‘value’ on holiday.