activity – Page 2 – In Pursuit of Great Mathematics Teaching

Exam Preparation Activity: Collaborative Practice Questions

My students are preparing for winter exams. As a review activity we are making our own revision questions. I set up two shared Google Docs: one for revision questions, and one for the solutions. Each student had to make up at least one revision question for everyone and add it to the first document.

Writing the questions requires an understanding of the concepts behind our topic, so this activity let me see what my students understood and how well.

Students had to say which MYP level their question was. Our upcoming exam focuses on MYP Criterion A: Knowledge and Understanding, which is graded from 0 to 8. We regularly discuss the criteria in class and so students are beginning to become familiar with the descriptions of the levels.

We had a good variety of questions added, and I circulated to encourage some students to fill holes I thought I saw. I urged some students to write harder questions. In the end, the activity is self-differentiating: each student works on problems at the exact right level. And for each student there are harder problems to stretch them, with me providing the stretch for the topmost students.

As for the solutions document, some students chose to type their mathematics using the (minimally acceptable) equation editor on Google Docs’ Insert menu. Others worked on their mini whiteboards and then took photos to upload to the document.

After students had made at least one question, I encouraged them to go on to make another, harder one or to answer the questions of their classmates. I assigned as homework to work through all the questions in preparation for our exam.

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What exam preparation strategies work for you and your students?

Make Your Own Normal Distribution Questions

Today we were building our familiarity with the normal distributions. I had a scan of a textbook page with lots of normal distribution sketches, like the one below. I copied them onto yellow card and cut them out, discarding the textbook’s instructions and numbering.

Each student got a sketch and I asked them to make up a normal distribution question to go with it. Here are my instructions. Students were working on their mini whiteboards.

The students got out of their seats to solve other their classmates’ problems. There was a lot of collaboration and those who found writing the question hard got plenty of input from their peers. I was free to circulate and able to clarify some important ideas about continuous distributions and the appropriateness of the normal distribution as a model.

I was impressed by the questions’ variety and ingenuity.

I don’t think I emphsized thoroughly enough that students need to specify that the data they have chosen to write about is normally distributed. However, students were able to solve a wide range of questions, some more difficult than others.

This was definitely much more successful than a page of textbook questions!

Number Sets Activity

Which numbers are real? Rational? Natural? Whole? Here is an easy activity to help meet the number sets objective.

I made this set of cards with numbers from the above sets. As students enter, I’ll give them a card. Then I will ask the students to walk around the room, see what numbers others have, and organise themselves into groups based on their number. The instruction is purposely vague enough that many possible groupings are possible. When students have grouped themselves, I’ll start a group discussion about the way they are grouped.

I anticipate (I haven’t tried this activity yet) that I may have to prompt the students to think again about the groupings and ask questions to help them explore the idea of number sets. And then maybe ask if there are some numbers that are “purer” than others. I think students have a sense that whole numbers are more “number-y” than items like 2.4 or negative four fifths.

I think it would be interesting to put students holding whole number cards in the centre of the room and then build the number sets outwards around them. I think this would elucidate the idea of natural numbers being contained in the set of integers, and rational numbers being contained in the set of real numbers.

I think it’s my responsibility to introduce the names for the number sets once students have developed the concepts behind them. I’ll write the names and symbols for them on the board to conclude our discussion.

How do you teach about number sets?

Quiz-Quiz-Trade: Ways of Getting Students Out of Their Seats

My new school’s lessons are usually 80 minutes long. I think I shall try to get students out of their seats (at least) once each lesson – otherwise it is too long for them to be sitting. I also think it’s too long for me to plan in a single block. I can’t imagine any lesson where we work on the same thing for 80 minutes. My attention span isn’t that long and I can’t imagine any teenager’s is either.

Thus begins this series of posts on ways to get students out of their seats. Quiz-quiz-trade was an activity I learned about in Kagan Cooperative Learning (a brilliant book, by the way, which I thoroughly recommend). I have used quiz-quiz-trade regularly for years and adapted it in a few ways.

Preparation:
Print out some cards with questions on them. These could be taken from a textbook, revision sheet, made up by you, or made up by students.
Cut them up.

Activity:
Give one card to each student. While they are still sitting down, ask them to work through the question and verify that they know the correct answer.
Ask students to get out of their seats and meet someone new. Student A quizzes B, then student B quizzes A. They thank each other, then swap cards and move on to meet someone else.
After several trades, each student has met many other students and has also answered many questions.

Works Well With…
1. Questions that aren’t too long to solve. Or let students take mini whiteboards with them (pictured above).
2. Worksheet or textbook questions that you think are too boring as a worksheet. Just cut the sheet into strips and hand the questions out. Make sure you have enough for each student to get one.
3. Revising for exams. Use past papers cut into questions.

Adaptions:
1. Before quiz-quiz-trade, ask students to make up questions to demonstrate their understanding of a topic. Then you can use this questions for quiz-quiz-trade, either immediately or later.
2. You can print the answers on the back (for safety!).

What are some ways you get students out of their seats?

Check back next week for the next post in the Out of Their Seats series.

A Peek Inside My Resource Cupboard: How I Organise My Card Activities

My students use a lot of manipulatives, sorting cards, and activities. I store them all in the tall cupboard at the back of my classroom.

Each of the boxes contains a class set of cards. I like to have seventeen sets so that there are enough for the students to work in pairs plus a few extras (because I always lose a few random cards). Each set of cards is packed into a little snack-sized zipper bag. (I import these from Canada in bulk when I visit.)

The seventeen sets of cards are then packed into a plastic box. They are just Chinese food takeaway boxes. (My husband and I have eaten a lot of takeaway food over the years!)

I’ve been using sticky notes on the shelves to divide the boxes into number, algebra, calculus, shape/measurement, and data/probability activities. This helps my colleagues, because they sometimes pop their heads into the cupboard to borrow something.

I’m always interested in organising strategies. How are your hands-on activities organised?

Standard Form (Scientific Notation) Sorting Cards

Each card in this set of sorting cards shows a conversion between a very big (or very small) number and its equivalent in standard form. However, quite a few of the conversions are incorrect. The students need to sort the cards into which are correct and incorrect. Then they need to correct the standard form conversions.

They could also order the numbers from smallest to biggest or find further uses for standard form to write very big or very small numbers. Students could also make up several questions and make deliberate errors for their classmates to find.

Download the cards or the instructions and answers slides.

Fractions, Decimals, and Percentages Number Line

Sometimes my students struggle with all the interconnected ideas about fractions, decimals, and percentages. I really want them to understand that these interchangeable representations of the same number. And to know that fractions can be placed on a number line, just as they are used to doing with other numbers.

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I asked my students to cut out this set of cards. Then they had to add to each card so that it had three representations of the same value. Finally, they had to draw a number line and place the cards on the line.

Both my students and I learned a lot from this activity. For my part, I learned that a few of these these particular students found drawing the number line troublesome; their first attempts weren’t evenly spaced or long enough. I learned that my class are able to translate among fractions, decimals, and percentages, though for some this is still a stuttering process. My students learned that they are able to move between the three representations for any number, even unfamiliar fractions or decimals.

The cards for this activity and a slide of instructions
are available here.

Laws of Logarithms

My year 11 students are nearing exam time and the last item on our course is an introduction to logarithms. They had just learned the laws of logs and so we finished the lesson with this activity. I put some pink papers around the classroom, each with a requirement.

Each group of students had to use their sticky notes to add one or more expressions to each pink poster. I was quite impressed by their responses and it was clear they had understood our lesson objectives.

Intersections of Curves Treasure Hunt

My year 13 class were ready to practice finding points of intersections of two curves using their calculators. Instead of a boring textbook exercise, I made this treasure hunt for them.

There are ten orange cards stuck to the walls, windows, chairs, and surfaces of my classroom. Each one has a question. Students travel around the room in pairs, solving the questions. Then they look for the answer on another card.

The students know they have finished when they have visited all ten cards and solved ten problems. They need to tell me the card numbers of the loop they followed, which allows me to check their work.

Treasure hunts are easy to make and are a clever way of turning a worksheet or textbook exercise into a more social exercise that students enjoy. The cards are available here as a document and as a pdf.

Equations of Lines, and Other Coordinate Geometry

This is just a simple worksheet with twelve questions about finding the equations of straight lines and about gradients and the distance between two points. It’s laid out as twelve questions and I asked my students to work through them in any order.

A few of my students really like to cut out the questions individually and paste them in, writing their answers below. It helps them keep their work neat. I like anything that makes a worksheet more interesting for them! Even just giving them the choice of what order to do the questions in seems to make them feel more resilient.

The worksheet is available here in pdf format.