# Focus on Math

## Helping children become mathematicians!

### It’s About TImeDecember 10, 2013

In this day of digital clocks and watches, more and more children are having trouble with telling time on analog timepieces. The clock face with its two (or three) hands remains shrouded in mystery for many of the students.

I recently had the privilege of going into a grade 5/6 classroom and doing a lesson with the students in the area of measurement. One of the parts of the lesson included telling time on an analog clock.

Each student was given a sheet of paper with a circle marked on it. Together we added the numbers 1 to 12 for the hours: first we placed the 12 and 6; then the 9 and 3; then we “filled in” between those anchor numbers. There was much discussion at that point about even that particular part of clocks. Student were quick to share that some clocks have only the four anchor number, some have Roman numerals for the hour numbers, and some clocks have no numbers at all – just lines or “ticks” marking the hours.

We discussed as a class the idea of half and quarter hours. Of course, this must be done in the context of the whole hour having 60 minutes. We also noted that in money quarters denote 25’s, but in time quarters denote 15’s. Finally we pointed out that with referring to quarters of hours we speak of “quarter past” or “quarter after” an hour, and we speak of “quarter to” or “quarter ‘til” an hour, but we do not usually refer to three-quarters past an hour.

Each student was also given a large Post-It note arrow to be used as the hour hand. I wanted to render the idea of telling time down to the most simplest elements, and thus set about showing how one can tell time with a reasonable degree of accuracy just by using the hour hand of the clock.

We placed the arrow to show several “o’clock” times (e.g., 12:00, 4:00, 7:00 — see first picture) and then did some “half past” or “—thirty” times (e.g. 12:30, 4:30, 7:30–see second picture). The point of this is, of course, that when it is half past an hour, the hour hand has moved half the distance to the next hour number. Thus a 7:30 the hour hand is half-way between the 7 and the 8.

We even pointed out that we could tell the quarters fairly closely as well. If, for instance, the hour hand were slightly past the 9, the time was approximately 9:15 or quarter past 9. Alternately, it the hour hand were slightly before the 10, the time was approximately 9:45 or quarter to 10.

We did add the minute numbers around our clock and discussed that using the minute hand added accuracy to our time reading, but by focusing on just the hour hand all of the students were able to make sense of the analog clock, some for the very first time.

Mathematically yours,

Carollee

### Ten Uses for Sticky Notes in Math ClassSeptember 9, 2013

Sticky notes (that wonderful — though accidental — invention that 3M first marketed as Post-It Notes©) are a wonderful tool to use in mathematics. I have always found that students enjoy using those little sticky pieces of paper! So here are ten ideas for incorporating them into math lessons:

1) Ordering numbers: Write 4 or 5 different numbers on sticky notes and have students work in pairs to put them in order from least to greatest. This is great practice for multi-digit numbers, for decimals, for fractions, etc.
2) Creating numbers: Write 4 or 5 different digits on sticky notes and have students work to create specific numbers: greatest possible; number closest to a particular given number (whole number or fraction); a number between two given numbers, etc.
3) Using operations: write several digits on sticky notes. Then use them and operations that the students know how to use to make number equations with as many different answers as possible or to get as close as possible to a particular answer.
4) Writing word problems: Give students numbers, operation signs, and possibly other math symbols (such at a percent sign) on sticky notes and have them create a word problem that uses all of the notes.
5) Graphing: Create the axis of a graph on chart paper or the chalkboard. Add your categories (4-6 work well). Give each student a sticky note and have them create a bar graph with then .(I usually have kids make their choice at their seats and write it on their notes so they don’t just add to a single category to make it “win”.)
6) Scavenger hunt: each student has a sticky note with math geometry word on it. Students must find an example in the room to represent the term and place the sticky note there (e.g., perpendicular lines, acute angle, sphere, etc.).
7) Measuring area: Cover a book or other object with sticky notes and calculate the area using the notes as the unit of measure. A particular book or surface may be covered by notes of one size, then by notes of another size and the area calculations compared.
8) Estimating on a number line: draw a number line on the board with only the endpoints marked (endpoints may vary according to grade: 0-10, 1-100, 0-1, 20-80, 1-1000, etc.). Give each student a number that appears on between the endpoints and have them come and place their number where they think it would go and explain their reasoning for placing it there.
9) Commenting on each other’s work: teach students to peer-evaluate problem solving work. Students can exchange their papers after working on an open-ended problem. The evaluator can make comments and ask questions regarding the strategies, visual representations, etc. by writing their comments on sticky notes.
10) Transformational geometry: Use sticky notes to show transformations, often called “flips”, “slides”, and “turns”. Light coloured sticky notes tend to be translucent. Using a sticky note, student can trace a shape from its original location on a grid and then use the sticky note to show the desired transformation (e.g., down two, left three; 90 degree clockwise rotation; reflection over a particular line).

I hope you try one or more of these in the next weeks. Let me know how it goes!
Mathematically yours,
Carollee

### Mrs. Norris’ “String Theory”August 20, 2013

I was having a conversation with my brother just the other day about measurement. Warren is a finish carpenter and deals with measurements that have to be very exact. For instance in creating a wood inlay of almost any size, being off by even 1mm is noticeable — there is almost no margin of error. Our conversation went on to be about the idea of estimating linear measurements and what is “acceptable” when doing so. I went on to tell him one of the ways I give elementary students experience with estimating using string. It was Warren who suggested that I had my own “string theory”.

I give each student in the classroom a randomly cut piece of string, usually in lengths from about 8 cm long up to about 120 cm long. I then ask the students to take their individual pieces of string around the classroom and find some things that are about the same length as their string.

Once they have done this I give them a chance to share their various discoveries, and something interesting always happens: the students notice that the longer the string is, the greater the amount of leeway in the estimation. For instance, someone with a string nearly 120cm long may have as their item something about 110 cm long, a difference of 10 cm. But that difference is greater than the total length of string for the student who has only a piece of string 8 cm long. For a short string, the margin for saying “about as long” must be much smaller. Eventually the students notice that “about” is relative to the initial measurement.

Of course this principle of is true for measuring any attribute, whether mass, time, area, volume, etc., and it is important for students to have experiences with various units of measure to develop this understanding for themselves. It is easy to vary this activity by giving students either weights or particular items and asking them to try to find something in the room that has the same mass. It is interesting to watch them comparing with their hands as if using a balance scale. For sharing, make sure you have a scale available that will weigh both the original item (if it is a random item) and the “found” item.

I hope you will give “string theory” a try in your classroom!
Mathematically yours,
Carollee

### In the Dog HouseMay 16, 2011

I found this question in Everybody Counts (Mathematical Sciences Education Board, 1989, p. 32) and thought it would be a great one to do if your class is learning about area.

Design a dog house that can be made from a single 4 ft. by 8 ft. sheet of plywood. Make the dog house as large as possible and show how the pieces can be laid out on the plywood before cutting.

This is a great place to say that even though here in Canada we are officially a metric country, we are bombarded in real life with the Imperial system of measurement. I, for one, think students should be “bilingual” in both metric and Imperial! If Imperial measurement are not in your curriculum, it is still fine to work with those units. It just means you don’t assess for a grade regarding Imperial measures.

Mathematically yours,

Carollee