Focus on Math

Helping children become mathematicians!

Looking at Numbers on a 144 Chart October 31, 2013

144 chart picI was recently doing a math lesson in a grade 3-4 classroom here in my district. The teacher told me the students had been working with place value and patterning of numbers on a 100 chart. For my lesson I decided to have students consider how number patterns would look if the patterns were marked on a 144 chart instead of a 100 chart. More importantly, I wanted students to be thinking about WHY the patterns would appear differently.

The students had already coloured skip-counting patterns on their 100 charts. They had looked at the “easy” patterns of counting by 2, by 5 and by 10, but they had also looked at the patterns of counting by 3, 4, 6, 9, and 11.

With that prior investigation in place, I gave students a sheet with 4 of the 144 number charts on it so they could colour those same patterns on the new configuration of numbers and compare the visual patterns to those on the 100 chart. The students were asked to notice things that were different between the two charts and to think about why the differences were there. In particular, we wanted the students to think about why the patterns looked like they did on the 144 chart.

The students were enthusiastic in their discussion about the number patterns and we were able to lead them into a discussion about base 10 and place value.

A great follow up activity is to colour the same number patterns on a calendar (regular or extended) and notice again how the patterns look different, asking, of course, WHY?

Download 144 charts here:
One per page
Two per page

Download 100 charts here:
One per page
Six per page

Happy patterning!
Mathematically yours,
Carollee

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Compatible Pairs for building Number Sense October 29, 2013

Compatible numbers picHere is an activity to use with elementary students of any age that helps build number sense. For any given grade level (or level of individual achievement) just choose a target that is appropriate for the student(s). It is great to do the activity on a repeating basis (i.e., once a week for a while) – just change out the pairs for the particular target each time.

Compatible Pairs: to 10. 50, 100, etc.                               Target: K-6
Write numbers on the chalkboard or prepare a transparency for the overhead. Include 5 or 6 pairs of numbers (mixed up in presentation) that will add to a target goal. Students write the numbers in compatible pairs as they see them.
When sharing the answers, ask students what strategies they used to find the pairs.
The difficulty of this exercise depends on the target sum as well as the similarity of the numbers given. Here are some suggestions for target numbers as well as some suggestions for number pairs.

Click here to download a chart with other some target numbers and some suggested sets of numbers.

I hope you will try this activity with your class soon!
Mathematically yours,
Carollee

 

Geometry Concepts: 2-D Shapes October 18, 2013

shape sort picShape and Space is one of the four strands of mathematics that is part of the BC curriculum (indeed, part of the WNCP curriculum in Canada as well). In today’s session with grade 6 teachers in SD#60, we talked about using a set of 2-D shapes in lessons involving lines, angles, etc. I first came across the shape set in a text by John Van de Walle. After printing the shapes on coloured card stock, cutting them out, laminating them, and cutting them out again, I found they could be used over and over for a variety of activities at different grade levels. Note that when doing the activities students may have a full set of shapes or a partial set. (I had personally printed full sets of the shapes in four different colours and found that to be adequate for the activities that I did).

Ideas for using the set(s) of 2-D include (but are not limited to)…

  • Have students randomly chose a shape and then describe it using as many mathematical words as they can (e.g., name the shape if it has a specific name, name kinds of angles, kinds of lines, number of vertices, etc)
  • Have students each select any two shapes then tell what is the same and what is different about them.
  • Have students place 4 of 5 shapes in a group, all having something in common. Other try to guess the “common rule”.
  • Have students randomly pick three shapes and try to find something that is the same/different for all three.
  • Sort the shapes using a single rule (e.g., those with/without an acute angle; those with/without a curve ; those that are/are not regular, etc.)
  • Create a large two circle Venn diagram and sort the shapes according to two rules (e.g. sort by having parallel lines and having an obtuse angle)
  • Ask students to find and hold up a shape with a particular feature that you name (e.g., an obtuse angle, two pairs of parallel lines; exactly one pair of parallel lines, etc.)
  • Ask students to find and hold up a shape with two particular features that you name (e.g., a right triangle, a pentagon with three obtuse angles, etc.)
  • Ask students to find all shapes that have two particular features
  • Students play “Shape Find” by picking one shape that is in their set to be the mystery shape (it remains on the table); then other players must ask yes/no questions to eliminate all the other shapes until only the chosen one remains.

I hope you will print off one or more of the shape sets (as needed) and try some of these activities. And please, if you have other ideas to add to the list, I’d love it if you would share those with us.

Download the shape set template here.

Mathematically yours,

Carollee

PS: Thanks to all the grade 6 teachers who participated in today’s session here in SD#60. There was such a lot of positive math talk going on all afternoon!

 

Number Sense: Anchoring to 100 October 17, 2013

Filed under: General Math,Parents,Primary Math Ideas & Problems — Focus on Math @ 9:13 pm
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Screen shot 2013-10-17 at 9.08.13 PMI was working with a teacher today, and in the course of our conversation we were talking about the relationship of numbers to  “anchor” numbers. For low numbers we anchor to 5 and 10. For larger numbers we anchor to multiples of those.

I have previously written about anchoring to 20, anchoring to 30, and anchoring to 100.

I wanted to add here a great activity sheet that anchors numbers to 100. The student colors the particular number (given by you or generated by dropping a bean on a 100 chart, etc.) and then looks to see how many more it takes to make 100.

The activity makes a great number sense warm-up activity for young students.

Thanks, Pat, for commenting about the colouring. I have students use the broad side of a highlighter for this task (or a wide light-coloured marker would also do nicely. We always swipe across a full row at a time (or at least in fives). I particularly stress that they are NOT to colour one dot at a time, that the important thing is to represent the number. It’s NOT art class here 🙂

I prefer using the 100 dot-array to a solid 100 grip because of the vertical and horizontal “anchoring” lines. It is easy, for instance to colour 60 and not lose track, colouring too few or too many rows: one colours the first 5 rows (to the anchor line) and one more row.

Download the anchoring to 100 activity sheet here.

Mathematically yours,

Carollee

filled in how far to 100

 

Math Bowling October 1, 2013

math bowling pic This “Math Bowling” activity is one that students tend to love! It is great for practicing math facts as well as for stretching students’ thinking.

The activity is done as follows (students alone or in pairs):
Roll three dice (your choice whether to use regular six-sided dice or include one or more different dice, such as a ten-sided die). Write the numbers in the boxes marked “strike”. Using all three numbers each time exactly once, students work to write equations to equal each of the numbers 1 to 10 of the “pins” marked on the sheet and thus “knock them down”. Students may use whatever operations they understand: addition, subtraction, multiplication, and division are standard, but students may also use exponents, roots, and factorials if those are in their realm of mathematical knowledge.

For instance, if the numbers rolled are 2, 3, and 6, students might “knock down”
1 = 6 – 2 – 3 OR 1= 6/(2 x 3)
3 = [( 3!)/6] + 2
4 = (2 x 6) ÷ 3
5 = 6 + 2 – 3
6 = (6 ÷ 2) + 3
7 = 3 + 6 – 2
9 = (6 ÷ 2) x 3

If the students did equations for those 7 numbers/pins, that would constitute the first throw of the ball. Since all the pins are not knocked down, the player may roll the dice a second time, record the numbers in the boxes marked “spare” and try to knock down the three remaining pins using that second set of numbers to score a spare. If that is not accomplished, the student scores the number of pins knocked down in the two “throws”.

If you wish, as players take multiple turns, you can calculate scores in the manner that 10-pin bowling is actually scored. As someone who was on a youth bowling league in my younger days, I know the scoring system well. There is some good math in the score keeping, too! If you are not familiar with that scoring system, here is a website which will walk you through the scoring process.

http://www.bowling2u.com/trivia/game/scoring.asp

Download the “Math Bowling” sheet here.
Download the score sheet here.

I hope you will give math bowling a try with your class.
Mathematically yours,
Carollee

math bowling score picScreen shot 2013-11-07 at 6.56.30 PM