Mathematical Thinking & Teaching Inspired by Marilyn Burns

Re-Building 100s Chart

In preparation for 2-3 digit addition/subtraction operations, it became evident early in the first week of school that grade 4s needed a major refresher of 0-100 numbers. The 1000s project completed in week 2 gave way for investigations into number patterns and number bonds and ‘short cuts’ that lead to base-10 answers (40, 50, 100, 400, 1000).

Investigating patterns on the 100s Chart:

Students were given hundreds charts to glue into their math books. As a group they were given one ‘rule’ or ‘direction’ at a time, to try and find patterns on the charts. The rules & lesson were taken from Marilyn Burns’ book A Collection of Math Lessons: Grades 3-6

Colour in all the even numbers

Colour all the numbers whose digits add to 8

Colour all the numbers whose digits differ by 1

Colour all the numbers with a 4 in them

Colour all the multiples of 3 (skip count by 3)

Colour all the numbers with double (same) digits

Immediately, students were confused by certain directions, and we needed to revisit ‘digit’ verses ‘number’. Students were also unfamiliar with the word ‘differ’ (for ‘difference’) and rather than find digits that add to 8, many students simply counted by 8. I also was able to see that several students, when counting by 3s, included the number they just coloured, thus they only were counting by 2s.

Once students understood the task of finding patterns and describing them, I introduce support activities to break up the class (20 students) so I could give ability groups appropriate guidance and attention.

I created the following activities for students to work on independently in groups:

   

Above (left) : Activity 1~ students reconstruct the hundreds chart by calling out practiced number patterns.

Above (right): Activity 3 ~ students created a jigsaw and followed instructions on a card to locate a number.

Below: Students benefited from reviewing Odd & Even numbers. This investigation sheet helped them create ‘rules’ to remember patterns in adding/subtracting even & odd numbers. (ex: odd + odd = even)

 Follow-up to 100s chart: Reflecting & Extending

As students started to finish their patterns, I introduced another set of ‘activity cards’ which had a lot more to do with writing about their mathematical thinking and processing. The reflection cards I developed helped me understand where the activity challenged them, and any gaps (or extensions) that needed further attention.

 

As a whole class I introduced the concept of ‘Arrow Addition’ which was mentioned in Marilyn Burns’ book. Students were very excited about this new way of adding/subtracting using the hundreds chart to guide counting by tens & ones:

Students created their own set of addition/subtraction based on this method, and traded books with each other to find answers.

Students also played a ’rounding game’ where they threw 4 dice to make the place value digit and rounded up/down for tens, hundreds and thousands. (below)

One of the most revealing tasks I had them complete was a reflection on the 100s chart pattern & games, and also a ‘Shortcuts’ page where students created rules for using the 100s chart.

Going beyond 100…to 300!

This extension I discovered from the Investigations series. It was perfect for students who were ready for a bigger challenge and has enabled students to extend application to 3-digit addition/subtraction strategies using the chart.

Students ran into some interesting challenges when filling it in (see below). Many had accidentally skipped or repeated numbers. Pretty soon, students picked up that they could add the ‘ones’ place first (vertically) followed by the ‘tens’ place. Having them complete this was an excellent formative assessment to see if students could transfer their understanding of the 100s chart. I was surprised that at least 5 students needed teacher guidance to complete their chart. I will continue to strengthen their understanding of the 100s chart before moving them onto patterns & addition/subtraction games with the 300s chart.

Below: This student has repeated numbers in several places breaking the ‘rule’ that the ones place doesn’t chance in the vertical columns. After talking over some rules to remember for the 100s chart, he picked up that he had repeated a few numbers (22 for example) and tried to work more slowly to work out the patterns on the chart.