A:PDQ Investigating Investigations

For our fall sessions, we decided to encourage use of Investigations.  In particular, Diane Campbell reported that each grade level is being urged to use the “Mathematical Thinking” book and at least one other.  The specific second recommended book is listed below:

Kindergarten:  “Patterns, Trains, and Hopscotch Paths”;

1^st Grade:  “Building Number Sense”;

2^nd Grade:  “Coins, Coupons, and Combinations”;

3^rd Grade:  “Landmarks in the Hundreds”;

4^th Grade:  “Landmarks in the Thousands”;

5^th Grade:  “Building on Numbers You Know”.

On Monday, September 8, 2003, we broke into small groups and tried out the following:

Kindergarten:  K-Mathematical Thinking, Investigation 1 (pgs. 2-23);

1^st and 2^nd Grade:  1^st-Mathematical Thinking, Investigation 2 (pgs. 24-59);

4^th and 5^th Grade:  4^th-Landmarks in the 1000s, Investigation 3 (pgs. 38-51).

We would have used 3^rd-Landmarks in the 100s, Investigation 1 (pgs. 2-29), but we did not have any 3^rd grade participants.

On Monday, September 22, 2003, we again had small groups trying the following Investigations:

Kindergarten:  K-Patterns, Trains, …, Investigation 3 (pg. 49-63);

1^st and 2^nd Grade:  2^nd-Coins, Coupons, …, Investigation 1 (pgs. 2-53);

4^th and 5^th Grade:  5^th-Building on Numbers …, Investigation 2 (pgs. 40-71).

Here are some brief notes on two of these small group activities.

1^st-Mathematical Thinking, Investigation 2 (pgs. 24-59):  We used number cards and played and discussed the first suggested games, which are variations on what the students may know as “war”, but without the competitive sense of winning or losing.  “Who has more?” with one card for each player.  “Who has more?” with two cards for each player (sums).  Linking cubes would be available for students who might need a hands-on aid for comparing and/or for adding.  We discussed variations on these games, as new mathematical concepts are introduced, including, “Who has less?” and using subtraction or multiplication in place of addition for the two-card game.  Another session of this Investigation included building stair-steps and matching number cards to the number of linking cubes for each step.  Remaining sessions and concepts were discussed.

2^nd-Coins, Coupons, and Combinations, Investigation 1 (pgs. 2-53):  We began by looking at the Investigations books as a whole.  Since our group included ESOL teachers, we especially noted the “Tips for the Linguistically Diverse Classroom” and “Preview for the Linguistically Diverse Classroom”, as well as other helps for teachers.  This is a long Investigation, with 11 sessions.  We just tried a few things and discussed the various activities, variations, and content.  We started with brief sharing on “Why is the number 10 important to us?”  This Investigation focuses heavily on the number 10.  We listed and counted ways to make 10 with two groups of objects (two addends).  We listed some and eventually counted ways to make 10 with three groups of objects (three addends), and thought about how we might organize lists for these.  We noted that part of the emphasis of this Investigation is on having students write down the results of their efforts and or of the games they play.  Then we played a round of “Turn Over 10”.  These games lead students to develop the ability to add strings of small numbers by regrouping (and to recognize groups of numbers with “nice” sums).  We also noted on-going classroom activities, such as the “Today’s Number” theme, as ways to incorporate numbers into the rest of the curriculum, and talked about how each session builds on what has gone before.  At the end of our time we briefly discussed some of the remaining sessions of this Investigation, including the games, “Close to 20” and “Beat the Calculator”.