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standing that ten ones is the same as one group of ten. The teacher ex plicitly taught that a group of ten is the same as ten ones when she mod eled grouping, and therefore she directly addressed common place value misconceptions. Group two included the group that were just beginning to grasp group ing into tens. These children needed continual grouping practice. As Fig ures 2a and 2b show, group two was asked how to make a group of ten. The teacher circled the ten, modeled by counting slowly, and then ex

entiated groups and how a teacher can directly target what individual students needed to increase their mathematical place value under standing. While the teacher pulled small groups, the other children were working on computer pro grams that supported number sense or a menu of pre - taught math activ ities/games asynchronously. With these targeted, differentiated les sons, the teacher could assure that the majority of the children would attain mastery of the place value unit.

Figure 3 : Triple Ten Frame to show groupings of ten and then the ones left over.

Lesson Two

plained how many were leftover. After modeling this several times, the teacher asked the children to make 18 circles on their whiteboard and then group the tens and show the numbers left over. The children put their whiteboard to the screen, and the teacher was immediately able to do an in formative assessment on the children ’ s under standing. Many children struggle with grouping ten and then identifying the leftovers. The teacher informally assessed the children ’ s understanding of grouping tens and ones while teaching the small groups. Group three included the children who were still learning to count to 20 or 30 and needed to have a triple ten frame to help them see the grouping. This group started by counting to 30 with the teacher still aiding them in the rote counting skills. As the children said the number, they put counters onto a triple ten frame. The teacher started in the teens and put fourteen counters on the ten frames. She showed them that one ten frame filled with red counters is a group of ten, and then there are four leftovers or ones. The misconception this group would be explicitly taught to avoid is that there is no need to count every red counter, be cause you can automatically see the ten in the completed ten frame. The teacher modeled starting with ten and counting on four until she got to 14.

The next lesson (45 minutes) that we taught was called Race to Fifty. In this place value lesson, we decided to integrate literacy into the place value unit, so that the children could work on it at home on interactive slides. As the anticipatory set to the lesson, we read the book “ Jack and the Giant Beanstalk. ” As seen in Figure 4a and 4b, the clas ses were taught the game synchronously on a slide that could be copied for all the children and sent home. First, the children roll the dice and put their manipulatives onto the place value boards on the ones part of the board, until they make ten. Once the group of ten is made, the children use the base ten block on the tens side of the board and put one group of tens into the tens column. They then have to remove all the ones and go back to rolling the dice again and repeating filling out the ones frame. The first person in the game to reach the target number of 50 is the winner. This game was modeled synchronously, but the aim was for the children to be able to play this game at home asynchronously. This modelling took an entire lesson, and the teacher played it sev eral times to show the children. The children then each got their own slide on which to play the game at home. The teacher is able to see the slides of each child and can then make informal assess ments. At this point, any misconceptions in the

These three 15 - minute lessons highlighted differ

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