I. Curricular Framework

Concept:

Holding

Essential Question:

How is “holding” a way to explain what is being done at each place in a number?

Bridge:

Manipulating the Concept

Content:

Place Value Concept

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To introduce/reinforce place value concept by allowing the children to physically be numbers.

Activity: Draw two large circles on the floor. Make them large enough for nine children only. Draw two large squares on the blackboard directly above and behind each circle. Give eleven children signs to wear, each with the number one on it. Have one of the children with the signs go up and stand in the first circle (the ones circle). Ask the children how many people are standing in the first circle. When they answer "one" put a 1 in the large square on the blackboard directly behind and above the ones circle. State clearly at this point "that what we have in the circle is one." This is the switch that is crucial, to switch from "things" to number notation terminology. Have another child go up and join the first child. Ask "How many ones do we have now?" When the answer is given, change the number 1 on the blackboard to number 2. And so on until you have nine children standing in the first circle. You must emphasize the distinctness of 2,3,4, etc. otherwise some of them do not understand why nine (9) is not. It is of course simple to us, but they need to know why we use the integer symbols at all. "How many ones?" "Nine ones." Each time erase the previous number and put the next one in its place. When the tenth child tries to join the group, note to the class there isn't really room in the circle for ten. Have the children join hands and all move to the second circle, the one on the left. They say to them, "We have ten ones but we also have one ten." This is the crux of the concept. If they understand this, they are well on their way. Then say, "To make it easier to work with big numbers we will make (Billy, Margy, or whomever) one ten. When Billy stands in the circle on the left, he is one ten. When he stands in the right circle, he is one one." Ask the other nine children to sit down. "Now Billy is one ten." Crucial. Erase the nine in the first square and place a one in the second square. Draw their attention to the fact that no one is standing in the first circle. Say "What we have is one ten and no ones." Then place a zero in the first square. Lastly, have another child go up and stand in the first circle. Ask the children what they see now. One ten and one one. Change the zero in the first square to a one. "One ten and one one." Then ask the children if they know the name for the number with two ones side by side. (Eleven.). Note: In other words, let them see it, by letting them "be" it. Stop at this point. One could easily adapt this to the teaching of bases in 6th-7th grade. "Why be limited to groups of ten, why not groups of 6,7 etc...?"

Assessment: Children's understanding of the concept.

2. Attend: Attending to the Connection

Objective: To allow the children to discuss/examine what happened.

Activity: Talk about it and let the children be other numbers; i.e. two children stand in the second circle, one in the first, what number "21" is, and so on.

Assessment: Participation and level of understanding of the concept.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To switch the concept to practice in another medium.

Activity: Give the children sticks and rubber bands. Let them manipulate the sticks in various combination of tens and ones. i.e. numbers apply to anything, people, toothpicks, apples etc. Teacher gives problems, 22, 17, 31 etc.

Assessment: Do the children understand? Teacher can assist those who need more help.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To teach place value concept through teacher instruction.

Activity: Teacher teaches. Any good primary math text will provide assistance.

Assessment: Objective test.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To give additional practice in the concept.

Activity: Workbooks from any good primary math text.

Assessment: Quality and accuracy of above.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: To introduce aural and kinetic practice methods (aural = listening; kinetic = use of body [tactile])

Activity: Have the children listen to problems and write answers. Have the children use tactile approach to problems, i.e., sandpaper numbers with blindfolds on ñ three dimensional numbers which are combined into problems manipulated also with blindfolds on, etc. Note: Always attempt to use aural and kinetic methods in addition to the visual. Children vary in their preferences for these methods.

Assessment: Quality of their manipulations.

7. Refine: Refining the Extension

Objective: To talk about making up problems of their own to try on each other. To make the learned material personal.

Activity: Have the children make up worksheets to try on each other. Now make toothpick structures on all problems from worksheets.

Assessment: Quality of worksheets.

8. Perform: Creative Manifestation of Material Learned

Objective: To share their learning.

Activity: Children give worksheets to each other, do them and correct (help) each other.

Assessment: Participation and sharing.

Assessment, Phase Five,Performance, Creative Use of Material Learned: