Students will explain that the number in the “tens” value refers to the number of groups of ten “ones”
Students will be able to do subtraction with “regrouping” of numbers from (0 to 20)
Students will be able to define subtraction
NCTM • Use multiple models to develop initial understandings of place value and the base-ten number system; • Organize and consolidate their mathematical thinking through communication • Communicate their mathematical thinking coherently and clearly to peers, teachers, and others California State Standards • Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1000: • Use words, models and expanded forms (e.g., 45 = 4 tens + 5 ones to represent numbers • Students estimate, calculate and solve problems involving addition and subtraction of two- and three-digit numbers • Find the difference of two whole numbers up to three digits long.
Description of Learners
Our target audience is 2nd grade students studying beginning subtraction. Our pilot group is a 2nd grad class at Barron Park Elementary in Palo Alto, CA
Information for Teachers
Opening: Call three students up to the front of the room. Explain that they are going to play squareball after school. Call two more students up. Ask how many we will have if we add two more. (five)
Now specify that one of the children’s parents as arrived to pick him / her up (specify name…have he / she leave). Now how many are left? (four)
Activities: (30 minutes) 5 minutes 1. Distribute a pre-assessment to each student. Assure them that they will not be graded on this activity . Rather, their teacher wants to get a sense for where they are right now. After the students have completed the • Pre-assessment- students will be placed in groups of 5. Each student will be given paper cut outs of bananas and paper clips. • They will be asked to group ten bananas into one bunch. • At the end of the exercise, they will be asked how many bunches of bananas and then individual bananas they have collectively as a group in order to determine their level of understanding of place value of numbers. 2. Separate the students into groups of five. It is okay if there are uneven numbers of students in each group. Have one group of students start the monkey math computer simulation. 10 minutes a. Money math. 1. Have the students push their desks together to form a group. Place the bank in the middle of the cluster. 2. Distribute a one hundred dollar bill to each student. Place the rest of the money in the bank. 3. Give each student a copy of handout one. 4. Tell the students to imagine they found a $100 bill on the playground. Distribute a $100 bill to each student. 5. Instruct the students to work in groups or three to complete the rest of the assignment. 6. If they finish early, have them write a story about how they would spend the $100. b. Monkey math instructions: 1. Explain the following to the students: Your sailboat just crashed on an island, where you meet Mr. Monkey. Mr. Monkey has all of the tools you need to make a raft to get back home. He will only give them to you if you help him eat his lunch, delicious bananas. Make sure you have enough bananas for Mr. Monkey to eat. 2. Distribute activity 2 3. Direct each student to a computer where they will work through the applet individually.
3. As a group finishes the monkey math module, have another group rotate on to the computers.
4. As the groups complete both activities, have them individually work on the assessment.
Activities and Assessments
Activities: “Monkey Math”: Five level (objects only, one digit minus one digit, two digit minus one-digit, two digit minus two digit, bonus round) interactive game with subtraction problems, starting with the purely representational (bananas) to the purely abstract. Premise is player must subtract number of bananas the monkey wants to eat from the number on a tree.
Assessment: The first type of assessment will be a computer version of “Mad minute” problem sheets already used by class. The second part of the assessment will be a guided student as teacher “interview” where student explains the concept of place value, and walks teacher through a subtraction problem. The first type of assessment can be integrated within the program, and occur at each level.
The second part of the assessment will take part in class. The teacher will ask the following questions: What is subtraction? Answer: Essentially, the answer should indicate the student understands conceptually what happens during the subtraction process. Ideally the answer would address the following issues: • From a given collection, take away (subtract) a given number of objects. • Compare two objects to find their difference. For example, the difference between $800 and $600 is $800 − $600 = $200. • It would also be valid to view subtraction as a kind of addition...that is the addition of the opposite. ~ Create a subtraction problem for your classmates. Solve it.
An interactive multi-level (difficulty) system providing immediate constructive feedback to student actions. Implemented in flash, the app is designed to consist of 4 scenes, training, standard, advanced, and superhard. Per scene the first frame is used to establish the initial code and objects which will be used throughout the scene. In general each subsequent keyframe is another problem. Problem specific state is managed by a transitionState func using conditional logic based on a problem state variable.
User Interface Summary
Both visual object based and numeric (symbol) based representations of subtraction are incorporated into the UI. Initial problems provide both representations as scaffolding. The alternate representation is smaller and peripheral. In later problems the alternate representation is removed. Clicking and dragging of tens objects to the ones place-value column is provided to link psycho-motor functions with "regrouping". Students are able to "feed the monkey" by click and dragging objects (bananas or bunches of bananas(10)) onto the monkey's stomach which then grows to provide engagement.
Summary of Field Test
We field tested on a Wednesday morning. There were approximately 22 students in the class and the test started will all students completing the assessment. Upon looking at the results, it became clear that while most students could describe subtraction as "take away", they were focused on the process, not the actual concept.
While observing, we noted the following things: -Are they engaged? entertained? -What kinds of emotions are around this? -Level of understanding/confusion? -What types of questions are coming up? -What kind of language are they using? i.e. are they saying regrouping or subtraction or just counting bananas? -How independent can they be? Are they needing a lot of support? asking neighbors? or waiting for one of us to help them?
We started a group of five on the computer and the other students worked at their desks on the money activity.
Things the students noticed: -Error on one screnn made a mystery banana appear. They students thought this was a hidden banana, which seemed to excite them (perhaps similar to video games they play) -Kids couldn’t see the rope…tie rope and raft together was missed -Click in box. This feature seemed to be a bit sensitive and the students became frustrated if the banana bunches did not separate into ones -The training moved too quickly and the students seemed to figure things out by clicking around -Students did not really notice the subpanel showing the subtraction numerically. -Little girl was a distraction. -Students liked the monkey getting fatter. -Scaffolding: didn’t need to get the prompts of how many bananas on the tens place- scaffold wouldn’t fall away for advanced kids became frustrating and confusing
Fix the following: -Sometimes the monkey does not eat bananas -Bunches should separate when moved anywhere into the ones place -Training needs to be more interactive. Perhaps a help key or something "just in time" for the students and then a more detailed training guide for the teacher? Regardless, all training screens should look the same as the activity screens -Students need to have their attention directed to the numerical representation. Perhaps have the monkey show the representation to force them to see it- not just the little girlpointing it out -Students are at wildly different levels of understanding. By giving an option to turn off scaffolding- or prompt scaffolding- then the tool can be differentiated to individual needs -No columns separating the tens, ones, etc. Design this like the money tracker activity (see lesson plan) -Move the monkey to the sand instead of the water -Don’t make them click mouse for text…text prompt should be automatic
Consider for the future: - incorporate hidden banana? - do we want to put numbers next to bananas? - adjusting the scaffolds: Do we want the table scaffoldto go away sooner? What about just having popups for place as opposed to table? Or should we give students an option between using numbers or bananas
Success of Curriculet
- Assessment results indicated that children liked seeing examples of what subtraction acutally means - Functionally and engagement wise it was a success (i.e. it was usable and the kids enjoyed it).
Highlights of Group Collaboration
- Communication methods: weekly meeting time, lots of email, occasional additional meetings and phone calls, specialized pair work - Rules : Our standard operating procedures were listed in abook we called the bible - Distribution of labor (mostly group work, some subgroup and individual task assignment)