1. Teacher Leader Endorsement Programme Modeling Exemplary Mathematics Teaching Session 3 Facilitator: Rebeka Matthews Sousa Mathematics Specialist Teacher, Ministry of Education 1

2. Designing a Garden A Principal would like a garden on their school grounds. They asked the students to design a rectangular garden that has an area of 24 square feet. I.Determine possible dimensions for this garden. II.State the dimensions of the garden that would result in the shortest perimeter. III.Explain and show all of your thinking. 2 ENGAGE

3. During this session, Teachers will:  Use our rubric/standard of teaching through problem solving to observe and enhance lessons  Share their own lesson clips and reflect on teaching through problem solving Key Understandings 3

4. 4 Using the rubric for Teaching Through Problem Solving

5. 8:50 In a P1 math class, students conduct their morning routines using the calendar to count the number of days of school. A student points to the various numbers as the students call the numbers out. The student then gets the students to express this number in tens and ones. 9:00 The teacher then puts a sing-a-long video that counts to 100 on the Smartboard. Students then use the hundreds chart to skip count, calling out all of the multiples of 2. Students continue doing this for 5’s and 10’s. 9:15 The teacher then tells the students that they will look at number pairs to 10 today. The teacher writes down 7 on the board and asks the students what number would be added to make 10. Students call out responses ‘1, 4, 3’. The teacher then writes 7 + 3 = 10. The teacher continues with three more problems. Writing down the number sentence once a student has called out the correct response. 9:30 Students complete a worksheet on addition. For the first set of problems, students are shown pictures 2 bears + 5 bears = ______ bears. The second part of the assignment includes general number problems 2+4 = ____ 3+4= ______. The last part of the assignment gives a word problem: 2 ducks are swimming in the pond, three more join. How many ducks altogether? The teacher walks students step by step through each problem. 9:55 The teacher calls the students to the carpet and asks them ‘what did you learn today?’ Two students give responses ‘how to add’ ‘adding two numbers together’. Students all take a washroom break before transitioning into reading.

6. For each of the math lessons scenarios identify: 6 Every class observation is a learning experience something you would use in your own lesson something that you would modify or improve to use in your classroom

7. 8:50 In a P2 math class, the teacher begins the lesson by asking the students to record on their whiteboards the double of the number. All students receive the same number at first, but gives a different number to a few individuals. Students write their response and show when asked. 9:05 Students are then asked to continue a pattern 5, 10, 15. The teacher asks “What can you tell me about the numbers in this sequence?” The teacher listens to responses. The teacher gives another pattern for the students to continue 130,120, 110… Students describe that they are going down in 10’s. The teacher points out the these numbers are multiples of 10. 9:10 Students receive a hundreds chart and the teacher explains the task while modeling the first few. ‘Tick multiples of 2, cross the multiples of 5, circle multiples of 10.’ The teacher explains to a few students that they will start with circling multiples of 10. When students have finished they are asked to give a written response about what they noticed about the numbers they have circled. Students work independently, but discuss work with students sitting next to them. 9:40 Students move to the carpet to discuss their findings. Students are matched with a pair to discuss what they discovered. The teacher selects a few student responses to be written on anchor chart entitled ‘multiples’ Two hula-hoops are used to create large Venn Diagram on the floor. Each student is given 2-3 numbers (multiple of 2, 5, or 10) Students must place the number in the correct place. The teacher directs a question about the numbers that will go in the centre of the Venn Diagram. The teacher uses a checklist to record whether students correctly place their numbers

8. 8:50 In a P3 math class, students complete their math message in their notebooks. Each student is given three questions to complete, making complements to 100. (eg. 75 + ‘ = 100 or 70 + ‘ = 100). 9:00 After completing the MM, students move to the carpet and collect a whiteboard. Students are instructed to write down the total of the coins shown on the Smartboard (2 Q, 1 D). Teacher asks students to show their response. Then asks ‘how much more would you need to make $1?’ The teacher adds 3 N to the problem and asks the same question. The teacher then introduces the task and problem, which is to find different ways to make $1 using only quarter, and/or nickel and/or dimes. Written on the board is the objective: ‘Mathematicians will know the value of each coin and create various ways to make $1’ 9:15 Students move to assigned pair groups to work collaboratively with peers on the problem. Students choose their assigned role: Group Leader or Recorder. The teacher prompts student thinking by asking them about the strategies they are using to make $1. The teacher also gives extensions by selecting some groups to start with a specific amount or to only use certain coins. Students select tools that they require to assist them with this problem such as: coins, number charts etc. 9:40 Students are asked to finish what they have written and are asked to take a gallery walk to view other group responses. Students are asked to look at the other responses thinking about what they see ‘how did other students complete the problem?’ ‘what is different and what is the same?’ Students discuss the various ways students solved the problem. Students complete a tiered exit card, where students had to state the coin value of various coins and how much more money they would need to make $1.

9. 8:50 In a P4 math class, the teacher begins the lesson by reviewing homework from the night before. Students are called on one-by-one to give answers. 9:10 Teacher then announces that they would be doing something ‘new’ today. The teacher writes the objective on the board: Students will look at 2D shapes and describe their properties. The teacher begins to show the entire group of students one shape at a time, asking them to give some properties. Students call out their responses as the teacher records their answers on the board. The teacher continues asking the students to give properties of six different shapes (square, rectangle, triangle, circle, rhombus, and parallelogram) 9:40 Students are given a worksheet where they are to match the name to it’s corresponding shape. Those who finish early begin to work on another review worksheet of multiplication facts. Students work quietly through the assignment. The teacher moves from student to student ensuring they are on task and putting checks in their notebook for the correct answers. At 10 o’clock, the teacher announces that students should pack up as they will now move into reading.

10. 11:20 In a P5 math class, students are presented with a multiplication problem (3 dig by 1 dig) and asked to solve it with a partner using any strategy. Three students share their ideas on how they solved their problem. Three different strategies are shared. 11:30 The students are then given some word problems where students are to multiply using any strategy. The teacher asks a student to read the first problem out loud. As students begin to work independently, they discuss how to solve the problems with their partner seated next to them, the teacher asks students about their strategies. 11:40 The teacher pulls a small group of students to the back table to work on the problems, which have been modified by the numbers used in the questions. 11:55 The teacher returns to monitoring the class using a checklist that identifies if students are on/above/below target with multiplying using various strategies. The strategy used is also noted. 12:05 The teacher asks three students to come to the front to explain their strategies to the rest of the class. Students ask questions about how they came to their answer. Student solutions are left on the board. 12:20 Students are given on exit card, where all students complete the same question. Multiplying a three dig by single dig. Students are to use two different strategies to solve the problem. At 12:30, students begin lunch time prayer and collect their lunches.

11. 8:55 In a P6 math class, students are asked ‘what is area?’ ‘how is it different from perimeter?’ students respond ‘one you multiply’ ‘the other you add’. The teacher accepts these answers and adds that ‘we can calculate the area of a shape by multiplying the length times the width’. The teacher shows some pictures of a rectangles on the board with various dimensions and shows students how to calculate the area of the rectangle using the formula and then shows the perimeter. The class does three examples together, where the teacher records responses on the board as the students call out answers. The teacher prompts by asking ‘what comes next?’ ‘and then?’ 9:25 Students are given their independent work, which is a worksheet with several rectangles. Students must state the area and perimeter of each shape. The teacher moves around to each student asking whether they would have to add or multiply to determine their answer. 9:50 Students are given an exit card to complete. There is one rectangle and students must calculate the area of the rectangle and state the perimeter, given appropriate units. A student collects the exit cards before transitioning into the reading lesson.

12. 12 Videos – Observing Mathematics Share your short video clip of your students being taught through problem solving with your year level partner. Reflection: Share how …  Students work on problems or tasks that require critical thinking and a variety of strategies to solve the problem for at least 50% of the class time.  Students work on problems or tasks that mean something to them and help them to connect to their community  Teacher asks probing questions to get students to expand on their strategies, math knowledge, and communication.  Students share strategies openly, justifying mathematical reasoning.  Teacher and students address misconceptions together. Discuss how aspects of the lesson could be enhanced

13. Next session date: Nov. 18 4-6 pm Questioning and Discourse in an Exemplary Mathematics Classroom and Reflecting on what we saw when we were observing teaching through problem solving Homework:  Use rubric in your school to observe (minimum of) 3 classes – submit form online: Due by October 23 rd  Reading: “Asking Effective Questions”  Set a coaching date (email): Due by November 2 nd  Any outstanding assignments for Module 2: Due by October 23 rd Confirmed dates: Nov 18, 25, Dec 16 13 What’s next?

14.  Submit two “good” (cognitively demanding and culturally relevant) tasks  Observe lessons using Teaching through problem solving Rubric (total 6 classes)  Reflect on observed lessons  Share through video two of your own lessons (mini clips)  Model exemplary mathematics teaching in your own classroom (3 coaching visits), including reflections on each lesson 14 Course Assignments