Meaningful Math & Problem Solving

I hope to document many of my math lessons throughout the year here on my blog. My goal is to reflect on my teaching after the lessons have been taught...what I noticed, what went well, what didn't go so well...and knew things that my students teach me! I'm always blessed with at least one very talented mathematician who shows me new ways of looking at math! If you are interested in any of the smart notebook files that go with my lessons send me an email!

Day 1

Belief Systems About Math
4 Corners of the Room Activity
On the Smart board Show 4 different images numbered 1-4 e.g. a hammer, shovel, light bulb, box of tissues. Have students consider which object most relates to them when they are solving problems in math. Without speaking have the students choose the corner of the room that the number associated with the picture of their choice has been placed. Have students partner up and using our Active Listening skills take turns explaining why they relate math to that object. Switch partners a couple more times then have volunteers share to the whole group what some of their friends said. Show students some examples of grade 5 math work from last year, discuss the way they will be discovering new understandings in math through Problem Solving, my philosophy on textbooks, partner and group work, investigations, more than one strategy for solving problems, learning to justify our thinking, meaningful math conversations etc.

Finally introduce our EXCITING Interactive Math Journals! I can't wait to get started using these as a place of reflection, consolidation, and creativity! Students will create a cover cutting out letters from magazines to spell Math Journal, set up their table of contents,and paste the "Left Side of the page Thinking Sheet."

Day 2

Teaching The Process of Using and Caring for Math Manipulatives
At each table group place a Math Bin that contains our manipulatives. Pose the question “How do these tools help us to be better Mathematicians?” Give students time to explore all the different manipulatives that are in the bin. They will then be asked to choose one which interests them. On the left side of their journal they will draw a representation or give an explanation of the manipulative in their math journal. Following the representation of the manipulative, students will then brainstorm possible mathematical uses for the manipulative they have chosen. They could include situations or problems when the manipulative could prove helpful or times when they have used it in the past. Have students may share their thinking with a peer, preferably someone who chose a different manipulative than themselves. Then share in whole group.

Day 3

Introduction to the Grade 5 Problem Solving Framework
1. Pose the question “How do you solve problems in Math?” Give students a minute to reflect on the question. Ask students to find a partner (or try a triad) and to take turns sharing their thinking. (remembering to use Active Listening). Share ideas in whole group. (Discuss which points are the most significant. Record student ideas on chart.
2. Show an image of an Oreo Cookie. Ask “How can an Oreo Cookie help us to solve math problems and clearly communicate our thinking?” what do you think the 3 parts of an Oreo have in common with solving a math problem?
3.  Have students share their thoughts. -the top and bottom hold it all together -the top reminds us to understand the problem, what we know, what we need to find out. -the middle is the good stuff the strategy, work, proof -the bottom reminds us to be sure we have answered the question and reflected on the reasonableness of our solutions.
4.  On the smart board have students drag the correct phrases to one of the matching 3 parts of the Oreo.
5. Finally share some Oreos!

Day 4

Interactive Math Journals
This interactive tool acts as an aid to help students remember the "steps" to problem-solving.

Have students begin by writing the title “Steps to Problem-Solving” and page number at the top of the left and right sides of the page.
On the right side of the page, have students write the curriculum expectation in the document language. (*See smart notebook file)
On the left side of the page, have students rewrite the learning goal in an I can statement. own words. Just underneath that, have them complete "What I Know" (1 – 2 sentences). Quickly review what steps students should use when problem-solving. 
Glue the outside edge of the Oreo template onto the right side of the journal under the learning goal and definition.
Cut the top middle and bottom into strips to flip open – writing the information into journal under each section of the cookie.
When students have completed this, have them finish the left side of the page thinking. They need to finish "What I Learned" (1-2 sentences) and "Reflection" (where they can show their understanding in any creative way)– have them refer to the Left Side of the Page Thinking handout they have glued in the front of their journals. Do not include "Proof" today as students aren’t completing a problem or learning a new concept.

Day 5

Back To School Shopping (our first attempt at problem solving ....model...model....and question!)

Warm Up

Have a volunteer share their Problem Solving Journal Entry. Use the Oreo model to the three step problem solving process with the Back To School Shopping problem. (*see smart notebook file)

Working On It

1. Have students read to understand the problem (break down each sentence to determine importance). Have students help to highlight the key information on the smart board.
2. Invite students to share what they know and what they need to find out.
3. Model how to record this in point form on the top of an 11X17 paper in marker.
4. Students observe and then record on their paper.
5. Give students time to turn and talk with a partner about possible strategies that would help to reach a solution.
6.  When they have had 3-4 minutes to discuss ask "What questions do you have?"  Take time to clarify any confusions.
7.  Give the partners time to tackle the problem.  Support students by reassuring them that they can make sense of the math.  Ask guiding questions, or have struggling students go and observe what other students might be doing.  Give the students 10 minutes to try their strategies in the middle of the 11 by 17 paper. The students will be negotiating a problem that has ways many ways of reaching a solution. Students will make conjectures as to which coupon would be the most beneficial. Circulate asking students how they can prove their conjectures? How do you know? What do you notice about the 6 markers and $18? How does that compare to 3 markers for &7.50? etc.

Consolidation

(Begin Modelling Math Congress) Choose a group that will be confident in sharing their solution. Model reflective language structures, as well as Active Listening. Model paraphrasing. Invite another student to paraphrase what was said. Invite students to consider if they had a similar or different solution. Model how to agree or disagree, or add on to solutions presented. Use this as an opportunity to introduce 1 or 2 accountable math talk sentence starters. Stay tuned for reflections and revisions on these lessons! After having students match phrases related to the process of problem solving to the correct parts of the Oreo Cookie organizer the students worked on their first entry in their Interactive Math Journals. Then they worked on the Back To School Shopping Problem with a Partner. The students had great success! WOW! They clearly communicated their thinking on paper, with many different strategies that we were able to highlight during the consolidation and discussion. It always amazes me the way the minds of my students work, and how teaching math through problem solving allows me a view into their thought processes.