Over the next week or so, I plan to post all of my problems for the first nine weeks of school. These problems are just a guide. Every class is different! Some classes need more time to develop basic skills--others are ready to move on more quickly. No matter what problems you choose, be ready to adjust them as you finish your beginning-of-year assessments and get to know your kiddos a little better.
I start problem-solving on the very first day of school. I purposely choose easy problems so that I'm able to teach routines and expectations alongside with them. This first week focuses on the expectations for using our problem-solving notebooks. Before we begin, we go over all of the Problem-Solving Expectations and glue them in our notebooks.
Day 1 This problem serves several purposes. First, it's very easy, so it will let the children experience success and gain confidence early on. (We want them to love--not dread--problem solving!) Second, it gives them a chance to practice the expectations they just learned (especially the One page at a time and Do your best work!) During Mathematicians' Chair, focus on notebooks that have neat, organized work (i.e.the eyes are clearly present). Look for children who wrote the number 2, but look for other ways that children may have represented the number 2 (for example--did anyone make two dots?) If nobody did, ask the kids for ideas about how they could represent the number 2. Call for volunteers to show different ways to represent the number 2 in the Big Class Notebook.
Day 2 is another fairly easy problem. The focus should be on How can you show your answer? Some children might draw a literal picture. Others might draw symbols. Many may write the actual number. During Mathematicians' Chair, ask the children how they found their answer. Get them to use the word count... "I counted!" Ask for several volunteers to demonstrate how they counted. Also, point out the variety of ways that children showed their answers. Point out children that used more than one way to show their answer.
Day 3 This is a good problem, because there is such a variety of answers. During Mathematicians' Chair, call on several volunteers to write their names in the Big Class Notebook and demonstrate how they counted. Begin to point out good counting strategies! Showcase journals that are neat and organized. Look for alternative ways to represent numbers.
This problem introduces pattern blocks. It also allows children to practice counting and representing number in a neat/organized way. I introduce the pattern blocks in warm-up, and go over all expectations for using them (i.e. do not throw them or stick them in your nose...) Then I let them have at it and "play" all they want. When we are ready to problem-solve, I give each student a baggie that has 20 pattern blocks that they can choose from so that they do not get carried away and create a monster that has 72 green triangles! They still have freedom to create what they want, but are limited in number. During Mathematicians' Chair, have children demonstrate how they counted their blocks. Did they leave them in their design, or did they mess up their design and line them up, or push them away as they counted? Did they touch each block as they counted? Have the children discuss what they think the best counting strategies are and record them in the Big Class Notebook.
This problem introduces unifix (or linker) cubes. I introduce them during warm-up--going over all the expectations (see pattern blocks above) and then letting them play.
When it is time to problem-solve, I demonstrate how to use one hand to grab as many cubes as I can. (This is a great problem to use throughout the year. Differentiate by using smaller manipulatives to produce bigger numbers and bigger manipulatives to produce smaller numbers!) Again--look for good counting strategies. If a child is unorganized and mis-counting, ask, "Can you think of an easier way to count the cubes? How can we make sure that we count all of the cubes? How can we make sure that we don't count a cube twice?"
During mathematicians' chair, call on several children to demonstrate how they counted their cubes. Add to the list of Good Counting Strategies. Hang it somewhere very visible so the children can reference it later.
(For all of the Investigations fans out there, this is a variation of the classic Grab and Count!)
This is not the only time we practice counting in my class! We spend the majority of our time in math warm-ups the first few weeks doing counting and number identification activities--I'll do a post about that soon. But by all means, if your class needs more time counting, give them some more counting problems!
And remember--do not worry so much right now about how the notebooks look--it won't be pretty! Most of the children are brand-new to all of this! Just reinforce the expectations, and praise the children who are neat and organized. You'll start seeing a big difference soon!