Written By: Suzanne Hood, Exemplars Math Consultant
Welcome to Exemplars! If you are reading this, you are likely at home hoping to help your child be successful with the math task they have been sent from school. What is an Exemplars task? As a parent, what are you supposed to do to help?
This blog will summarize what an Exemplars task is designed to do for your child. It will also provide you with a couple of helpful strategies that encourage your child to be engaged and successful in solving a task that may seem a little more complicated than what you are used to. Please let us know if there are any questions we can help you with. Email us at firstname.lastname@example.org.
What is an Exemplars Task?
Exemplars creates problem-solving tasks that are designed to engage your student in real-world mathematics. Exemplars tasks challenge students and help them grow as mathematicians. Successfully solving our tasks and sharing how they are solved build a student’s confidence and enhances their ability to solve many new problems they will encounter.
At Exemplars, we want students to do more than get the right answer. We want them to help us understand how they got the answer and to show and explain the thinking behind their final solution. We want students to convince others that their answer is correct. Showing and telling their math thinking helps others follow how the student used a diagram, chart, or table to get the correct answer.
Think about it this way: If I asked you to do a project for me, and you told me it was going to cost $10,000, I would want you to provide me with all of the details for how you arrived at that total. I would want you to help me understand why it costs that much.
Exemplars tasks help students deepen their thinking about their math problem-solving work. Slowing down and clearly showing their thinking helps students better understand the concepts they are learning. Teachers call this metacognition; the thinking about our thinking. Complex problems like Exemplars create the expectation for students to think flexibly about how they might solve a problem and to clearly show and explain their work using pictures, numbers, and words.
Allow your student some choice when working on Exemplars. It will grow their ability to stay with the task, solve it and show their thinking. Stay out of their way and try to resist giving hints or telling them how to solve it. Supply your student with objects around the house to act out the problems, but allow them to do the thinking for themselves. It is okay to help when they truly don’t know something, but try to ask questions that help them discover what they need to know and understand.
The Problem-Solving Hand
Exemplars has developed a specific process for helping students become strong problem solvers. This process has been summarized for young learners with the Exemplars Problem Solving Hand. Each finger represents a different phase in the process.
Red - The Red thumb asks students to stop and understand the problem. We utilize a Three Reads Protocol to guide students through this process. Encouraging students to say the question out loud, in their own words, enables them to internalize the question and keeps them focused on the problem to solve.
Yellow - The Yellow finger asks students to think about different ways they can work to solve the problem. What strategies might they use? What diagram or representation might help them think about and solve the problem? Younger students often use a diagram: a sketch using symbols, numbers and words to show their math thinking on paper. Encouraging students to use a variety of strategies helps them develop flexibility in their thinking.
Blue - The Blue finger asks students to go for it! Try using your plan to solve the problem. Work to find a correct answer. Does a diagram work to show your thinking? Don’t stop now… this is a great time to get all your thinking on paper. You might try a table, ten frame or number line to show your work another way.
Green - The Green finger asks students to clearly show their mathematical thinking. How did you reach your answer? Can you include math words that are part of your thinking? Can you provide a clear representation that shows your strategy? Did you label your representation? Can you include a key to tell the reader the meaning of the symbols? Is your representation labeled with words and numbers? Often students draw a picture but they forget to include words and numbers with their work. Accurate and precise representations are part of being a proficient mathematician.
Purple - The Purple finger asks students to make a connection about the problem they have just worked to solve with other math ideas they already know. Can they solve the problem another way? Can they find a pattern as they work to solve the problem? What does this work make you think about? Sometimes, you might want to make connections like you learned in reading and writing like text-to-text, text-to-self, and text-to-world; these are literacy connections. Mathematicians make connections with the numbers and think about how the quantities are related.
Our tasks ask students to do more than simple calculations They ask students to read the problem carefully, utilize their toolkit of math skills to solve and use their writing skills to share their mathematical thinking about how they found their solution. When worked slowly and carefully, consistent practice with Exemplars tasks lead to rich math understanding and strong flexible thinkers.
Good Luck! And, we wish you great success in creating strong problem solvers!