This demonstration is simple and gives students an effective hands-on experience to understanding Real World Problems. As this is the start of the year, we are beginning with the use of addition and subtraction within 100 to solve one-step word problems involving adding to - sum unknown and take from - result unknown. Later students will have to extend their addition and subtraction skills to include taking from, putting together, taking apart, and comparing, with unknowns in all positions.
The mathematical practices addressed here are:
MP.1. Make sense of problems and persevere in solving them.
MP.2. Reason abstractly and quantitatively.
MP.3. Construct viable arguments and critique the reasoning of others.
MP.4. Model with mathematics.
MP.5. Use appropriate tools strategically.
MP.8. Look for and express regularity in repeated reasoning.
I engage my students using this fun lesson to help them better understand the methods of solving real-world math problems.
Before the lesson began the students and I gathered the things needed.
Students were gathered in a whole group setting (close proximity), as the teacher modeled how to solve word problems using shapes that connected the students to something real. After that, the students and I began with a quick model of how to solve problems using response, feedback, reasoning, and basic number sense.
Story: Rebecca has eight pink squares bracelets and four green triangles bracelets.
How many pink squares bracelets?
How many green triangle bracelets?
How many total bracelets does Rebecca have?
8 pink square bracelets + four green triangle bracelets= 12 bracelets
Retelling: Rebuke had 8 pink square bracelets. She added four green triangle bracelets so she now has 12 bracelets in all.
The students began to really open up as we discussed the steps used in solving this problem. However, I did go back and asked questions like “how/why” this problem was solve to check for understanding.
Since speaking and listening is one of the key mathematical practices, I thought it would be a good idea to extend this lesson. Therefore, the students complete a quick “think Sheet.” (See attachment) The “think Sheet” allow the students to reflect and explain how they solve their problem.
When the students and I completed our illustrations, I asked student volunteers to explain and share their math model with the class. This is important because it allows me to check for understanding, and it helps the students feel comfortable justifying how they got their answers!
The students and I move into small group sections, no larger than six students.
We worked collaboratively, solving word problems. While we worked on solving the given word problems, I guided students using the thinking map.
(Since this particular lesson involves students in a two-step problem it is imperative that you model how it should be done.)
The given stages will help students better understand the key steps in solving math word problems.
(Over the year, some students may no longer need the guided questions as the practices become a part of their everyday mathematical skills.)
UNDERSTAND THE PROBLEM
1. Read the problem carefully.
Do I understand what the problem is asking?
2. Picture the problem.
Can I draw or make a model of it?
(Students restated the story, and understood that the story help them solve the problem. They also recalled several ways to solve the given problem.)
SOLVE THE PROBLEM
3. Think about what you are being asked.
Is my answer going to be large or small?
4. Decide what operation to use.
Do I add or subtract?
(One of Common Core mathematical practices is to use reasoning skills, and know how/why the problem was solved.)
REVIEW YOUR ANSWER
5. Re-read the problem and your answer.
Does my answer make sense with the problem?
6. Check your work.
Did I calculate (add or subtract) correctly?
(Justifying answers allows the students to go back over their steps to ensure accuracy.)
After the students and teacher have carefully worked through each of the problem-solving stages, have the students to confirm their thinking process by explaining what they did during each stage of the problem solving process.
To extend this lesson students and teachers should come together in a large group setting and discuss what they learned during the lesson, and share the different ways they used to solve each problem.
After the students and teacher have discussed various ways real-world word problems can be solved and illustrated. The teacher will model how to make a math model using the following word problem.
Rebekah has eight pink square bracelets and four green triangles bracelets. How many total bracelets does Rebekah have in all?
The teacher stresses that Rebecca has eight pink squares bracelets by using the shape to trace eight squares into the first box, and then counting them aloud. Next, stress that Rebecca also has four green triangles bracelets while tracing four triangles into the second box. Pointing to the word clues (total, in all) I explain that these clue words help me determine the correct calculation (add, or subtract) for the given word problem. You can also have the students high-light or circle the clue words in each word problem and indicate the operation (add, or subtract) out beside the word problem.
After the modeling of how to illustrate math problems to solve them, each student is expected to apply these steps as they work independently.
This is where I transition into a facilitator / observer.
Using what they have learned, the students compose their own word problem, and explain the steps they used to solve it. Additionally, they create a math model, using shapes, to show how they solve their problem.