Math Classroom Challenge: Decimals
Students will be able to explain their mathematical reasoning and critique the reasoning of others.
- Write this problem (or something similar) on the board: Melissa multiplies 4.34 x 10. She gets the answer 0.434. Is Melissa's answer correct, or incorrect?
- Instruct your students to determine, without working out the problem, whether Melissa is right or wrong.
- Give students time to think. After a minute or so, request that each student turn to a partner and whisper their thoughts on the problem.
- Ask your students to give a thumbs up if they think they know the answer. Instruct your class to explain why Melissa is correct or incorrect with their partners.
- Walk around and listen to their discussions, asking guiding questions and encouraging students who are on the right track.
- Once you've made your way around the room, tell the class that Melissa's answer is incorrect. Explain that when solving the problem, Melissa moved the decimal point in the wrong direction.
- Tell your class that today, they will practice what they know about decimals, focusing primarily on their ability to explain themselves.
- Review the learning objective as a class.
Explicit Instruction/Teacher modeling(10 minutes)
- Write this problem (or something similar) on the board: Elizabeth wrote 45.867 in expanded decimal form. She wrote 40 + 5 + 0.8 + 0.06 + 0.007. Is she correct?
- Model how you want the students to respond. For example: Elizabeth is incorrect because she did not write the decimal in expanded decimal form. If she wanted to write in expanded decimal form, she would need to factor the terms even further: 40 = (4 x 10); 5 = (5 x 1); 0.8 = (8 x 0.1); 0.06 = (6 x 0.01); and 0.007 = (7 x 0.001). This is how she would need to write it in expanded decimal form: (4 x 10) + (5 x 1) + (8 x 0.1) + (6 x 0.01) +(7 x 0.001) because each term is factored with the digit and the place value. Those are then added together.
- Explain to your students that this is what you are looking for in their answers.
- Tell them that they will be writing their answers on a big white poster. In order to get full credit, their answers need to include written statements with mathematical vocabulary, models and equations.
Guided Practice(40 minutes)
- Divide your class into groups of three.
- Hand out the supplies to each group. Instruct your students to cut out the Decimal True or False Statement cards.
- Instruct your class to put the TRUE and FALSE cards side-by-side on a desk. They will be classifying each statement card as true or false.
- Show your students how to choose a card, read it to their group, and determine whether the statement on it is true or false. Remind them to justify their reasoning, like in the example above, and write it on their poster. Once they have finished, they must place their card in a column under the notecard labeled TRUE or FALSE, depending on what they proved on their poster.
- Instruct your students to repeat this process on their own with the other statement cards.
- Circulate the room to assist groups in their explanations and to correct errors.
Independent working time(15 minutes)
- After the groups finish their assignment, give your students a problem to work on in their math journal or on a lined sheet of paper. For example: Marcus divides 67.942 by 10 to the power of 2. He says his new decimal is 6,794.2.
- Instruct your students to determine whether the problem is true or false, and explain their reasoning using mathematical vocabulary, models, and equations.
- Enrichment Challenge your advanced students to create five of their own statements and respond to them using mathematical vocabulary, equations, and visual models. Alternatively, you can provide these for them. Also, advanced students can write a presentation where they have to talk through the steps of a problem. This will help them become fluent in mathematical vocabulary, and give them the practice with creating visual models.
- Support Have students who are struggling state whether the statement is true or false and support their answers with an equation. Gather these students into a small group so you can assist them with putting their strategies into words and on to the poster.
- Read through their journals and determine which students are still struggling with concepts and explanations.
- Look for students who have little explanation or are not connecting their explanation to the problem.
- Pull these students during the next days activity to offer support for using their reasoning skills to solve problems.
Review and closing(5 minutes)
- Close the lesson by reading several statements from the group posters aloud to the class. These examples should highlight good examples of mathematical explanations.