Mathematics

Targeted Group: Grade 7

Format: Number Sense and Numeration – Adding Fractions

Misconception: Adding fractions without finding common denominators or equivalent fractions.

Rationale:

Students have a great deal of difficulty with fractions and understanding why they need a common denominator in order to add them. As this seems to be an issue each year with grade 7 students I thought it would be a good idea to find new ways to address the concept.

Goals:

Students will be able to add fractions competently with like and unlike denominators, finding equivalent fractions in authentic problems.

Materials: Virtual fraction manipulatives

http://www.mhhe.com/math/ltbmath/bennett_nelson8e/VMK.html?initManip=fractionBars

Smartboard notebook software – Specific lesson plans

Authentic addition of fractions questions.

Process: This can be done individually or in pairs.

Step 1:

Give students a step by step adding fractions task sheet with three different tasks. The step by step process allows the students to see how the common denominator is found and how to add the fractions.

Step 2:

Direct students to the virtual manipulatives at the above URL. This would be in their Edmodo folder already so they just have to click on the link.

Step 3:

Direct students to create the model shown on the task sheet on the virtual page using fraction blocks. Students should write the addition statements on the virtual page, and then transfer them to their task sheet. They should continue to do this for all the questions on the task sheet.

Step 5:

Ask the students to create their own addition problem using the fraction bars for the other students in the class to try. Students should be sure to draw this on their task sheet including the correct addition statements.

Consolidation Activity: Smartboard Notebook Lesson

Task:

Introduce students to the Land Ownership task. Show them the picture of the land split into various areas for different owners in SmartNotebook. Students can use this software on the laptop computers using the mouse.

Work with a partner.

The map shows land owned by 8 families.

Determine what fraction of the land each family owns.

Four families sold land to the other four families.

Use the first map clues to help you draw the new map. You can use the back of the sheet to do this.

Write the addition to show each of the transactions.

CLUES

- When all the sales were finished, four families owned all the land – Smith, Perry, Haynes, and Chan.
- Each owner can walk on their land without having to cross another person’s property.
- Smith now owns 1/2 the land.
- Perry kept 1/2 of her land and sold the other half to Chan.
- Haynes bought land from two other people. He now owns 3/16 of the land.
- Chan now owns the same amount of land as Haynes.

Students use the tools in SmartNotebook to colour in the areas owned by each family and manipulate the shapes to find the smallest piece in order to determine the common denominator. Once they have done this, students find the equivalent fractions for each of the owners property showing the fraction in equivalent form and simplest form. For example: Perry = 1/4 or 16/64.

When they have found all the equivalent fractions it should be easier for them to rearrange the fractions for the four families to own all the land according to the clues. They need to show the new configuration on their screen or paper, and show the addition statements that go with their solutions.

Education Theories:

The educational theories that are associated with this lesson plan are Learning for Use and Anchored Instruction.

Learning for Use framework is a pedagogical framework that integrates the content with the processes of the subject matter. Using the virtual manipulatives allows the students to visualize the process of creating the equivalent fractions, how a common denominator is determined, and then how the two fractions are added together. Since the content is being able to add fractions with unlike denominators, the manipulatives allow the students to try a lot of different combinations of fractions to find their equivalents and add them. The virtual manipulatives also allow the students to discover these concepts for themselves, and build upon that understanding using the tiles to create a number of different combinations.

Anchored instruction is the process of presenting instruction in the context of an authentic environment with problems or issues which learners must resolve. The problems or issues which are presented to learners in the authentic environment are “anchors” which link learning of content and skills to authentic tasks and activities in which the learning must be used (Gittens, Thompson, & Carter). Although this is not a true representation of anchored instruction, the concept of buying and selling parcels of land is a real world connection. It is difficult to find authentic problems using fractions that the students would recognize. This problem could be related to their history or geography lessons particularly with New France and Seigneurial Systems or land use changes.

Using the virtual manipulatives aids the students in consolidating their understanding of equivalent fractions and common denominators, then transfer that understanding to a different task, using a different medium which demonstrates their understanding in environments other than those directly related to the specific learning environment (Dixon). Using a variety of mediums (virtual manipulatives, Smartboard tools, pencil and paper) students can consolidate their knowledge using anchored instruction and specific technology to augment their knowledge and increase their conceptual understanding.

Anne

References:

Dixon, Juli K, 1997. Computer use and visualization in students’ construction of reflection and rotation concepts. School Science and Mathematics, Volume 97(7), University of Nevada, Las Vegas.

Kathy-Ann Daniel-Gittens , Kelvin Thompson and Philip Carter (2014). Anchored instruction. In K. Thompson and B. Chen (Eds.), Teaching Online Pedagogical Repository. Orlando, FL: University of Central Florida Center for Distributed Learning. Retrieved April 3, 2017 from https://topr.online.ucf.edu/index.php?title=Anchored_instruction&oldid=3577