Chapter 8 Understanding Fractions
Data from June Instructional Report 2015:
- 3.NF.1, MC (3x), 70%
- 3.NF.2b, MC, 47%
- 3.NF.3a, MC, 23%, CR, 20% achieving maximum of 2 points
- 3.NF.3b, MC, 32%, CR 30% achieving maximum of 3 points
- Visnos: http://www.visnos.com/demos
- EngageNY: NF Video
- Fraction Bars (Not to share with students, very boring, but great for teacher learning on how to use concrete models to teach fractions.)
- Fraction Game from Marilyn Burns
Stage 4 Fluencies:
- Terms related to unit (whole, numerator, denominator, unit fraction, fraction, equal parts, names of fraction units)
- Making visual models
- Making congruent whole
Thoughts on Lessons:
- Tools: fraction bars, fraction circles, pattern blocks (See additional lesson here.)
- Models: bar model/tape diagram, number line diagram,
- Strategies: …
- Additional early lesson: Show students how to label visuals, record numerically and write words for fractional amounts.
- Lesson 8.1: Emphasize vocabulary, accurate modeling and equal partitioning. Prior to this lesson have an exploration of: a) where students might see fractions in their world…have them look in newspapers, magazines, etc., b) have students explore the tools that they will be using during the course of the unit. c) do the lesson using pattern blocks and focus on the unit names of the fractions (See page 456 Advanced Learners). It is vital to emphasis the equal partitioning, so showing example of items created by students that are not equally partitioned is key right here! Make this lesson in to a game…Find Someone Who…students could have index cards with the images from the book on the index cards. They have to find others who have a fewer or greater number of equal partitions. Students should work together to tell the number of parts and say the unit name, e.g. “This polygon (or shape if circular) has 4 equal parts, so it is fourths.” Use Google to search images for: “equally partitioned shapes”. This less is great to turn into a center later.
- Lesson 8.2: Use actual food, where possible, in this lesson. Emphasize equal partitioning. Know that this lesson is showing set (See: page 450 Share and Show) and area models, which can lead to confusion. The core does not emphasis set models unit 4th grade. They can be used, but name them explicitly for students. This is an opportunity to discuss the fact that the whole can change and consequently can change the fraction itself.
- Lesson 8.3/8.4: Emphasis what the unit fraction means and that we are just replicating the unit fraction again and again. As an extension to deepen thinking you can move beyond the whole to say that you have five one-fourths sized pieces. Look at the Advanced Learners on page 462 and use to adapt lesson. Also, use a Find and Fix My Error strategy in combination with shapes that are not equally partitioned. (Spend 2 to 3 days on these lessons.)
- Lesson 8.5: Use the bar model/tape diagram with the number line to structure students thinking. Also, emphasize that the bar must match the line segment of the whole on the number line. Use physical number lines and have students act out positions. Use of vocabulary is key. Play a game of Find Me on the Number Line…where students role a fractional amount and they have to find that amount on the number line using the strategies of drawing a bar model above the number line and equally partitioning the bar to find placement on the number line. Discuss what the unit fraction means and continue to emphasize that the number of equal parts the whole in segmented into is determined by the denominator. The numerator tells how many equal parts the fraction is away from zero based upon how the whole in segmented. Incorporate lesson 8.6 in terms of renaming the whole, but do not teach it explicitly.
- Lesson 8.7 – 8.9: Set model not tested. Save lesson until after state exam. Remove related items from End-of-Unit Exam.