Format
1. The program begins in the Math Lab with Professor Raab receiving a gift that is part of a whole collection.
2. Students generate a number line to keep track of Professor Raab's Collection.
3. Part 1 of the Fraction Hero video is presented. The pizza eating contest with Pizza Pirate leaves us with a question to answer: How can Fraction Hero's 5 slices be greater than Pizza Pirate's 6 slices?
4. Students model possible configurations for how the large pizzas were sliced.
5. Students create number lines to envision the slices consumed as part of the whole pie.
6. The two number lines are compared, and instances of Equivalent Fractions are identified on the number lines.
7. The fractions consumed are compared to one-half.
8. Students use multiple number lines to prove Fraction Hero has won the contest.
9. The second part of the Fraction Hero video is shown, resolving, reinforcing, and wrapping up the learning.
10. An informal assessment "Fraction Wars" game show is played comparing fractions.
Objectives
Among the learning objectives are:
Recognize and Show That Equivalent Fractions Refer to the Same Point on the Number Line (Lesson 21)
Generate Simple Equivalent Fractions by Using Visual Fraction Models (E.g., Fraction Strips) and the Number Line (Lesson 22)
Explain Equivalence by Manipulating Units and Reasoning About Their Size (Lesson 27)
Compare Fractions with the Same Numerator Pictorially (Lesson 28)
Compare Fractions with the Same Numerator Using <, >, or = and use a Model to Reason About Their Size (Lesson 29)
Standards Alignment
State Standards
Standards Alignment (Grade 3) — Part 3
National / Common Core (Grade 3)
CCSS.Math.Content.3.NF.2
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
CCSS.Math.Content.3.NF.3
Explain equivalence of fractions and compare fractions by reasoning about their relative size (using number line, distance, etc.).
CCSS.Math.Content.3.NF.3.d
Compare two fractions with different numerators and different denominators (e.g. 2/5vs. 3/7), by reasoning about their size.
________________________________________
New York State — Next Generation Mathematics Learning Standards (Grade 3)
New York’s standards for Grade 3 emphasize fractional understanding with denominators 2, 3, 4, 6, and 8, placing fractions on number lines, identifying equivalence, and comparing fractions.
NY-3.NF.2
Place fractions (unit and non-unit) on number line diagrams between 0 and 1 (and beyond for improper fractions).
NY-3.NF.3
Recognize and generate equivalent fractions
Compare fractions by reasoning about their sizes (especially when denominators are the same or when they can be related by equivalence)
Use number line reasoning and distance from 0 as a basis for comparison
________________________________________
Connections to This Program (Aligned to NYS 3rd Grade)
During Part 3, students will:
Extend fraction placement on the number line beyond just simple fractions to more complex ones (including possibly improper fractions)
Use visual models (e.g. fraction strips, region models, number line models) to map fractions to exact points
Recognize and generate equivalent fractions (for example, show that 4/8=1/2) and use equivalence for reasoning
Compare fractions that have different numerators and denominators by reasoning about their positions on a number line
Use distance from 0 as a way to reason about which fraction is larger
Engage in tasks or challenges where students must reason or infer using their number line and equivalence strategies
Reinforce connections among visual models, numeric notation, and spatial (number line) reasoning