Fractions

Basic fractional concepts

Operationsü

Division of fractions (1)

Understanding division of fractions (1.a)

Lesson Abstract: Before students begin using algorithms for the division of fractions, they should have a conceptual understanding.

Tier 2

Students who are at risk for mathematics failure

Intervention plan

Overall goal:

The mastery of fractions so as to be able to meet adequately the requirements in the general education classroom (tier 1)

Lesson Goals:

ð Division of a fraction by a whole number

ð Division of a fraction by a fraction

Learning outcomes

ð Using area models to demonstrate a simple division of fractions (e.g. 1/2:2, 2:1/4)

ð Describe and explain how they work

ð Solving simple problems.

Instructional Resources/Materials:

transparent measuring cups (or transparent plastic water bottles 3/4, 1, 3/2 & 2 liters), rectangles area fraction models

Explicit instruction (teaching model)

CRA (instructional strategy)

Critical content: concepts (division, Partitioning, equal shares), vocabulary terms (fraction language e.g. numerator, denominator), skills (partitioning with Area Models, understanding equivalent fractions).

Statement of the lesson’s goals and expectations: division of fractions/learning outcomes.

Introduced lesson with activating prior skills and knowledge (warm-up): starter activities with division word problems that include only whole numbers (both type: partitive and measurement). [28 euros to buy 7 tickets. How much does each ticket cost? / A serving is 3 cookies. How many servings can I make from 36 cookies?]

After the introduction of the lesson, the teacher starts applying the first phase of CRA strategy. Teacher using 1-liter bottle full of water asks students to empty their contents equally into two empty bottles (as shown in the figure below). Provide interaction via the use of appropriate questioning, immediate affirmative and corrective feedback. Then teacher demonstrate the activity and clarify the decision-making processes needed to complete the procedure in order to show students a model of proficient performance. As students share thinking that indicates they are beginning to understand the mathematical concept, there can be transit to representational phase. Finally, the mathematical symbols are used to represent the operation of division.

Guided and supported practice

“I have showed you how I solve two problems, I am going to have you try two yourself”, “show two different ways to model the solution for each problem”. [e.g. If you have 3 liters of milk, how many bottles holding 3 quarts each can you fill?]

Independent and cumulative practice (homework)

Students practice the skill or solve the problems without any assistance or prompts from the teacher