Fractions Representations with Set Area Models  OttawaCarleton DSB KNAER Lesson (Gr 6)
MO 10 min A 35 min C/D 15 min 60 min 
Learning Goals Students will:

Materials 4 of each of the following baggies of pattern blocks

Minds On... 
Whole Group Mind Map Ask students what they know about fractions. Create a mind map using their input and organized to align with your preplanned mind map for the unit. 
Using the unit outline to create the mind map ahead of time will allow for the strategic placement of student ideas. Using a different colour each day will highlight the learning that students are gaining through the unit. 
Action! 
Small Group Activity Provide each group with one baggie. Ask small groups to generate as many fractions as they can with the blocks. Thinking can be provoked and extended with the following types of questions:
Whole Class Sharing Ask small groups to each share a fraction and the corresponding representation. Consider having students either use pattern block paper to record their answers, sharing their work using a document camera, or having pattern blocks cloned on an interactive whiteboard for the sharing of their solutions. Record the following information as it arises from the student talk:
Some questions which may be useful:

Some examples:
Set model...

Consolidate/ Debrief 
Whole Group Discussion Review the terminology with students, making explicit connections to their responses. Allow them to ask any further questions that they may still have. Highlight that fractions have multiple meanings and show the multiple meanings that are demonstrated in their responses. 

Home Activity or Further Classroom Consolidation Select one fraction and represent it using each of the different meanings discussed today. 
BLM 1.1 Teacher Notes
What we anticipated students to say:
Drawing  Fractional Representation  Drawing  Fractional Representation 

3 red hexagons
7 hexagons total
(partwhole; area or set**) 
1 green hexagon
5 hexagons total
(partwhole; area or set**) 

2 blue hexagons
6 hexagons total
(partwhole; area or set**) 
3 red hexagons
4 hexagons total
(partwhole; area or set**) 

2 blue hexagons
4 pieces total
(partwhole; set**) 
1 green hexagon
4 hexagons total
(partwhole; area or set**) 

6 rhombus pieces
10 pieces total
(partwhole; set**) 
6 triangle pieces
10 pieces total
(partwhole; set**) 

6 trapezoid pieces
10 pieces total
(partwhole; set**) 
4 hexagon pieces
10 pieces total
(partwhole; set**) 

4 hexagon pieces
10 pieces total
(partwhole; set**) 
4 hexagon pieces
10 pieces total
(partwhole; set**) 
** Students may be seeing these are sets of hexagons or areas of figures. It is important to uncover their thinking by asking probing questions.
What the students said:
Drawing  Fractional Representation  Drawing  Fractional Representation 

^{1}⁄_{2} One trapezoid is ^{1}⁄_{2} of the hexagon. (partwhole; area ) 
^{1}⁄_{6} One triangle is ^{1}⁄_{6} of the hexagon. (partwhole; area ) 

^{1}⁄_{3} One trapezoid is ^{1}⁄_{3} of the hexagon. (partwhole; area ) 
^{1}⁄_{3} One triangle is ^{1}⁄_{3} of the trapezoid. (partwhole; area ) 

^{2}⁄_{3} One rhombus is ^{2}⁄_{3} of the trapezoid. (partwhole; area ) 
^{1}⁄_{2} One triangle is ^{1}⁄_{2} of the rhombus. (partwhole; area ) 

^{6}⁄_{4} There are 6 rhombus pieces for 4 hexagons. (partpart; set ) 
^{6}⁄_{4} There are 6 triangle pieces for 4 hexagons. (partpart; set ) 

^{6}⁄_{4} There are 6 trapezoid pieces for 4 hexagons. (partpart; set ) 
^{4}⁄_{6} There are 4 hexagon pieces for 6 rhombuses. (partpart; set ) 

^{4}⁄_{6} There are 4 hexagon pieces for 6 trapezoids. (partpart; set ) 
^{4}⁄_{6} There are 4 hexagon pieces for 6 triangles. (partpart; set ) 

^{2}⁄_{2} 2 trapezoids cover the whole hexagon (partwhole; area ) 
^{6}⁄_{6} 6 triangles cover the whole hexagon (partwhole; area ) 

^{3}⁄_{3} 3 rhombuses cover the whole hexagon (partwhole; area ) 
^{2}⁄_{2} 1 of the 6 vertices of the hexagon are circled. (partwhole; set ) 