Activating Prior Knowledge in Fractions (Grades 4-6)



Activating Prior Knowledge in Fractions (Grades 4-6)

Facilitator’s Notes

The purpose of this workshop is

✓ to make grade 7 teachers aware of the curriculum around fractions in grades 4-6.

✓ to activate prior knowledge in an engaging manner.

✓ to use formative assessment to inform teaching.

✓ to examine samples of student work to inform instruction.

Materials:

✓ P-3 curriculum (1 copy)

✓ 4-6curriculum (found in binders)

✓ Grade specific sheet to record main idea on fractions

✓ Chart paper and markers

✓ Number Cubes

✓ Colored pencils or crayons

✓ Handouts as indicated below

1. 9a.m. - 10 a.m.(60 min.)

Put teachers into groups of four. Give one group the P-3 curriculum and the Fraction Activity for Grades P to 3 (03_P-3_fract_activity.doc). Assign the other groups each a specific grade (4, 5, or 6). Give them the appropriate sheet (04_gr4_fract_activity.doc) or (05_gr5_fract_activity.doc) or (06_gr6_fract_activity.doc) to record their work. They can use the curriculum guide in their binder. Have each group examine their specific grade to determine what work is done on fractions and record their observations on the sheet. If you have more than one group per grade, have each group work individually first and them come together to compare their work. Have them then record their work on chart paper and post. Each grade (P-3, 4, 5, 6) can then briefly present the main ideas of fraction development for their grade(s). An answer key is provided for each grade (03A-P-3 Fractions Answers etc.).

Explain to teachers that the purpose of this activity is to make Grade 7 teachers aware of what students are doing with fractions prior to grade 7.

NOTE: You may wish to do one outcome together first to model what teachers should be looking for. For example you may want everyone to look at Grade 4

A1 Identify and model fractions and mixed numbers

and discuss together what the main ideas are. Also there will probably be discussion around the fact that outcomes in strands such as probability and data management have been identified as dealing with fractions and why that is so.

NOTE: The worksheets and answers are to be printed off on legal size paper.

2. 10-10:20 a.m. (20 min.)

Pass out the sheet on 2 ¼ (07_think-pair-share_2_one_fourth.doc). Have teachers do a think-pair-share on everything they know about 2 ¼ and record on the sheet.

Discuss with all teachers.

Two versions (07A) & (07B) have been included. Choose the one you prefer.

Explain to teachers that the purpose of this activity is a quick way to activate students’ prior knowledge about fractions. When the class discussion takes place most of the language around fractions should come out. (numerator, denominator, mixed number, proper fraction etc. )

If teachers hear a student mention that they see “three numbers”, that is a sign of conceptual misunderstanding. Students are not seeing the ¼ as a number and will need some direct instruction on the meaning of fractions. Knowing how fractions are developed in grades 4-6 will help teachers plan the instruction for this student.

Nutrition Break – 20 min.

3. 10:40a.m. -11:30 a.m. (50min)

Have teachers play the game “More than One-Half”.

Print off the file (08A_more_than_one_half.doc) for yourself and read through the directions prior to doing this activity. Print off enough observation charts for each teacher (08B_more_than_one_half_obs_sheet.doc) but do not pass out.

Provide each pair of teachers with the materials listed in file 08A and go over the directions for the game. Have teachers play the game for about 15 – 20 minutes. As the game is being played circulate about the room, modeling how to use the observation sheet and asking the questions that are on the first page of file 08A under the heading –“Questions to ask when observing students”.

Before starting the discussion of this activity, give everyone a copy of the observation chart.

Explain to teachers that the purpose of this activity is to activate prior knowledge about fractions in an engaging and fun way. Ask the teachers to discuss what knowledge about fractions, grades 4-6, will come out of this activity.

Using the observation chart makes it a formative assessment task. Discuss how to use the chart for teacher observation and peer evaluation. (The observation chart may be used in two ways. The entire chart may be used for teacher observation or part of the chart may be used for peer evaluation (columns 1-3) and the rest of the chart (columns 4-5) for teacher observation.)

NOTE: An extra file of the playing sheets has been included (08C_more_than_one_half_move_circles.doc) in Word. Teachers can manipulate these circles if they want to make changes.

4. 11:30 - noon (20- 25 min.)

Pass out to teachers the 5 exit cards (09A_exit_cards_equiv_fractions.doc). Discuss the purpose of an exit card as another example of formative assessment. (See Mathematics 7: A Teacher Resource, page 106). Have teachers work on these cards for about 10min, then discuss their purpose and use. The cards have varying levels of complexity. (For day 2, teachers could bring in copies of student’s work for these exit cards and discuss)

Exit card templates (09B_sample_exit_card_templates.doc) have been included on the website.

Lunch 12:00-1:00

5. 1- 1:30 p.m.(20- 30 min.) Student Work on Equivalent Fractions

Context for this activity: After teaching a lesson on equivalent fractions, the grade 5 classroom teacher gave her students an exit card which they completed and passed in. Here are 4 samples of student work. (10_student_work_equiv_fractions.pdf)

Pass out copies of the 4 samples of student work to each teacher.

a) Ask the teachers to work in pairs to examine all 4 samples and decide if any student or students exhibit any misconceptions about equivalent fractions. Allow time for group discussion. (Answer –Student D talks about “make a smaller fraction into a bigger fraction”. This could indicate a misunderstanding about equivalent fractions

Concept: Two fractions are equivalent if they are representations for the same amount or quantity – if they are the same number.

b) Ask the teachers - Can we assume the rest of the students understand the concept of equivalent fractions? Discuss

c) Ask the teachers to identify a question they could ask to further probe student thinking in these four samples?

6. 1:30 – 2 p.m. (20-30 min) Have teachers examine the Get Ready for Chapter 2 in Mathematics 7: Focus on Understanding. The message is that teachers should not do the entire GR at once but do the parts of the GR as they are needed to teach the chapter. Have teachers

✓ Identify which parts of the GR are needed for each section of the book.

✓ Compare the GR to what they did at the start of the workshop to see if it reflects the important understandings students need from Grades 4-6. Discuss.

✓ Decide if teachers would like to have students do some questions in the GR and bring these in on Day 2 to discuss.

NOTE: Three extra practice sheets on equivalent fractions have been included (11_proportional_practice_gr7_support.pdf). They are from Proportional Reasoning, part of the AIMs Activities Grade 6-9 books. The explanation of the correct developmental progression starts on page 22 in that book. This book should be in all junior high schools.

NOTE: Teachers could be asked how they could use what they learned about formative assessment and ways to activate prior knowledge in this workshop to help them prepare other topics throughout the school year.

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