Differentiating Mathematics Instruction Session 3 Assessment for Learning

Differentiating Mathematics Instruction Session 3: Assessment for Learning: Diagnostic Adapted from Dr. Marian Small’s presentation August, 2008

Goals for Session 3 • Develop knowledge about a variety of diagnostic assessment strategies • Connecting importance of diagnostic assessment data to inform differentiated learning instruction • Practise creating diagnostic assessments

Session 2 Follow-up Exit Card - Questions or concerns Share response with a partner: How does considering big ideas help in differentiating learning?

Integer Task • Choose 4 integers so that the product < quotient < sum < difference • Is this a task for assessment of, for or as learning? • What range of students would this task be appropriate for?

Diagnostic Information Meaningful diagnosis leads to successful differentiation responding appropriately to challenge or scaffold students’ learning Pre-assessment activities include: tasks, interviews, quizzes, graffiti exercises, concept maps, anticipation guides, games, …

Grade 8 Integers The focus for teaching integers in Grade 8 is multiplication and division and problems involving all four operations, considering order of operations.

Task (sample) 1. Figure out what you think each of these products and quotients might be and why. a) 3 x (-4) b) (-4) x 3 c) (-3) x (4) d) (-12) ÷ 3 e) (-12) ÷ (-3) f) 12 ÷ (-3) 2. Choose 4 integers so that the product < quotient < sum < difference M Small

Interview (sample) 1. Name three integers between +2 and -8. How would you represent them? 2. Which is greater: their sum or their difference? How do you know? 3. The sum of a positive and negative integer is -4. What could the integers be? What situation might this describe? 4. The difference between two negative integers is +8. What could the integers be? Use a number line or counters to show me why.

Paper-and-pencil (sample) • Insert the appropriate inequality signs: -2 [ ] -4 , -8 [ ] 10 , 4 [ ] -1 • Fill in the blanks: -2 + 4 = [ ] -10 – 2 = [ ] + -4 = 8 etc. • Explain why the sum of two negatives has to be negative.

Paper-and-pencil (sample) • Choose 2 positive and 2 negative integers. • Show to compare them, add them, and subtract them. • Which of the tasks was easiest for you to do? Why?

Graffiti Exercise (sample) Questions to which groups respond: • When do you ever use integers? • How are integers like whole numbers? • How are integers different from whole numbers?

Anticipation Guide (sample) Do you agree or disagree? Be ready to explain. • You can predict the sign of the product of two integers if you know the sign of the sum. • The sign of the quotient of two integers has to be the same as the sign of the product. • You can either multiply first or add first when working with integers, e. g. [(-2) x (-3)] + 4 = (-2) x [(-3) + 4] M Small

Your turn … Choose one of these topics: • Grade 8 fractions • Grade 9 linear relations • Grade 10 quadratics Create two diagnostic assessments for collecting information on your topic.

Diagnostic Strategies q Task q Interview q Paper-and-pencil items q Graffiti exercise q Anticipation guide q Game

Home Activity In your reflection journal, write about: • something you learned that you think might be useful in your teaching. • something with which you disagree with or have doubts about. • the role diagnostic assessment plays in differentiating learning and planning for instruction.