1. Formative Assessment Lessons Map.mathshell.org

2. Mathematics Assessment Project Classroom Challenges Lessons that support teachers in formative assessment – both reveal and develop students’ understanding of key mathematical ideas and concepts Grades 6, 7, 8, High School Aligned with Common Core Content Standards and Standards for Mathematical Practice Categories – Problem Solving – Concept Development

3. FAL Structure Pre-assessment: Individual assessment task designed to reveal current understanding. Teacher reviews responses to assess understandings/misunderstandings and creates questions for students to consider when improving their work. Students work in small groups on a collaborative task Whole-group lesson/discussion Post-assessment and/or revision of pre- assessment

4. Let’s Try One … Fractions, Decimals and Percents Complete the pre-assessment task individually

5. Collaborative Group Work Form groups of two or three Take turns to fill in the missing decimals and percents. Leave the blank card alone for now.

6. Decimals and Percents (pink)

7. Working Together continued – ordering cards 1.Place a number card where you think it goes on the table, from smallest on the left to largest on the right. 2.Explain your thinking. 3.The other members of your group must check and challenge your explanation if they disagree. 4.Continue until you have placed all the cards in order. 5.Check that you all agree about the order. Move any cards you need to, until everyone in the group is happy with the order.

8. Working Together 2 – Area Cards Take turns to: 1.Match each area card to a decimals/percents card. 2.Create a new card or fill in spaces on cards until all the cards have a match. 3.Explain your thinking to your group. The other members of your group must check and challenge your explanation if they disagree. 4.Place your cards in order, from smallest on the left to largest on the right. Check that you all agree about the order. Move any cards you need to, until you are all happy with the order.

9. Areas (yellow)

10. Working Together 3 – Card Sets: Fractions and Scales Use the same procedure to add these cards to your arrangements Continue to complete blank cards so each number is represented in each of the four ways: decimal/percent, area, fraction, scale Note: During this process, teacher’s role is to note different student approaches to the task and to support student problem solving.

11. Fractions (orange)

12. Scales (blue)

13. Making Posters Once students have had a chance to match/order all 4 sets of cards, give them a piece of poster paper and a glue stick and ask them to glue their cards in the agreed order. Students should include justifications for their matches and be encouraged to include details of any changes they made during the activity.

14. Whole-Class Discussion Discuss what has been learned and explore the different orders in which the cards have been placed. Focus for discussion - What methods have students used? What misconceptions were surfaced?

15. Fractions, Decimals and Percents (revisited) Return original pre-assessment task to students. (If teacher has not written questions on individual student work, questions may be written on board.) Directions to students: Look at your original responses and the questions written on your paper (or board). Think about what you have learned. Now look at the new task sheet, use what you have learned to answer these questions.