1. 3-5 Math Best Practices workshop 2018
Please start reading the article “13 Rules that Expire”
Julia Stozub, Stephanie Cohen and Eileen Cass

2. Reading: 13 Rules That Expire
The authors describe math rules that expire as “tips and tricks that do not promote conceptual understanding, rules that “expire” later in students mathematical careers,or vocabulary that is not precise.” After reading the article discuss with a partner:
●Where do math rules that expire come from and why do students continue to learn/use them?
●Which rules, notations, or inappropriate math language do you use/have you used that have proven difficult to give up?

3. Meaning vs. Algorithm
The biggest problems created by teaching the steps of traditional algorithms are:
The focus is on individual digits, not on whole quantities and relationships among the quantities
Rely on memorizing rules without reasons can lead to common errors
The central goal is mastering a series of steps rather than understanding meaning and use of the mathematical operation

4. What is computational fluency?

5. Mathematical Tasks: A Critical Starting Point for Instruction
There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics. Lappan & Briars, 1995
… all tasks are not created equal - different tasks require different levels and kinds of student thinking. Stein, Smith, Henningsen, & Silver, 2000
If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level cognitively complex tasks. Stein & Lane, 1996.

7. Try out these problems!
A farmer has 22 cows and 8 chickens in his barn. How many legs are in the barn?
2. A farmer has a total of 30 animals in his barn. Some are cows and some are chickens. If the animals have 74 legs in all, how many chickens does the farmer have?
Discuss: Which problem has a higher cognitive demand? Why?

8. Why are fractions so important?

9. Fraction models

10. How do students develop fraction sense?
We must provide opportunities for students to explore a range of tasks with a variety of models/manipulatives that involve:
a) modeling fractional amounts and naming unit and non-unit fractions
b) performing concept-of-unit activities
c) generating equivalent fractions
d) comparing and ordering fractions

11. Common misconceptions

12. Common misconceptions

13. Van Hiele Model: Levels of geometric thinking

14. Van Hiele Model: Levels of geometric thinking

16. Which one doesn’t belong? Why?