# Page History

## Key

• This line was removed.
• Formatting was changed.

...

1. Symbols - Discussion about what symbols are; writing messages or "stories" with symbols; interpreting symbols.
2. Comparisons - Comparisons and comparison operators: =, ≠, <, >.
3. Comparisons and Attributes - Work with comparisons and comparison operators (=, ≠, <, >).
4. Comparing Heights I - Students compare the heights of two children, measure, compare, and represent one's own height in relation to a peer's height, and focus on the differences between heights.
5. Comparing Discrete Quantities - Students compare amounts of tokens and unknown amounts of discrete quantities. In both cases they are guided to adopt line segments to represent discrete amounts and the differences between them. They are also asked to discuss composition of measures: "the difference plus the smaller amount is equal to the larger amount" and, "the larger amount minus the difference is equal to the smaller amount".
6. Heights as Functions - In this class children will work on the functional representation of two unknown heights and on the composition of the shorter height plus the difference between the heights as equal to the second height.
7. Candy Boxes - This class centers on the possible amounts of candies two children, John and Maria, have. They each have the same, unspecified number of candies inside their own candy box. John has, in addition, one extra candy and Maria has three extra candies. What are the possible total candies they might have?
8. Part-Whole Relations - This class follows the discussion from the Candy Boxes I class. The challenge is to work with a visual representation of the relationships among the various quantities in the candy box problem and to relate the visual and numerical information contained in visual diagram(s) to verbal descriptions and to algorithms for finding unknown values.
9. Number Line - Locations - Students place themselves at points on the number line. Main contexts: stairs, age, money, temperature, and pure number.
10. Number Line Shortcuts - The students will use a number line to see how two addends or subtrahends are equivalent to one single change once combined.
11. Partial and Total Changes - Students learn that two partial changes are equivalent to a single total change. On the number line, this corresponds to the idea of a shortcut. Three notations are emphasized: words, number lines with hopping arrows, and numerical expressions.
12. Multiple Number Lines - Students continue to learn that two partial changes that start at different points on the number line are equivalent. At the end, they will work with notation for variables (N + 5 - 3 or N + 2).
13. N-Number Line I - Students work with the table they built in the previous class for multiple number lines, focusing on the notation for variables (N + 5 - 3 or N + 2).
14. N-Number Line II - Students use the N-Number line to make generalizations about an unknown amount of money in a piggy bank.
15. Piggy Banks - The whole lesson revolves around a multipart story problem involving changes in two quantities over several days of a week. The initial quantities are equal yet unknown. Then transformations are applied to the quantities. Students are asked to compare the quantities throughout the week even though only their relative relationship can be determined.
16. Guess my Rule - Tables - Two children create secret rules for transforming input numbers. The teacher uses a doubling rule.
17. Guess my Rule - Tables - Two children create secret rules for transforming input numbers. The teacher uses a doubling rule.