Use the Common Core State Standards for Mathematics (p. 88), K-5 Progressions for Operations and Algebraic Thinking (p. 6-21), Mathematics Learning in Early Chilldhood (p. 32-35) to answer the following.

1. What are key traits of the following problem types?

- add to - action oriented
- take from - action oriented
- put together / take apart (PTTA) - action may be physical or conceptual; sometimes called "part-part-whole"
- compare - no action; "more" or "less"

2. Look at the table below consisting of problem types and unknowns. If the type and unknown go together, place a "check" (√).

unknowns | add to | take from | put together / take apart |
compare |
---|---|---|---|---|

addend | √ | |||

bigger | √ | |||

both addends | √ | |||

change | √ | √ | ||

difference | √ | |||

result | √ | √ | ||

smaller | √ | |||

start | √ | √ | ||

total | √ |

3. In the above table, write an equation for each unknown for "add to" and "take from" problem types.

4. What grade level (K, 1, 2) are the problem types and unknowns introduced? mastered? See K-5 Progressions for Operations and Algebraic Thinking (p. 6-21).

unknowns | add to | take from | put together / take apart |
compare |
---|---|---|---|---|

addend | XXXXX | XXXXX | 1st | XXXXX |

bigger | XXXXX | XXXXX | XXXXX | 1st→2nd |

both addends | XXXXX | XXXXX | K | XXXXX |

change | 1st | 1st | XXXXX | XXXXX |

difference | XXXXX | XXXXX | XXXXX | 1st |

result | K | K | XXXXX | XXXXX |

smaller | XXXXX | XXXXX | XXXXX | 1st→2nd |

start | 1st→2nd | 1st→2nd | XXXXX | XXXXX |

total | XXXXX | XXXXX | K | XXXXX |

5. Based on grade level expectations, what are types and unknowns are easiest for children? most difficult? Why?

Vocabulary:

**CCSS problem types:**add to, take from, put together / take apart (PTTA), compare**CCSS unknowns:**addend, bigger, both addends, change, difference, result, smaller, start, total