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Math Final
Look back to PowerPoints, Check for Understandings, and Textbook
| Question | Answer |
|---|---|
| Retrieval (developmental phases for learning basic facts) | Facts are instantly retrieved from memory |
| Face value (5 levels of place value understanding) | Starting to connect that position affects digit value, but they are still inconsistent and often need manipulatives or drawings |
| Full understanding (5 levels of place value understanding) | Fully understands how the number system works |
| Factors | Parts of a multiplication problem (ex. 8 and 7 in "8 x 7") |
| Single numeral (5 levels of place value understanding) | Only sees the number as the whole Ex. sees 437 as "four hundred thirty-seven" |
| Aera model (fractions) | Fractions are shown as part of a shape (think a shaded in portion of a "pie") |
| 5 levels of place value understanding | 1. Single numeral 2. Position names 3. Face value 4. Transition to place value 5. Full understanding |
| Regrouping | Trading between place values while keeping the total value the same (ex. 437 -> 43 tens and 7 ones) |
| Unitary grouping stage | "I see numbers as single ones" |
| What to do when teaching students basic facts | - Work on facts overtime - Use technology - Make fact practice enjoyable - Focus on self-improvement |
| Reasoning (developmental phases for learning basic facts) | "I can figure it out using what I know" |
| Non-proportional models | The size of each piece does not match the value (symbolic, not visual) (ex. dice, money, place-value chips) |
| Make 10 (compensation strategy) | You have the problem 6 + 5. To solve it, you take 4 from the 5 (making the 5 a 1) to make 6 a 10. 10 + 1 = 11 |
| Developmental phases for learning basic facts (counting, reasoning, retrieval) | Counting, reasoning, retrieval |
| Measurement model (fractions) | Number lines; fractions are shown as distance or movement/steps along a path |
| Partitioning | Breaking a number into parts based on place value (ex. 437 -> 400 + 30 + 7) |
| Equivalent grouping stage | "I know groups can stand for the same amount"; Fluently works with groups of 10, can count using nonstandard base-ten groupings |
| Partial sums algorithm (addition) | Writing the numbers in expanded form, then solving the problem. |
| What not to do when teaching students basic facts | - Use public comparisons - Expect automaticity - Proceed through facts in order from 0-9 - Use long timed tests |
| What are basic facts? | Involve all combinations of single-digit addends and factors (if 2 of the 3 number in the sequence are single digits, it is a basic fact) |
| Decomposition algorithm | Standard subtraction algorithm |
| Base-ten grouping stage | "I fully understand the place value system"; recognizes 10 as a unit, counts by groups of tens and ones |
| Partial products algorithm (multiplication) | Multiplying the numbers in the 10s place, each 10 by the numbers in the 1s place, then multiply the numbers in the 1s place. The products from this are called partial products. Add the partial products up to get your final product. |
| Addends | Parts of an addition problem (ex. 2 and 4 in "4 + 2") |
| Product | Answer to a multiplication problem |
| Sum | Answer to an addition problem |
| Prevents overly regrouping | Prevents overly regrouping |
| Algorithm | The process of solving a math problem (are useless if students don't understand them) |
| Magnitude | The size or amount of a number |
| Automaticity | The quick recall of facts |
| Think outside the box | Everything in forward, everything in reverse. Multiple ways to solve problems |
| Counting | "I have to count it out" Students DO NOT have facts memorized yet |
| Face value | Sees each digit at just its face value Ex. For example, in 437 they think: 4 = 4 3 = 3 7 = 7 They may say: “4 + 3 + 7 = 14, so 437 is 14.” |
| Position names | Knows place names, not the values Ex. "The 4 is in the hundreds place” but not understand that it means 400 |
| Iterating | Sectioning a shape into equal-sized parts is called partitioning Ex. Understanding that 3/4 is comprised of three parts called fourths |
| Ladder algorithm | Division - down |
| Chimney algorithm | Division - up |
| Multiplicative model (fractions) | A fraction of something Fractions are seen as groups of groups "What is half of 10?" |
| Pre-grouped base-ten models | Stripes and squares, ten-frame cards |
| Proportional | The size of each piece matches its value Ex. base-ten blocks, rods, fraction strip |
| Groupable base-ten models | counters and cups, rods |
Created by:
Haleigh14