Place-Value Development

1. Place-Value Development

2. Pre-Base-Ten Concepts • Developmentally appropriate for 1st/2nd grade • If asked to count out 53 tiles, can easily do so • If asked “what number is ten more?”, usually have to start at 53 and count on 10 more. • If asked “what number is ten less?” is more problematic

3. Unitary Thought • Children’s pre-base-ten understanding is unitary • There is no automatic grouping of ten • Children rely on unitary counts to understand quantities

4. The Hundreds Chart • The hundreds chart is an important tool in the development of place-value concept. • K-2 classrooms should have a hundreds chart prominently displayed.

5. Patterns on the Hundreds Chart • Have children work in pairs to find patterns on the hundreds chart. Let them verbally express ideas. Have children explain patterns found by others to be sure all understand ideas.

6. Skip-Count Patterns • Whole class skip count by twos, threes, fours, etc. Then have students record a specific skip-count pattern on their own copy of the hundreds chart by coloring in each number they count. Every skip count produces an interesting pattern on the chart.

7. Missing Numbers • Give students a hundreds chart on which some of the numbers have been removed. Their task is to replace the missing numbers in the chart. Begin with random missing numbers, and continue with sequences of several numbers from 3-4 different rows. Lastly, challenge students to complete an empty chart all on their own.

8. More & Less on the Hundreds Chart • Circle a particular missing number on a hundreds chart. Students are to fill in the designated number and its “neighbors.” See the relationship – numbers to the left and right or either “one more” or “one less.” Numbers above and below are either “ten more” or “ten less.”

9. Equivalent Groupings • Unitary – count-by-ones • Base-ten – groups-of-ten • Equivalent – nonstandard base-ten (see Fig 12.1, p. 179)

10. The Role of Counting in Constructing Base-Ten Ideas • Counting by ones • Counting by groups and singles • Counting by tens and ones

11. Counting by Ones • This is the method children develop on their own • A count by ones is the only way they are able to “tell how many” • To compare three groups, all groups must be counted by ones

12. Counting by groups and singles • Counting groups of ten – although not ready to construct the thought of counting by tens • For example: “One, two three, four, five bunches of 10, and one, two, three singles.” • Does not tell directly how many items there are

13. Counting by tens and ones • “Ten, twenty, thirty, forty, fifty, fifty-one, fifty-two, fifty-three.” • The count ends by saying the number that is there.

14. Base-ten Language • 5 tens and 3 • 5 tens and 3 ones • 5 groups of 10 and 3 leftovers • 5 tens and 3 singles • Etc.

15. Relational Understanding Base-Ten Concepts Standard & Equivalent Groupings To Physically Represent Quantities Counting • By Ones • By Groups & Singles • By Tens & Ones Oral Names Standard: thirty-two Base-Ten: Three tens and two Written Names 32

16. Models for Place Value • Groupable Models – counters & cups, interlocking cubes, bundles of sticks. Anything children can physically group. • Pregrouped or Trading Models – such as base-ten singles, ten strips, and hundreds “flats.” Children cannot actually take them apart or put them together.

17. Grouping Activities • Groups of 10 (p. 185) • Bags of counters • Placed at stations • Children count contents • Record findings • Group as 10’s, if possible • Record groupings • Switch groups

18. Grouping Activities • Fill the Tens (p. 185) • Each child has a record sheet showing ten frames • Give instructions to get “x” amount of counters • Fill up the ten frames by drawing dots • Record number of tens and number of extras

19. Other Fun Activities • Base-Ten Riddles (p. 188) • Counting Rows of 10 (p. 188)