Place-Value DevelopmentPlace-Value Development

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

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

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.

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.

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.

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.

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.”

Equivalent Groupings• Unitary – count-by-ones

• Base-ten – groups-of-ten

• Equivalent – nonstandard base-ten(see Fig 12.1, p. 179)

The Role of Counting in Constructing Base-Ten Ideas1. Counting by ones

2. Counting by groups and singles

3. Counting by tens and ones

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

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

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.

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.

Relational UnderstandingBase-Ten Concepts

Standard & Equivalent Groupings To Physically Represent

Quantities

Oral NamesStandard: thirty-two

Base-Ten: Three tens and two

Written Names

32

Counting•By Ones

•By Groups & Singles•By Tens & Ones

Models for Place Value1. Groupable Models – counters & cups, interlocking

cubes, bundles of sticks. Anything children can physically group.

2. Pregrouped or Trading Models – such as base-ten singles, ten strips, and hundreds “flats.” Children cannot actually take them apart or put them together.

Grouping Activities1. Groups of 10 (p. 185)

1. Bags of counters2. Placed at stations3. Children count contents4. Record findings5. Group as 10’s, if possible6. Record groupings7. Switch groups

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

Other Fun Activities• Base-Ten Riddles (p. 188)

• Counting Rows of 10 (p. 188)