Place value is such a fundamental concept, and it’s very difficult for kiddos to understand.
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Let’s think about the typical place value progression:
- Kindergarten: Understanding the meaning of numbers from 11-19. Double ten-frames are a great tool, as students see, for example, that 12 is a full ten-frame and 2 more. The ten-frames become a very visual representation of tens and ones.
- 1st Grade: Students explore 2-digit numbers and understand that the two digits represent quantities of tens and ones. Beginning with the ten-frames provides a familiar context for students. Full ten-frames represent the tens and “leftovers” represent the ones. Move from ten-frames to groupable objects. Early experiences with groupable objects might include taking a scoop of dried beans and putting the beans by groups of ten into small paper cups. Traditional base-10 blocks are too abstract for this age, but linking cubes joined into trains of ten are a great bridge toward the base-10 blocks, because they look similar. The advantage of the linking cubes is that they have to be physically joined to make a ten train, and they can be broken apart (Van de Walle).
- 2nd Grade: Begin with the linking cubes and transition to traditional base-10 blocks. Have students practice skip counting by tens and then counting on by ones. With a number built in front of them, have students explore hundred chart patterns (10 more than, 10 less than, 1 more than, 1 less than). As hundreds are introduced, practice the same patterns (100 more than, etc.) so students start to understand the patterns in our place value system. This is also an appropriate time to introduce the idea that numbers can be decomposed in more than one way. For example, thirty-four can be 3 tens and 4 ones, but it can also be 2 tens and 14 ones. This is the fundamental understanding behind subtraction with regrouping.
- 3rd Grade: STILL building numbers with base-10 blocks! Now students are understanding that the ones, tens, hundreds pattern repeats in each group of three numbers as they work with numbers to the hundred thousands.
- 4th Grade: At this point, it becomes difficult to use manipulatives to represent numbers, as students are working with numbers to the millions. Manipulatives do come into play, however, as students explore decimals. Using the same base-10 blocks they used to model whole numbers to now model decimals sends a powerful statement about the patterns in our place value system. Place value discs can also be used to model larger whole numbers and fractions.
- 5th Grade: Students should now really be able to use the patterns in the place value system to read any whole number, and they should be well on their way to the same understanding for decimals.