mathematical thinking

Learning about Place Value

Children begin to learn about place value from the time they are very young and they continue to make sense of our base ten number system through middle school. They use what they understand about numbers and place value to solve math problems. Young children will count by 1’s to solve simple addition and subtraction problems. Middle school students solve problems with decimals which requires them to understand that decimals are fractions whose denominator is a power of ten.

Place value tray with items to help children build, label and represent quantities.

Learners can feel frustrated when math problems require an understanding of number that they have not yet attained. This is similar to asking children to read and comprehend a text that is beyond their current reading level or one that reflects a topic they know little about. When we observe how children solve a math problem we can gain a glimpse into their developing number sense and find the concepts that they are still working to understand.

For example, a child might be able to count 110 objects but when asked to record the amount the child might write, 10010 or 1010. Many of the mistakes children make are common as they develop their number sense. Through repeated experiences counting, representing numbers, solving math problems and discussing their ideas children can develop a strong number sense.

Vocabulary cards, place value dice, felt numbers and base ten blocks

Place value is defined as, “the numerical value that a digit has by virtue of its position in a number”. Place value is made up of many smaller ideas and concepts about number that children need to put together to fully understand it. Most learners benefit from having explicit lessons related to place value followed by opportunities to practice new skills and solve problems.

Learners with language impairments or learning disabilities benefit from instruction that is individualized and explicit because they have difficulty processing information, organizing it, forming abstract ideas, storing and/or recalling information, and/or expressing their ideas. Some students also have fine and gross motor difficulties that make writing cumbersome so they benefit from using materials to visualize and solve math problems. We can help students develop a strong number sense by approaching place value through a series of small lessons so we can guided learners through the ways numbers can be written, represented and manipulated.

A ten frame is used to organize mini-erasers and helps to represent addition problems.
Rolling a die to count and add to 100.

Before students use the base ten blocks and the place value dice, we first use a variety of counters, snap cubes and Unifix cubes to solve word problems and represent numbers. Once students can count by 10s and 1’s and can easily represent and visualize numbers through 100 we begin to use the base ten blocks to work with quantities beyond 100.

The Place Value Tray

The place value tray contains the following items:

  • Vocabulary cards
  • Base Ten Blocks
  • Place Value Dice
  • Place Value Chips
  • Felt numbers

Place Value Lessons and Activities:

  • Introduce the materials and the vocabulary
  • Identify the base ten blocks and the quantities they represent
  • Use the felt numbers to label and name quantities.
  • Use the base ten blocks to represent given numbers from 100-1000
  • Use place value die to write and add numbers in expanded form, 500+30+7= 537.
  • Use the place value dice or chips to write numbers in expanded notation, (5×100) + (3×10) + (7×1) = 537 (Middle school students learn scientific notation: 5.37 x 10^2)
  • Use the place value dice or chips to practice addition by rolling twice or creating two numbers with the chips.
  • Use the base ten block to model and visualize computation and word problems.
  • The base ten blocks can also be used to visualize decimals when the 10×10 square is used to represent 1. The green bars become tenths and the yellow cubes hundredth.

Resources

The following teachers and educators have more information relating to place value ideas and number sense.

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