Student Actions

Teacher Actions

• Develop deep and conceptual understanding as students explore place value.  Formal  work with place value begins as students describe two-digit numbers in terms of tens and ones; i.e. 37 can be represented as 37 ones or as 3 tens and 7 ones or as 2 tens and 17 ones.

• Represent mathematical ideas and develop strategies for problem solving as students model two digit numbers using a variety of concrete sets of objects, as well as pictures of sets, hundreds charts, number grids, base 10 blocks, bundles of sticks, pocket charts, etc...

• Communicate mathematical ideas to one another through examples, demonstrations, models, drawing, and logical arguments when solving tasks about place value while using appropriate vocabulary such as tens, ones, regrouping, before, after, one more, one less, base ten blocks, etc.. 

• Elicit and use evidence of student thinking as she helps students organize, record, represent, and communicate their thinking with place value with a variety of tools such as hundreds charts, number grids, base ten blocks, etc.

• Implement tasks that promote reasoning and problem solving about place value as they encourage students to find a variety of solutions to problems during whole group instruction, small group instruction, and games. For example, teachers can model and discuss ways to make 37 with 3 tens and 7 ones, 2 tens and 17 ones, 1 ten and 27 ones, or 37 ones.

• Pose purposeful questions to create meaningful discourse when using place value. Such as, How many ways can you make _____?, What number comes before ______? What number comes after ____? Can you think of another way to show that number?  

Key Understandings

Misconceptions

• Identify place value, such as ones and tens.

• Understand that the position of a digit gives the value;

• Use base-ten language.

• Identify relative position and magnitude of whole numbers and of ordinal and cardinal numbers;

• Identify whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;

• Make connections with number words and numerals to the quantities they represent, using various physical models and representations. 

• There is only one way to represent a whole number in terms of tens and ones. For example, the number 75 can only be represented using 7 tens and 5 ones. Seventy-five can also be represented using 75 ones, 5 tens and 25 ones, 2 tens and 55 ones, etc. There are many ways to represent a number.

• Of 4 bundles of ten as 4 single units instead of 4 "tens" or 40 ones.

• They have to decompose groups of ten into ten ones in order to determine how many.