Getting Started Misconception/Error

The student does not understand the value of each digit in the number.

Examples of Student Work at this Level

The student is only able to state that each digit is the same in the number 777. The student does not know the value of each digit and says that they are each a “seven.”

Questions Eliciting Thinking

If you made the number 77 using base ten blocks, how many tens blocks would you need? How many ones?

What do you know about the ones, tens, and hundreds places?

The seven in the tens place here (point to the seven in the tens place) does not represent just seven. What do you think it could represent?

Instructional Implications

Provide the student with place value experiences and encourage the student to see numbers modeled with base ten blocks. Allow the student to represent given three-digit numbers using base ten blocks.

Provide the student with other examples. Model for the student how to determine the value of the digits and then to observe that the value of the digit to the left is ten times greater than the value of the digit to its right.

Have the student use base ten blocks to build numbers. Model for the student that 50 is 5 x 10. Build a set of five and repeat it ten times. Continue with 500. Build a set of 50 and repeat it 10 times. Then have the student model 70 and 700.

Moving Forward Misconception/Error

The student needs significant prompting to articulate how the value of the digits change.

Examples of Student Work at this Level

The student knows that each seven represents seven, 70, and 700 but struggles to state that each digit is ten times greater than the digit to its right. The student needs much prompting and lots of time to determine how the digits compare.

Questions Eliciting Thinking

The seven in the hundreds place here (point to the seven in the hundreds place) does not represent just seven. What do you think it represents?

How much greater is the seven in the tens place than the seven in the ones place?

If this is the tens place, and this is the ones place, how much greater do you think the seven in the tens place must be? What about the seven in the hundreds place?

Instructional Implications

Provide place value experiences for the student using base ten blocks.

Allow the student to represent given three-digit numbers using base ten blocks.

Show the student a hundred block and a ten block. Ask the student how many of the ten blocks make the hundred block. If the student is able to articulate this, try it with two hundred blocks and two ten blocks. Ask guiding questions to help the student observe that there are ten times as many in the two hundreds as there are in the two tens.

Encourage the student to use base ten blocks to model the numbers 1000, 100, and 10. Help the student to determine patterns within the numbers and the models. Then provide the student with the numbers 263 and 632. Have the student model the numbers and then compare the value of the digit three in each of the numbers.

Consider using MFAS task Family Vacations (4.NBT.1.1).

Almost There Misconception/Error

The student needs prompting to describe the relationship between the seven in the tens and hundreds place.

Examples of Student Work at this Level

The student can state the value of each of the sevens in the number 777, and knows that 70 is ten times greater than seven. However, the student needs prompting to determine that the seven in the hundreds place is also ten times greater than the seven in the tens place.

Questions Eliciting Thinking

How much greater is 100 than 10? Can that help you determine how much greater 700 is than the 70?

What do you know about the ones and tens place? How many ones are in a ten? How many tens are in a hundred?

Instructional Implications

Encourage the student to explain his or her thinking to other students in the class.

Provide opportunities for the student to talk and write about the value of each digit in a number and how its value compares to the value of the same digit in a place to its left.

Got It Misconception/Error

The student provides complete and correct responses to all components of the task.

Examples of Student Work at this Level

The student states that the digit seven in the tens place equals 70. He or she also states that there are seven tens in the number 70.

The student states the value of each of the digits in the number 777 and is able to describe how much greater the value of each digit is when compared to the digit to its right.

Questions Eliciting Thinking

Do you think this pattern continues?

What if you went to the ten thousands place? Would it be ten times greater than the thousands place?

Can you say why this is always true?

What is the relationship between the numbers seven and 700? How many times greater is 700 than seven?

Instructional Implications

Consider using MFAS task Family Vacations (4.NBT.1.1).

Encourage the student to generalize the pattern observed in place value as one moves to the left within a number. Allow the student to explain what happens to place value as one moves to the right within a number [i.e., that each digit to the right is one-tenth as large as the same digit to its left (5.NBT.1.1)].