Primary Type: Formative Assessment
Status: Published
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Resource ID#: 118446
Decompose Two-Digit Numbers
Students are asked to decompose two-digit numbers in three different ways.
Subject(s): Mathematics
Grade Level(s): 1
Intended Audience: Educators
Keywords: MFAS, decompose, tens, ones
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DecomposeTwoDigitNumbers_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually, in small groups, or in a whole-group setting. If the task is given in a whole-group setting, the teacher should ask each
student to explain his or her thinking and strategy.
1. The teacher provides the student with the Decompose Two-Digit Numbers worksheet and reads the directions aloud.
2. The teacher should also provide the student with base ten blocks; however, it is not necessary for the student to use the blocks if he or she can complete the task
without them.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand place value.
Examples of Student Work at this Level
The student writes numbers on the blanks of the worksheet without regard to the meaning of the ones and tens places.
page 1 of 4 Questions Eliciting Thinking
In the number 27, what digit is in the ones place? What digit is in the tens place?
What does the digit two represent? What is the value of the two? How many tens are in the number 27? What about in the number 56?
Instructional Implications
Provide instruction on place value, specifically the tens and ones places. For example, have the student first decompose numbers in the range 10 – 19 into 10 ones and
some more ones using base ten blocks. Then guide the student to exchange the 10 ones for a ten rod by physically joining the 10 ones together to form a new 10.
Explicitly relate the model (e.g., one ten rod and three ones) to the way numbers are written (e.g., as 13). Transition the student to modeling larger two-digit numbers
again relating the models to the way the numbers are written. Use the terminology of place value when explaining the relationship between the model of the number and
the numeral (e.g., if there are three ten rods and two ones in the model then there is a three in the tens place and a two in the ones place in the numeral).
Another approach is to use ten frames to model numbers with counters. For example, ask the student to organize a group of 23 counters on ten frames so that as many
ten frames as possible are filled. Relate a completed ten frame to the unit 10. Then relate the numbers of tens and ones to the way the number is written.
Provide the student with daily opportunities to count objects in amounts greater than 10. After counting, guide the student to be explicit about the number of groups of
10 and the number of objects remaining.
Play a game of composing tens and ones in which you show the student a model of a two-digit number using base ten blocks (e.g., four ten rods and three ones) for only
two seconds. Ask the student what number was represented and to explain how he or she determined this. Repeat with new amounts.
Eventually, provide different models of the same number (e.g., model 32 with three ten rods and two ones as well as two ten rods and 12 ones). Explain why both ways
correctly model the number although only one way corresponds to how the number is written.
Consider using the MFAS task How Many Tens and Ones? (1.NBT.2.2).
Moving Forward
Misconception/Error
The student is able to determine only one way to decompose each of the three numbers.
Examples of Student Work at this Level
The student successfully determines that there are seven ones and two tens in the number 27. However, he or she cannot determine another way to decompose the
number 27 into tens and ones.
Questions Eliciting Thinking
Let’s look at the number 25. How many tens and ones are in the number 25? Suppose I want to decompose 25 into some tens and 15 ones. How many tens would I
need?
How would you model 24 using base ten blocks? Could you model 24 using only ones cubes?
Instructional Implications
Provide different models of the same number using base ten blocks (e.g., model 32 with three ten rods and two ones as well as two ten rods and 12 ones). Explain why
both ways correctly model the number although only one way corresponds to how the number is written. Model all of the ways that a number such as 56 can be
decomposed into tens and ones using base ten blocks. Then present the student with another two-digit number and ask him or her to decompose it in at least three
different ways. Encourage the student to record the decompositions with drawings or in words.
Almost There
Misconception/Error
The student is unable to find three different ways to decompose each number.
Examples of Student Work at this Level
The student correctly finds at least two ways to decompose some or all of the two-digit numbers but is unable to find three different ways to decompose all three two-digit
numbers.
Questions Eliciting Thinking
I see you found that there are seven ones and two tens and also 17 ones and one ten in the number 27. How many tens would there be if we have 27 ones? Is
there another way we could decompose the number 27?
Instructional Implications
Provide additional opportunities for the student to decompose two-digit numbers in multiple ways. Encourage the student to find all of the ways a number can be
decomposed into tens and ones. Then have the student explain his or her strategy for decomposing to a student at the Moving Forward level.
Encourage the student to examine and describe the relationship between decomposition models (e.g., using base-ten blocks) and equations of the form 27 = 20 + 7.
Got It
page 2 of 4 Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student successfully finds three different ways to decompose each of the numbers. The student may decompose the numbers in the following ways:
27
seven ones and two tens
17 ones and one ten
27 ones
56
six ones and five tens
16 ones and four tens
26 ones and three tens
36 ones and two tens
46 ones and one ten
56 ones
83
three ones and eight tens
13 ones and seven tens
23 ones and six tens
33 ones and five tens
43 ones and four tens
53 ones and three tens
63 ones and two tens
73 ones and one ten
83 ones
Questions Eliciting Thinking
Could you find even more ways to decompose any of these numbers into tens and ones?
How many tens are in the number 115? What about in the number 230?
Instructional Implications
Ask the student to find all of the ways to decompose each of the given numbers into tens and ones. Encourage the student to be systematic in both the strategy used
and in recording the decompositions.
Ask the student to find the sum of a two-digit and a multiple of 10 such as 53 + 10 or 36 + 30.
Allow the student to apply his or her understanding of tens and ones to solve problems such as 23 + 41. Guide the student to add by combining the tens (i.e., 20 + 40),
combining the ones (i.e., 3 + 1), and finally combining the tens and ones to complete the sum.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Decompose Two-Digit Numbers worksheet
Base ten blocks
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Understand that the two digits of a two-digit number represent amounts of tens and ones.
a. 10 can be thought of as a bundle of ten ones — called a “ten.”
page 3 of 4 MAFS.1.NBT.2.2:
b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine
ones.
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens
(and 0 ones).
d. Decompose two-digit numbers in multiple ways (e.g., 64 can be decomposed into 6 tens and 4 ones or into 5 tens
and 14 ones).
page 4 of 4