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Chapter
Addition and Subtraction Concepts
| Total and Parts |
| Counting On and Counting Back |
| Joining Sets |
| Number Line Proficiency |
| Take Away Subtraction |
| Missing Part Subtraction |
| Comparison Subtraction |
| Adding and Subtracting Tens |
| Adding Doubles and Near Doubles |
| Fact Families—Addition and Subtraction |
| Partial Sums |
| Partial Differences |
| Near Tens for Addition and Subtraction |
| Equal Differences |
Total and Parts
What is the Total and Parts Concept?
The total and parts concept encourages students to see the parts of whole numbers. By focusing on total and parts, students learn about addition and subtraction. They begin to understand that the parts make the total and that the total is made of parts. The beauty of teaching total and parts is that we can present early addition and subtract concepts at the same time rather than teaching these operations separately.
CCSS
Operations and Algebraic Thinking
Number and Operations in Base Ten
Formative Assessment
To find out if a student understands total and parts, ask the student to describe the total and parts of the following trains of cubes:
Notice if the student provides the total and parts in the descriptions. If the student is successful, try different parts and larger totals. Identify which totals and parts the students know and which they do not know.
Successful Strategies
Interchange addition and subtraction ideas as students work with total and parts. Encourage students to read aloud and record the parts and total. Using different colors to show the parts often helps students better identify the parts. Grouping the parts is also beneficial. As students gain comfort with total and parts, begin working with more than two parts of each total.
Math Words to Use
total, whole, parts, addition, subtraction
Questions at Different Levels of Cognitive Demand
Recall: What is the total?
Comprehension: How do the parts relate to the total?
Application: How could you show different parts of the total?
Analysis: How could you compare the parts of more than one total?
Evaluation: What helps you understand the parts of a total?
Synthesis: What if the total had many parts?
Rigorous Problem Solving with the Concept of Total and Parts 1
The teacher gave each student 12 stickers.
David placed 3 stickers on his folder, 5 stickers on his agenda, and some stickers on the class chart.
Sandy placed 8 stickers on her folder, some stickers on her agenda, and 3 stickers on the class chart.
Eugene placed some stickers on his folder, 4 stickers on his agenda, and 2 stickers on the class chart.
Part A
Which equations represent the students’ stickers?
| o | 3 + 5 = 8 |
| o | 3 + 5 + 2 + 2 = 12 |
| o | 3 + 5 + 4 = 12 |
| o | 8 + 3 = 11 |
| o | 8 + 1 + 3 = 12 |
| o | 6 + 4 + 2 = 12 |
| o | 4 + 2 = 6 |
| o | 6 + 6 = 12 |
| o | 7 + 3 + 2 = 12 |
Part B
- How many stickers were placed on the class chart?
- How many stickers were placed on the agendas?
- How many stickers were placed on the folders?
Justify your answers with equations.
Rigorous ...
