Illuminations: Comparing Connecting Cubes

# Comparing Connecting Cubes

## Counting Back and Counting On

 In this lesson, students model subtraction with connecting cubes while the teacher reads to them from counting books. Then children make a train of connecting cubes and write in vertical and horizontal format the differences suggested by adding to and subtracting from the train one cube at a time. Finally, they record, in written form, a train showing one cube being taken away and record the difference in vertical and horizontal format.

### Learning Objectives

 Students will: count to 10 model numbers to 10 write and recognize numerals to 10 subtract 1 from numbers to 10 record differences in vertical and in horizontal format

### Materials

 Connecting cubes in two or more colors One More, One Less Activity Sheet Bibliography of Children's Counting Books

### Questions for Students

 How many connecting cubes are in this train? (Show a train with ten connecting cubes.) On this train? (Show a train with nine connecting cubes.) Which train has more? How many more? Which train has less? How many less? [10; 9; the one with 10 has 1 more; the one with 9 has 1 less.] What number sentence would show that you started with eight connecting cubes and compared it with a train with nine cubes? One with ten cubes? [9 - 8 = 1; 10 - 8 = 2.] What is alike between the two ways we recorded the comparisons? What was different? [They both have the same numbers, they are just displayed differently.] How could you help a younger child model 7 – 1? [Student responses may vary.] Can you write an equation to show that you compared a train of eight connecting cubes with a train with seven cubes? [8 - 7 = 1.] What does the minus sign mean? [It means to subtract.]

### Assessment Options

 Documenting information about students’ understanding and skills throughout the unit can help you focus on individual needs and strengths and foster appropriate additional learning opportunities. A recording sheet, Class Notes, is provided. You may find the information you record useful when discussing children’s progress toward learning targets.

### Extensions

 Put several “counting back” books from the Bibliography of Children's Counting Books (or other sources) in a center along with paper, crayons, and connecting cubes. These items will encourage children to continue to read books with a subtraction theme and to practice recording subtraction examples.

### Teacher Reflection

 Were the books you chose well received? What others might you use? Which children met all the objectives of this lesson? What extension activities would be appropriate for those children? Which children did not meet the objectives of this lesson? What instructional experiences do they need next? What mathematical ideas need clarification? Were all students able to model the numbers? What adjustments would you make the next time that you teach this lesson?

### NCTM Standards and Expectations

 Number & Operations Pre-K-2Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers. Use multiple models to develop initial understandings of place value and the base-ten number system. Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations. Understand the effects of adding and subtracting whole numbers. Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators. Develop and use strategies for whole-number computations, with a focus on addition and subtraction. Develop fluency with basic number combinations for addition and subtraction.
 This lesson prepared by Grace M. Burton.

1 period

### NCTM Resources

 More and Better Mathematics for All Students
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