Lesson plan

Subtraction Towers

Help build your students subtraction skills by finding the unknown! This lesson will help your students understand the relationship between addition and subtraction, as students build towers to find unknown addends.
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Students will be able to subtract by finding the unknown addend within a problem.

(5 minutes)
  • Present a short scenario to the class. Tell the students that you were asked by a famous toy company to design some towers for a model city.
  • Show the class a tower of six interlocking cubes. While holding the tower, tell the class that the current tower is too short and that the toy company said it must have a total of 11 cubes.
  • To gain the class's attention, count out 11 cubes and purposely add them to the six cubes. Show the new tower to the class.
  • Ask students if they think the toy company would add this tower to their toy model. Ask students to give an explanation on why or why not.
(10 minutes)
  • Holding up the tower of linking cubes, explain that the current tower has 17 cubes and therefore will not work for the model. Disassemble to show the original tower of 6 cubes.
  • Write 11 – 6 = _____ on the board. Tell the class that one way to solve this problem is by finding the difference between both numbers, or by using subtraction. Explain that the 11 represents the total needed in the tower for it to be used as a model, and 6 are how many we started off with.
  • Pointing to the equation on the board, ask students if you would be able to show this equation using your current tower. Have students explain why or why not.
  • Tell students that addition can be used to find the difference between the two numbers.
  • Write 6 + ____ = 11 on the board. Label and explain that the 6 represents the number of cubes in the tower already and 11 represents the total number of cubes needed.
  • Circle the empty space on 6 + ____ = 11. Label and explain that this area is known as the unknown addend.
  • Tell students that finding the unknown addend can help them solve a related subtraction problem. Show that 6 + ____ = 11 and 11 - 6 = ____ are related.
  • Model adding additional cubes to the tower of 6 and stopping at 11. Ask students how many cubes were added to make a total of 11. Tell students that 5 is the unknown addend and write it on the board. Therefore, 6 + 5 = 11 and 11 – 6 = 5.
(10 minutes)
  • Give each student 20 linking cubes.
  • Write 8 + ____ = 15 on the board. Ask students to use their cubes to solve for the unknown addend. Model building a tower of 8 cubes and adding on to reach a total of 15 cubes. Count aloud so your class can hear the unknown addend.
  • Repeat with ____ + 5 = 12, 9 + ____ = 12, and ____ + 3 = 11.
  • Next, tell the class that based on their new knowledge, they will solve for 17 – 9 = ___ with their linking cubes.
  • Remind students that the subtraction problem can be rewritten as the addition equation, 9 + ___ = 17. Allow time for student learning, and then model how to solve.
  • Repeat using 13 – 8 and 10 – 4.
(15 minutes)
  • Have students divide a blank sheet of paper into three equal parts.
  • Ask students to copy the following problems at the top of their first column. 9 + ___ = 12 and 12 - ___ = 9.
  • Tell students to create a visual model of the problem in two different colors. For example, the 9 may be drawn as 9 yellow cubes and 3 red cubes may be on top to show a total of 12 cubes.
  • Students will solve and provide a visual model for: 6 + ___ = 13 and 13 - ___ =6 and ___ + 4 = 11 and 11 -4 = ___ in the final two columns.
  • Monitor the classroom to check for student understanding.
  • Enrichment: Students can create their own unknown addend equations for classmates by either providing a written equation or creating a visual model for students, to allow them to write a matching equation.
  • Support: Provide small group instruction to assist in subtraction by modeling with linking cubes. Have students practice rewriting subtraction problems as an addition problem, and then solve for the unknown addend.
(10 minutes)
  • Visual observations will be made throughout the lesson, as students are working with their linking cubes to solve for subtraction.
(10 minutes)
  • Write a subtraction review equation on the board. Ask students to solve using their linking cubes.
  • Have students share how they solved the equation.
  • Ask students to share what they learned in today’s math lesson.

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