# squares have roots - lesson plan by steph777

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Concepts: Square roots and the structure of the integers Description of activity: The activity segment reinforces the geometric interpretation of the square root of a number n as the length of the side of a square with area n and investigates the distribution of the square numbers in the integers. Anticipatory set: What is a square number? What is a square root? What kinds of patterns can we find in the integers? Materials: Some sort of blocks or tokens that the students can arrange into squares. State standards: NO 1.7.6 Recognize subsets of the real number system, NO 3.7.5 Represent and solve problem situations using square roots, A4.7.3 Interpret and write a rule for a two operation function table. Prerequisite skills: Students should be proficient with integer arithmetic, but that‟s really about all. Key Questions: What is the definition of a square? What is the only property that distinguishes one square from another? Can numbers that are not square have square roots? Management and organization suggestions: This lesson gets a little abstract towards the end, so it is absolutely imperative that you keep the children engaged. Ask them for their opinions frequently. Include them in the discovery process. Procedure: Begin by asking students for the definition of a square. They often immediately say “a shape with four sides” or “a shape with four corners”, but usually have to stop and think before giving the full definition as a figure with four equal sides and four right angles. If you can, draw an example on the board of a shape that isn‟t a square but that does satisfy their incomplete definitions. For example, if they define the square just to be a shape with four right angles, draw a rectangle on the board (a shape with four right angles that is not a square). This bit helps illustrate the importance of good definitions, and can be used to introduce the idea that the search for good definitions underpins a large portion of research mathematics. Now that they have a firm definition of the square, ask them what information one needs to know about a given square in order to be able to produce it. All plane figures are made up of only two components, lines and angles, each of which has only two properties, number present and measure. Our definition prescribes the number of sides and angles and also the measure of the angles. The only thing about a square we can choose is the length of the sides. Thus, if one knows the length of a square‟s side, one knows everything there is to know about the square. So if we have only a line segment of a given length we can “grow” it into a square, so it actually makes sense to call the side