This unit provides an opportunity to focus on the strategies students use to solve digital problems. The matching patterns are all based on linear relationships. This means that the increase in the number of matches needed for the term “next” is a constant number added to the previous term. This is level 1; Linear sequences of matching patterns. ∴ The pattern of the letter T is 2n, where n = number of matches T can be formed by multiplying the number of sticks needed to form the letters by the variable n, where n is the number of letters. The models of the letters (a) T (b) Z (c) U (d) V (e) E (f) S (g) A require (a) 2n (b) 3n (c) 3n (d) 2n (e) 5n (f) 5n and (g) 6n respectively. Filling in the first three cells of the table is simply counting the number of matches needed to create the first three models. This week we looked at the models in mathematics that were created with matches We spent the first semester, the second semester, . the tenth mandate, .
and so on, trying to find a relationship between the number of matches and the number of the term. For example, we looked at this model with correspondences: relationships can be represented in several ways. The purpose of representations is to allow the prediction of other terms and the corresponding value of other variables in an increasing model. For example, representations can be used to determine the number of matches required to create the tenth term in the model. Important representations include: Ex 11.1, 1 Find the rule that specifies the number of matches required to create the following matching patterns. Use a variable to write the rule. (a) A pattern of the letter T like the letter T Make T using matches So, for the IT number for matches = 2 For 2T number for matches = 4 For the number 3T for matches = 6 So we write number of matches = 2n where n = number of T Ex 11.1, 1 Find the rule that indicates the number of matches, that are required to create the following matching patterns. Use a variable to write the rule. (b) Make a model of the letter Z as the letter Z Z with a correspondence So, for 1Z Number of matches = 3 For 2Z Number of matches = 6 For 3Z Number of matches = 9 So we write, number of matches = 3n, where n = number of Z. Ex 11.1, 1 Find the rule that specifies the number of matches required to create the following matching patterns.
Use a variable to write the rule. (c) A pattern of the letter U asLetter U Make U with matches So, for 1U Number of matches = 3 Similar for 2U Number of matches = 6 For 3U Number of matches = 9 So we write, number of matches = 3n, where n = number of U. Ex 11.1, 1 Find the rule that indicates the number of matches, that are required to create the following matching patterns. Use a variable to write the rule. (d) A sample of the letter V asletter V Creating V with matches So, for 1V Number of matches = 2 Similar for 2V, Number of matches = 4 For 4V, Number of matches = 6 So we write, number of matches = 2n, where n = number of V. Ex 11.1, 1 Find the rule indicating the number of matches required to perform the following matching patterns. Use a variable to write the rule. (e) A sample of the letter E as the letter E Make E with correspondences So, for an E Number of matches = 5 For 2E, number of matches = 10 For 3E, number of matches = 15 So we write, number of matches = 5n, where n = number of E. Example 11.1, 1 Find the rule that specifies the number of matches, that are required to create the following matching patterns. Use a variable to write the rule.
(f) An example of the letter S asEx 11.1, 1 Find the rule that specifies the number of matches required to create the following matching patterns. Use a variable to write the rule. (f) A pattern of the letter S asSo, For an S, Number of matches = 5 Similar, For 2S, Number of matches = 10 For 3S, Number of matches = 15 So we write, number of matches = 5n, where n = number of S. Ex 11.1, 1 Find the rule that specifies the number of matches required to create the following matching patterns. Use a variable to write the rule. (g) Make a model of the letter A as letter A A with correspondences So, for 1A, number of matches = 6 For 2A, number of matches = 12 For 3A, number of matches = 18 So we write number of matches = 6n where n = number of A (A) If we remove 1 match from each figure, then they make a multiple of 3, i.e. 3, 6, 9, 12, … The required equation = 3x + 1, where x is the number of squares. (B) If we remove 1 match from each figure, then they make a multiple of 2, i.e. 2, 4, 6, 8, .. The required equation = 2x + 1, where x is the number of triangles.
Vey-un has another way to calculate the number of matches for a pattern of 10 triangles. He wrote 10 x 3 – 9 and got the same number of matches as Kiri and Jamie, 21. We already know the rule for the pattern of the letters L, C and F. Some of the letters of Q.1 (data above) give us the same rule as that of L. What is it? Why is this happening? The context of this unit can be tailored to your students` interests and cultural backgrounds. Matches are an inexpensive and accessible resource, but may not be of interest to your students. You might be more interested in other thin objects such as leaves or lines on tapa (kapa) fabric. You can find growth patterns in the friezes on the buildings of the municipality. Be aware of learning opportunities that connect to your students` everyday experiences. Encourage students to think about linear models by focusing on the different strategies that can be used to calculate consecutive numbers in the model. For example, the pattern of the path of the triangle of 9 matches can be seen in different ways: 3 + 2 + 2 + 2 + 2 1 + 2 + 2 + 2 + 2 + 2 3 + 3 X 2 1 + 4 X 2 (A) Look at the following matching pattern of squares (see figure).
The squares are not separated. Two adjacent fields have a common match. Look at the patterns and find the rule that shows the number of matches versus the number of squares. (Note: If you remove the vertical stick at the end, you will get a pattern of Cs.) (B) The given figure gives a pattern of triangle correspondence. As in Exercise 11(A) above, you will find the general rule that specifies the number of matches in relation to the number of triangles. Note: All templates used in this unit are available in PowerPoint 1 for easy sharing with a data projector or similar. This unit builds the concept of a relationship with growth patterns created with matches. A relationship is a connection between the value of one variable (variable quantity) and another.
For matching models, the first variable is the term, i.e. the number of steps in the figure, for example term 5 is the fifth number in the growth model. The second variable is the number of matches needed to create the figure. (A) Number of matches required to create one = 2 ∴ number of matches required to create a pattern of letter T as = 2n (B) Number of matches required to create one = 3 ∴ number of matches required to create a pattern from the letter Z = 3n (C) number of matches, required to create a = 3 ∴ number of matches required to create a pattern from the letter U as = 3n (D) number of matches required to make one = 2 ∴ number of matches required to create a pattern from the letter V as = 2n (E). Number of matches required to create one = 5∴ number of matches required to create a pattern of letter E as = 5n (F) Number of matches required to create one = 5∴ number of matches required to create a pattern from the letter S = 5n (G) number of matches, required to create one = 6∴ number of matches required to create a pattern from the letter A as = 6n In this session, we will examine a simple pattern created by merging matches into a contiguous path of triangles. Radha draws a rangoli dot (a beautiful pattern of lines connecting the dots) with chalk powder. She has 9 points in a row. How many points will you get for r lines? How many points are there if there are 8 lines? If there are 10 lines? In the given model, two matches are used. ∴To create 1 such template, we need 2 matches. ∴To create 2 of these templates, we need 2×2=4 matches. ∴To create 3 such templates, we need 2×3=6 matches. The unit examines patterns created with matches and tiles.
The relationship between the number of the term of a model and the number of matches of that term is studied to find a general rule that can be expressed in different ways. You may have noticed the number of additional matches needed to create the next pattern in the sequence. It`s the same every time you change one model for the next. In this case, it`s 5. The ideas of the first three sessions will be expanded and strengthened in a broader context. This time, the problem gives a rule and the students find the model. For more details on developing representations for growth models, see pages 34-38 of Book 9: Teaching Number through Measurement, Geometry, Algebra, and Statistics.