This unit offers the opportunity to develop students` knowledge in the field of factors, multiples and divisibility rules. Work on the station will last approximately three days. Each day, you will meet the entire class at an appropriate time to discuss the results of their work. Check that they were able to answer all the questions correctly and understand what they did. Hardware for these stations can be found on Copymasters 5 and 6. The children were invited to answer various questions that were asked of the copy masters. On the first of these copymasters we have a different shape number – this time the hexagon. So the numbers are 6, 12, 18, 24. The general rule is that the number of samples is 6 times greater than the number of terms. On the second of these copymasters, we look at a model that increases several times, which is a fraction. Here are the numbers 8, 12, 18, 27, 81/2, . In general, the number of previous terms should be multiplied by 3/2. However, this trend can be continued in other ways.
Students could 8, 12, 18, 26, . Here the numbers increase by 4, 6, 8, . So, in this case, it is easier to look at the repetition rule. Finding the general rule is quite difficult. Gather the class and discuss some of the models they created. Focus on the general rule of these models. Try to get all students to put into words the general rule. Ask them to do so. If number models involve multiples of numbers, this can be used to develop knowledge of basic facts, especially factors, multiples, and divisibility rules. This week, we looked at trends that have to do with multiples of numbers. We looked at the general rule and the repeat rule for models.
The general rule is a rule that gives you the number of squares in a building when you specify the number of buildings in order. The repeat rule tells you how to go from the number of squares in one building to the number of squares in the next building. You may need to remind students that if they are stuck, a good way to continue is to create a board. Pay special attention to the general rule present in each model. Tell them to be careful, because sometimes there is more than one model to find. The general rule tells us about the value of any number in the pattern. So for model 2, 4, 6, 8, . The general rule is double the number of the term.
In this unit, we focus on models with a relatively simple general rule. It is usually a multiple of a number or the power (square or cube) of a number. In this work, pay close attention to the ability to put the general rule into words. It shouldn`t be too difficult. In the first case, the numbers are 4, 8, 12, 16, . and therefore the general rule is four times the number of the term. In the second case, the numbers are 5, 10, 15, 20, . and therefore the general rule is five times the number of the term. Hardware for these stations can be found on Copymasters 7 and 8.
Again, students answer questions that are about copymasters. Again, focus on the general rule. In these templates, there are at least two rules that you can find here. One is easier to manage with the general rule and the other is easier with the repeat rule. Encourage them to find both rules. However, it can be difficult to describe the second of these rules. In Copymaster 7, the patterns are 1, 2, 4, 8, 16, . and 1, 2, 4, 7, 11, . The first model is the powers of 2 (as a general rule: the number of patterns is increased to 2 at the power of the term minus one). In the second model, the difference between consecutive terms is model 1, 2, 3, 4, . The increase between two terms is the integer of the first of the two terms (the repetition rule).
In Copymaster 8, the patterns are 1, 3, 9, 27, 81, . and 1, 3, 9, 19, 33, . The first model is the powers of 3 (as a general rule: the number of patterns is increased to 3 at the power of the term minus one). In the second model, the difference between consecutive terms is model 2, 6, 10, 14, . The increase between two terms starts at 2 and increases by 4 more between each pair of consecutive terms (the repeat rule). This second rule is much more difficult to describe. In this unit, for the first time, we pay special attention to the general rule of a model. We look at odd and even numbers as well as multiples of small numbers. We also look at squares and cubes of numbers and see that it is possible to make more than one pattern from the same three initial sterms. Models are an important part of mathematics.
They are one of the general themes of the subject. It is always valuable to be able to recognize the relationship between two things to predict what will happen and understand how they relate to each other. Ask your student if they can continue with the following model. Say what the general rule and repetition rule are. Can you solve this problem together? The models also provide an introduction to real algebra, as the rules of simple models can first be discovered in words and then written using algebraic notation. The main rule that we focus on here is the general rule, although the repetition rule is necessary in subsequent tasks. On the last day, ask the class to create their own drawings. You need to focus on creating a building model that has a simple general rule (such as shape patterns) and a building that has two possible patterns. You must specify the general rule or recurrence rule, whichever is simpler.
We start with an activity that should be simple for most students. Then we look at another one where the pattern is clear, but can be more difficult to express accurately in words. In addition to the students putting the patterns into words here, we also look at some basic characteristics of even and odd numbers. These properties are that each even number plus each even number is even; Each odd number plus each odd number is even; and any even number plus any odd number is odd. What about all the numbers in that order? Students now work at different stations and continue different pattern numbers. The models examined here are the powers of a number and “figurative” numbers (such as square numbers, pentagonal numbers, and hexagonal numbers). Will the number be 156 in that order? (or, if applicable, another number) Some links in the Figure It Out series that you might find useful are: Log in or sign up to create plans from your planning area that include this resource. Can you see an easy way to check if the numbers will be in that order? The material for these stations is on Copymasters 3 and 4.Students must answer the questions asked about copymasters. .