Patterns+and+Algebra

|| QT Elements Generates, describes and records number patterns using a variety of strategies and completes simple number sentences by calculating missing values. ** Indicators: **Students: * Generate, describe and record number patterns using a variety of strategies. * Build number relationships by relating multiplication and division facts to at least 10 x 10. * Complete simple number sentences by calculating the value of a missing value. || ** Main Idea- Identify and describe patterns when counting forwards / backwards by 3,4,6,7,8 & 9 **  Students are given the numbers 3, 6,9,12. As a class the pattern is continued. Option is there to continue as far as you like. Have the students work backwards as well. The same is then done for the numbers 4,6,7,8 and 9. This information can be recorded in their books. Discuss with the students the strategies they can use for adding the numbers. For e.g. When going up by 3, they might add 2 and then another 1. Or when adding 6, they might add 5 and then add another 1.  Game: Have the students sit or stand in a circle. Using the numbers 3, 4,6,7,8 or 9 have the students go up by the chosen number. For e.g. 1st Child says 4, 2nd Child says 8 and so on. If a child gets a number wrong then they are out. The last one left standing / sitting is the winner. Record the highest number that you get to for each number for future reference and re-visit the game throughout the week or in later weeks. ||  ||  ** Main Idea- Finding a higher term in a number pattern given the first five terms. **  <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">The students are given the first 5 numbers of a certain number. For e.g. 4, 8,12,16,20 Now ask the students to * Find the 7th no? 4 x 7=28 or Find the 10th no? 4 x 10=40 Show through these and other examples the link to multiplication. Emphasise not having to write out every number to get it. For example: to find the 11th number of a pattern beginning with 3 and going up by 3, you would calculate 3 x 11 which equals 33. Discuss with the students the term ‘Rule’ and have them write what the rule would be. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Look at the patterns for 3,6,7,8 & 9. These would have been studied in the previous lesson. Have the students record a number of examples in their books, ensuring that they write the rule for them. These examples could be numbers that are going up or down. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Extension: Have the students begin with a different starting point and then calculate the higher term. For example: 5, 8,11,14,17 Find the 7th no or the 10th number? Remind the students to include the rule for each. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Extra- Worksheets provided if required / needed for further work and / or reference for types of questions. || =      = || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Main Idea- Building number relationships by relating multiplication facts to 10 x 10. ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Explain to the students that in this activity the = sign is to mean ** ‘the same as’ ** rather than finding the actual answer. For e.g. 4 x 3 = 6 x 2 Discuss with the students what the actual answer is (as they will need to know it) and have them come up with any others for 4 x 3- They will come up with 1 x 12. Do some other examples as a class. For e.g. 4 x 5 = 2 x 10 (Some may say 1 x 20) <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Discuss the concept of ‘factors’ of a number. After doing a few examples as a class (if needed) have the students find some other equivalent number relationships. For those students who may require it, (or if decide to do as a whole class with a large tables chart) give the students a tables chart to help them look for equivalent number relationships. Have the students record the number relationships in their books and discuss their findings. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Extra- A4 Tables Chart provided || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">  || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Main Idea- Relating Multiplication and Division Facts  ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Have the students come up with various Multiplication facts that can be written on the board / chart. For e.g. 3 x 6 = 18, 5 x 4 =20, 7 x 9 =63 Ask the students to suggest ways that these fact families can be changed to include the division symbol. Explain that multiplication and division are inverse operations. For e.g. 3 x 7 = 21 is related to 21 divided by 3 = 7 <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Introduce the fact triangles and discuss the information displayed in each. Have the triangles displayed while students complete their own fact triangles. You may begin with providing them with one number and then they complete the triangle. For e.g. Give them 24 and they find 2 and 12 or 3 and 8. To reinforce the relationship between the multiplication and division facts have them write in their books, 2 x 12=24, 12 x 2 =24, 24 divided by 2 =12, 24 divided by 12 =2 <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Alternatively ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">For those students who struggle with their tables knowledge have them create fact triangles using addition and subtraction facts. See the Addition / Subtraction Fact triangles and have them write the families in their books. For e.g. 8 + 9 = 17, 17 -9 =8 and so on. Have the students create their own fact triangles in the blank ones provided. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Worksheets- Multiplication/Division fact triangles, Addition / Subtraction fact triangles, Blank fact triangles || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">  || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Main Idea- Complete number sentences by calculating the value of a missing number ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Explain to the students that in this lesson they will be using different strategies to find the value of a missing number. Give the students a question such as 5 +? = 13 Remind the students about the previous lesson with the fact triangles and discuss how the question could be solved. You are looking for the students to come up with 13-5=? The missing value then being worked out as 8. As a class do some other examples where you begin with a subtraction question first. For e.g. 20 - ? = 12 Have the students see that this question can be done as 20-12=? Or 12 +? = 2  <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Have the students go through the same process but this time with multiplication and division. For e.g. 28 =? x 7 This is the same as doing 28 divided by 7 =? or saying 7 x? = 28 You may like to have tables charts on hand for those who need it or the Fact triangles used from previous lesson. Do various questions for the students to attempt in their books. <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Extension **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Some students could be given more open ended type questions. For e.g. 5 +? + @ = 20 What can ? and @ equal <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">or <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">2 x ? x @= 18 What do / can ? and @ equal? || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">
 * ** <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">Term 1, Week: **
 * <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">1  ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">2   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">3   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">4   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">5   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">6   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">7   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">8    ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">9    ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">10   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 14pt;">11   ||
 * <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">DK  ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">DU   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">PK   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">HOT   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">M   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">SC   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">EQC   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">E    ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">HE    ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">SS   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">SSR   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">SD   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">BK   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">CK   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">KI   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">I   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">C   ||  <span style="font-family: 'Century Gothic','sans-serif'; font-size: 10pt; line-height: 150%;">N   ||
 * ** <span style="font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Outcome: **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 9pt;"> PAS 2.1
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 1 **  || = __<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt; text-decoration: none; textunderline: none;">Register <span style="font-family: 'Century Gothic','sans-serif';"> __ = ||
 * <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">**Number Patterns**
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 2 **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">   || = __<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt; text-decoration: none; textunderline: none;">Register  __ = ||
 * <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">**Number Patterns**
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 3 **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">   || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Register  ||
 * ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Number Relationships **
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 4 **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">   || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Register  ||
 * ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Number Relationships **
 * ** <span style="font-family: 'Century Gothic','sans-serif';">Lesson 5 **<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">   || <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Register  ||
 * ** <span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 9pt;">Number Relationships **