Multiplication+Division+Patterns+Algebra

Term 3
 * **Outcome: ** NS2.3 Uses mental and informal written strategies for multiplication and division.
 * Indicators: **
 * Learn table facts 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
 * Use arrays and groups to link multiplication and division facts up to 10x10
 * Recall multiplication facts up to 10x10 using a variety of mental strategies
 * Record remainders to division problems
 * Determine factors for a given number using table facts
 * List multiples for a given number
 * Find square numbers using concrete materials and diagrams
 * Outcome: **PAS2.1: Generates, describes and records number patterns using a variety of strategies and completes simple number sentences by calculating missing values.
 * Indicators: **
 * Transform a division calculation into a multiplication problem
 * Build multiplication facts to at least 5x10 by recognising and describing patterns eg. 4x6=6x4
 * <span style="font-family: 'Century Gothic','sans-serif'; font-size: 12px;">Complete number sentences involving one operation by calculating missing values ||

<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Ensure that students understand the term “arrays.” Demonstrate an array using a set of 15 counters. Ask students how the array can be interpreted 3 rows of 5 = 15 or 5 rows of 3 = 15. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">* If students are not familiar with the commutative property of multiplication complete Activity Sheet 1- Students roll dice and draw arrays to match, focussing on making matching times tables sums. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*If students are familiar with this concept discuss how the rows of the array can be separated. Demonstrate by physically pulling the rows away from each other. Discuss with students how division undoes multiplication. With students, record the appropriate division sums. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Students complete Activity Sheet 2 – Groups/Arrays Dice Roll with a partner. Students record appropriate multiplication and division sums for each dice roll. Discuss patterns when recording sums. For example, the biggest number is always the answer in a multiplication problem and it is the first number when recording a division problem. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Students then complete Activity Sheet 3 independently, writing multiplication and division sums to match the arrays and then choosing an appropriate number sentence to demonstrate their understanding of a written division problem. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Arrays can also be investigated using All Staff- Student Resources, Nelson Maths NMLO 3. ||  ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Lesson 1 ** ||  <span style="font-family: 'Century Gothic','sans-serif';">Register   ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Focus: Working with arrays to demonstrate the relationship between multiplication and division **

<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Discuss with students patterns that were introduced in previous lesson. Revise and discuss how one multiplication or division sum can help in creating other related multiplication and division sums. Give students one sum to begin with. For example 2x6=12. Have students then attempt to record the other related multiplication and division sums (6x2=12, 12-2=12. 12-6=12). Students complete further examples in books with the starting sum provided by the teacher. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Students complete Activity Sheet 4 where they need to match multiplication and division sums together and use these sums to calculate the missing values of some number sentences. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">* Discuss with students how our knowledge of known multiplication and division facts can also help us to solve further multiplication and division facts. Demonstrate to students using simple times tables. For example if 2x2=4, 3x2 means that we add another group of 2 so this would equal 6. Apply this to other more difficult multiplication problems. For example 2x9=8. Use this fact to work out 3x9. Students could complete further examples in their books. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">* For further work on missing values and the building of multiplication number facts have students complete Activity Sheet 5 where they need to use different strategies to solve the multiplication problems. Encourage students to use a variety of strategies (skip counting, doubling, working from a known fact). ||  ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Lesson 2 ** ||  <span style="font-family: 'Century Gothic','sans-serif';">Register   ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Focus: Recognising and Describing Patterns, Calculating Missing Values **

<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Begin with a game of circle tables. Students form a circle, teacher stands in the middle and throws a bean bag randomly to students calling out a times table that students must answer. Discuss with students what the answer to the times tables questions are called. They are known as multiples. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Show students the Multiples poster from the “Teach This” website. Brainstorm multiples of 2 and record. Discuss how the multiples of a number can be determined (skip counting, knowledge of times tables facts, patterns eg. for the multiples of 4 the number in the ones column follows the pattern of 4, 8, 2, 6, 0, 4, 8, 2, 6, 0. For the multiples of 9 the numbers in each answer add to make 9). When confident that students understand the concept of a multiple organise students into small groups to record the multiples of a given number. To encourage faster recall, groups could also race against each other to record the multiples of a given number. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Multiples Game. Students take turns in throwing a die and moving a counter along a hundreds chart. (Activity Sheet 6) Move along the 100s chart the number of spaces indicated on the die. If the counter lands on a multiple of 3 they jump forward to the next multiple of 3. If they land on a multiple of 5 they jump backwards to the previous multiple of 5. Two counters may land on the same square. The winner is the first player to reach or pass 100. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Possible questions include: //Which numbers are multiples of 3 and 5?// //<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Variation: //<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">The pair of multiples could be changed, or the sum of two dice could be used to indicate the number of squares the counter moves. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*For further work on Multiples, students could complete Activity Sheet 7 or for greater challenges, visit the website [|www.primaryschoolresources.co.uk/maths/mathsb2.htm] Scroll down to the heading Factors, Multiples and Divisibility Rules. ||  ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Lesson 3 ** ||  <span style="font-family: 'Century Gothic','sans-serif';">Register   ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Focus: Multiples **

<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Revise with students the term “multiples” which was addressed in the previous lesson. Show students the poster from the website “Teach This” titled “What Is A Factor?” A factor of a number is any number that divides exactly into that number. Demonstrate to students that the factors of a number are the two numbers that make up their multiplication sum and the multiple is the answer to the multiplication sum. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Display for students the star print outs from the attached document “factors-display.” Explain that the small star numbers are the factors of the large star number. Have students use the small star numbers to make times table facts equalling the large star number. For example the factors of 10 are 2, 5, 10 and 1. So 2x5=10, 1x10=10. Work as a whole class and then in groups as students develop greater confidence. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Stand Up Factors game. Use the attached game titled “Stand Up Factors” to practise recall of known factors. Students are given a random number card with 3, 5, 7, 6, 8 or 4. Teacher calls out a number and students must stand up if their number is a factor. (Activity Sheet 8) <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Extension task. For further work on factors and multiples students could complete Activity Sheet 9 – “Multiples and Factors Extension Quiz” where they can investigate common multiples and answer more difficult factors questions. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">* For additional work on factors visit the website [|www.primaryschoolresources.co.uk/maths/mathsb2.htm] Scroll down to the heading Factors, Multiples and Divisibility Rules. ||  ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Lesson 4 ** ||  <span style="font-family: 'Century Gothic','sans-serif';">Register   ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Focus: Factors **

<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Revise with students the concept of division and its relationship with multiplication. As a class complete some basic division problems without remainders. Write division sums related to these problems. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Explore with students division situations where there are some objects left over after equal sharing. Give one student 16 counters and ask them to share the counters equally among 5 friends. Discuss the sharing process and what to do with the counter left over. Familiarise students with the term remainder to describe the leftover counter. Record the sum on the board, 16 divided by 5 = 3 with a remainder of 1. Repeat this with other division such as 17 divided by 3 and 21 divided by 2 <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Division Dice: Students in pairs play a game of Division Dice. Provide each pair of students with up to 20 counters and a dice. Students take turns to roll the dice. If they roll a 4 they have to put the counters into groups of 4. Any counters left over become that student’s score for the round. Student’s swap roles after each turn. Each time they add the score onto their total from the previous round. The first student in each pair who scores 10 is the winner. Ensure that students record their division sum and the remainder as they have their turn. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">* Students work individually to complete Activity Sheet 10, where they need to complete division problems involving remainders. Encourage students to use their times tables knowledge. Provide counters for students experiencing difficulty. ||  ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Lesson 5 ** ||  <span style="font-family: 'Century Gothic','sans-serif';">Register   ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Focus: Division with Remainders **

<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Begin lesson by revising with students the formation of arrays. Students sit in a circle. Place 16 counters on the floor and have students make a square array of 4 rows of 4. Have students make 3 rows of 3, 2 rows of 2 and 5 rows of 5. Record the times table sum for each array on the board. Ask students to consider what is the same about each array that they have created. Discuss that each of the arrays forms a square and that the answers to these arrays are known as square numbers. Demonstrate how the square numbers can be written as 2 squared, 5 squared. <span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">*Students complete Activity Sheet 11 investigating how to draw square number arrays and how to record square numbers. Students can also learn to use the counting pattern outlined in Part 7 of Activity Sheet 11. ||  ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Lesson 6 ** ||  <span style="font-family: 'Century Gothic','sans-serif';">Register   ||
 * **<span style="font-family: 'Century Gothic','sans-serif'; font-size: 13px;">Focus: Square Numbers **