# Teaching & Learning Plans. Integers. Junior Certificate Syllabus

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Teaching & Learning Plans Integers Junior Certificate Syllabus

2 The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve. Prior Knowledge points to relevant knowledge students may already have and also to knowledge which may be necessary in order to support them in accessing this new topic. Learning Outcomes outline what a student will be able to do, know and understand having completed the topic. Relationship to Syllabus refers to the relevant section of either the Junior and/or Leaving Certificate Syllabus. Resources Required lists the resources which will be needed in the teaching and learning of a particular topic. Introducing the topic (in some plans only) outlines an approach to introducing the topic. Lesson Interaction is set out under four sub-headings: i. Student Learning Tasks Teacher Input: This section focuses on possible lines of inquiry and gives details of the key student tasks and teacher questions which move the lesson forward. ii. Student Activities Possible Responses: Gives details of possible student reactions and responses and possible misconceptions students may have. iii. Teacher s Support and Actions: Gives details of teacher actions designed to support and scaffold student learning. iv. Assessing the Learning: Suggests questions a teacher might ask to evaluate whether the goals/learning outcomes are being/have been achieved. This evaluation will inform and direct the teaching and learning activities of the next class(es). Student Activities linked to the lesson(s) are provided at the end of each plan.

3 Teaching & Learning Plan: Integers Aims To familiarise students with addition, subtraction, multiplication and division of integers To engage students in activities that will help their mental arithmetic using integers To engage students with the everyday uses of integers Prior Knowledge Prior knowledge and experience of handling addition, subtraction, multiplication and division of natural numbers addition and subtraction of natural numbers from primary school positive and negative numbers on a number line addition of simple positive and negative numbers with the aid of a number line Note: The notation encountered by students at primary level is different to the standard notation used at post-primary level. For example, , is read as positive 5 and negative 7. It may be an idea to start students with this notation initially when dealing with integers. For example (read as negative 6 plus negative 7) gives - 13 (read as negative 13). Learning Outcomes As a result of studying this topic, students will be able to: investigate the properties of arithmetic, commutative, associative and distributive properties and the relationships between operations including inverse operations appreciate the order of operations, including brackets investigate models such as the number line to illustrate the operations of addition, subtraction, multiplication and division in Z explore some of the laws that govern these operations and use mathematical models to reinforce the algorithms they commonly use Catering for Learner Diversity In class, the needs of all students, whatever their level of ability level, are equally important. In daily classroom teaching, teachers can cater for different abilities by providing students with different activities and assignments graded according to levels of difficulty so that students can work on exercises that match their progress in learning. Project Maths Development Team

4 Less able students, may engage with the activities in a relatively straightforward way while the more able students should engage in more open ended and challenging activities. Selecting and assigning activities appropriate to a student s ability will cultivate and sustain his/her interest in learning. In interacting with the whole class, teachers can employ effective and inclusive questioning. Questions can be pitched at different levels and can move from basic questioning to ones which are of a higher order nature. Relationship to Junior Certificate Syllabus Topic Number 1.6 Number Systems Z: the set of integers, including 0. Description of topic Students learn about The binary operations of addition, subtraction, multiplication, and division and the relationships between these operations, beginning with whole numbers and integers. They explore some of the laws that govern these operations and use mathematical models to reinforce the algorithms they commonly use. Learning outcomes Students should be able to investigate models such as decomposition, skip counting, arranging items in arrays and accumulating groups of equal size to make sense of the operations of addition, subtraction, multiplication and division, in N where the answer is in N investigate the properties of arithmetic: commutative, associative and distributive laws and the relationships between them including their inverse operations appreciate the order of operations, including the use of brackets investigate models such as the number line to illustrate the operations of addition, subtraction, multiplication and division in Z Project Maths Development Team

5 Introducing the Topic Students should be familiar with the concept of directed numbers from primary school. The number line with directed numbers on it will reinforce concepts learned at the primary level. Opposite Integers Negative Direction Positive Direction Real Life Context The following examples could be used to explore real life contexts. Temperature Money e.g. Owing 10 being the same as -10 Golf scores Heights above and below sea level Counter on a DVD player or rewinding live TV Project Maths Development Team

6 Student Learning Tasks: Teacher Input Student Activities: Possible Responses Lesson Interaction Teacher s Support and Actions Section A: Number Line Assessing the Learning Teacher Reflections In this lesson we will be investigating positive and negative whole numbers. Where have you used, or seen the use of, negative whole numbers? Temperature. Golf scores. Rewinding live TV. Depth below sea level. Credit Union book displaying deposits or borrowings. If the students have no suggestions, ask a few leading questions such as What was the lowest temperature last winter? or Does anybody know what was the lowest score Rory McIlroy shot? Did students come up with several varied suggestions? We will now begin by looking at a number line. Working in pairs, draw a number line from -12 to +12 on a blank sheet of squared paper. Does the number line begin at -12 and finish at +12? We marked in from -12 to 12 but the number line keeps going on in both directions. Ask a student to draw a number line on the board going from -12 to +12. Check the number lines drawn by the students to see if they have put in the arrows at each end. Check to ensure that the positive and negative numbers are in the correct places. Do students reaslise that number lines extend indefinitely in both directions? Are students putting negative numbers to the left of the zero and positive numbers to the right of zero? Project Maths Development Team KEY: next step student answer/response 4

7 Student Learning Tasks: Teacher Input Student Activities: Possible Responses Teacher s Support and Actions Section B: Ordering Assessing the Learning Teacher Reflections Is -3 greater than 3? Can you give me some everyday examples to verify your answers? -3 C is lower than 3 C. Owing 3 is worse than having 3. Can students come up with varied, real life examples? Do you understand the difference between the symbols > and <? How do you remember which is which? Greater than or less than The open side is always facing the biggest number. Draw the symbols > and < on the board. Ask some students to put examples on the board. Allow for discussion on the best way to remember which is which. Working on your own,do Section B: Student Activity 1. Distribute Section B: Student Activity 1. As students are filling in Student Activity 1, circulate to monitor progress. Can students use the > and < signs without too much hesitancy? Project Maths Development Team KEY: next step student answer/response 5

9 Student Learning Tasks: Teacher Input Student Activities: Possible Responses Teacher s Support and Actions Section D: Multiplication of positive and negative integers Assessing the Learning Teacher Reflections We are going to have a look at what happens when positive and negative numbers are multiplied together. Can anyone give me an example of a sentence where two negatives make a positive? I can t not go means you have to go. I haven t got no money means you have money. I ain t having none of it means you re having some of it. Being in debt Remind students about what happens in the English language when you have two negatives. Facilitate a discussion on how two negatives make a positive in language. Draw a number line on the board and ask students to show examples of taking away a debt. If we think about money, owing money is negative. What s another way of saying owing money. Is being in debt positive or negative? Negative Is taking away positive or negative? So if we take away a debt, are we using positives or negatives? If we compare this to the language example, what type of answer will we get? Which direction would taking away a debt go on a numberline? Working in pairs, complete Section D: Student Activity 3. Negative Two negatives If it s two negatives, it makes a positive? To the right Distribute Section D: Student Activity 3. Allow students to present their work and facilitate discussion and questions from other groups. Are students comfortable with two negatives making a positive? Project Maths Development Team KEY: next step student answer/response 7

10 Student Learning Tasks: Teacher Input Student Activities: Possible Responses Teacher s Support and Actions What about - (-6) Use the Powerpoint show available at OR Use the method outlined in Appendix 1, Class Demonstration. Have a number line on the wall, projected or as a poster, and relate this exercise to the number line. Assessing the Learning Can students relate the demonstration to the operations on the number line? Are students using zero instead of nothing by the end of the lesson? Teacher Reflections Working in pairs, complete Section D: Student Activity 4. Guide the students language towards using zero rather than nothing. For practise, do the first exercise in Appendix 2, Mental Maths, with the students. Distribute Section D: Student Activity 4. As you circulate, ask the students to explain their solutions i.e. verbalise their reasoning. Ask individual students to write the solutions on the board and explain what they are doing. Are students becoming familiar with the operations and relevance of the signs outside the brackets? Are students able to answer the questions without too much hesitancy? Project Maths Development Team KEY: next step student answer/response 8

11 Student Learning Tasks: Teacher Input Student Activities: Possible Responses Teacher s Support and Actions Assessing the Learning Section E: Multiplication of positive and negative integers Teacher Reflections Complete Tables 1 and 2, from Section E: Student Activity 5. 3 Times Result 3 4 = 12 + Ans 3 3 = 9 + Ans 3 2 = 6 + Ans 3 1 = 3 + Ans 3 0 = (-1) = -3 - Ans 3 (-2) = -6 - Ans 3 (-3) = -9 - Ans 3 (-4) = Ans 3 (-5) = Ans 5 Times Result 5 4 = 20 + Ans 5 3 = 15 + Ans 5 2 = 10 + Ans 5 1 = 5 + Ans 5 0 = (-1) = -5 - Ans 5 (-2) = Ans 5 (-3) = Ans 5 (-4) = Ans 5 (-5) = Ans Distribute Section E, Student Activity 5. Circulate to monitor progress and guide or prompt where necessary. Project Maths Development Team KEY: next step student answer/response 9

12 Student Learning Tasks: Teacher Input Student Activities: Possible Responses Completed sentence (a) A positive number multiplied by a positive number gives a positive number (b) A positive number multiplied by a negative number gives a negative number. Teacher s Support and Actions Assessing the Learning What do you notice about 5 x (-3) and -3 x (5)? This is called the Commutative Law. Write down examples of the Commutative Law. The order of the numbers doesn t matter for multiplication. 2 x -3 = -3 x 2 10 x -2 = -2 x 10 Ask a student to write completed sentences on the board and explain their reasoning. Write the following on the board: 2 x -3 = -3 x 2 = 5 x -3 = -3 x 5 = 1 x -10 = -10 x 1 = Write Commutative Law on the board or add it to the Word Bank. Can the students complete the sentences correctly? Teacher Reflections Project Maths Development Team KEY: next step student answer/response 10

13 Student Learning Tasks: Teacher Input Complete Tables 3 and 4 from Section E: Student Activity 5. Student Activities: Possible Responses -2 Times Result -2 4 = -8 - Ans -2 3 = -6 - Ans -2 2 = -4 - Ans -2 1 = -2 - Ans -2 0 = (-1) = 2 + Ans -2 (-2) = 4 + Ans -2 (-3) = 6 + Ans -2 (-4) = 8 + Ans -2 (-5) = 10 + Ans -4 Times Result Teacher s Support and Actions Circulate as students work. Ask students to check for the Commutative Law for Multiplication. If students are having difficulties allow them to talk through them so that they can identify their misconceptions for themselves. Emphasise that we can only multiply integers in pairs (or two at a time). Assessing the Learning Teacher Reflections -4 4 = Ans -4 3 = Ans -4 2 = -8 - Ans -4 1 = -4 - Ans -4 0 = (-1) = 4 + Ans -4 (-2) = 8 + Ans -4 (-3) = 12 + Ans -4 (-4) = 16 + Ans -4 (-5) = 20 + Ans Project Maths Development Team KEY: next step student answer/response 11

14 Student Learning Tasks: Teacher Input Summarise what you know about multiplying signs. Student Activities: Possible Responses Teacher s Support and Actions Assessing the Learning A positive number multiplied by a positive number gives a positive number. A positive number multiplied by a negative number gives a negative number. Teacher Reflections A negative number multiplied by a positive number gives a negative number. A negative number multiplied by a negative number gives a positive number. NOTE: Some discussion as to what should be included here. Three separate bank accounts all of which have an overdraft of 100 gives a total debt of 3( ), for example. Or three jumps to the left of 5 units on the number line moves us how many units in the negative direction? etc. Are students correctly completing the sentences? Project Maths Development Team KEY: next step student answer/response 12

15 Student Learning Tasks: Teacher Input Student Activities: Possible Responses Teacher s Support and Actions Section F: Order of Operations (BIMDAS) Assessing the Learning Teacher Reflections Evaluate x 7 How did you get your answers? Which of the answers is correct? Think of examples in real life where order matters. Students offer their solutions and then explain how they arrived at them. Multiply 4 by 7 and add 2 Add 2 and 4 together and multiply by 7 Both? We re not sure Following a recipe Doing a science experiment Getting dressed Write x 7 on the board. Write the answers 30 and 42 on the board and allow students to talk through their work so that they can identify misconceptions. If students have difficulty coming up with ideas, prompt with an example like Does it matter in what order you go through the classes in primary school? Let s look at another situation and see if we can decide. You charge 7 per hour for babysitting. If you do 4 hours babysitting and get a 2 tip, how much will you have? 30 Project Maths Development Team KEY: next step student answer/response 13

17 Student Learning Tasks: Teacher Input Student Activities: Possible Responses Teacher s Support and Actions Assessing the Learning Section G: Multiplying a number of integers by each other Working in pairs,answer questions 1-3 from Section G: Student Activity 7. Now complete Section G: Student Activity 7. What patterns did you notice? Anything multiplied by 5 ends in 0 or 5 Anything multiplied by an even number is an even number Anything multiplied by 0 = 0 Minus x minus = plus Minus x plus = minus Plus x plus = plus Distribute Section G: Student Activity 7. Circulate and check students work. Engage students in talking about their work. If students are having difficulties, allow them to talk through them so that they can identify their misconceptions for themselves. Ask individual students to show their work on the board. Write students suggestions on the board. Teacher Reflections Plus x minus = minus Like signs multiplied together have a plus answer. The students may benefit from some practise with Math Walls from Appendix 2. Are students doing the calculations correctly? Students write into their copybooks what they have learned. Project Maths Development Team KEY: next step student answer/response 15

18 Student Learning Tasks: Teacher Input Working in pairs, complete Section H: Student Activity 8. Fill in the tables using the diagram with the arrows and circles. Student Activities: Possible Responses Teacher s Support and Actions Section H: Division of Integers It looks like the table we filled in for multiplication. Division Result 12 4 = 3 + Ans 25 5 = 5 + Ans -3 1 = -3 - Ans It may help to use physical manipulatives to remind students about the meaning of multiplication and division. Distribute Section H: Student Activity 8. Assessing the Learning Are students using the table correctly to get the answers to the division questions? Teacher Reflections Do you recognise this diagram? Do you think order matters for division? In other words, does the Commutative Law hold for division? The Commutative Law doesn t hold for division. (-6) (-2) = 3 + Ans (-10) 2 = 5 + Ans 12 4 = 3 + Ans (-8) (-2) = 4 + Ans 15 (-3) = -5 - Ans (-20) 5 = -4 - Ans 10-2 = -5 - Ans Division Result (-12) 3 = -4 - Ans 15 5 = 3 + Ans 20 (-2) = 10 + Ans 8 (-4) = -2 - Ans 16 (-2) = -8 - Ans -2 1 = -2 - Ans 4 4 = 1 + Ans 6 1 = 6 + Ans 20 (-4) = -5 - Ans (-20) (-10) = 2 + Ans Explain the relationship between the numbers in the circles and the numbers on the edges where the arrows point to. Circulate, asking questions where necessary and listen to students conclusions. Write completed sentences on the board. NOTE: Some discussion about the reasons behind these rules should be held here. Ask students to put examples on the board to show whether or not it holds. NOTE: This provides a nice opportunity to discuss with students that when a proposition fails in one instance in Mathematics it fails in all instances (the proof by contradiction). Can students verbalise to the class what they know about: 1. Ordering 2. Addition and subtraction of integers 3. Multiplication of signs outside brackets 4. Multiplication of positive and negative integers 5. BIMDAS 6. Division of positive and negative integers Project Maths Development Team KEY: next step student answer/response 16

19 Student Learning Tasks: Teacher Input Student Activities: Possible Responses Teacher s Support and Actions Section H: Division of Integers A negative number divided by a positive number gives a negative number. Assessing the Learning Teacher Reflections A negative number divided by a negative number gives a positive number. A positive number divided by a positive number gives a positive number. A positive number divided by a negative number gives a negative number. 6 2 = = ⅓ Reflection: Summarise what you know about integers. Students write into their copybooks what they have learned. Project Maths Development Team KEY: next step student answer/response 17

20 Section B: Student Activity 1 Ordering 1. Mark in all the integers from -12 to 12 on the number line shown below Use the number line above to say which is greater (a) 0 or 7 (b)-1 or 2 (c) -6 or 7 (d) -4 or 2 (e) 7 or -5 (f) -10 or -2 (g) -10 or -12 (h)-5 or Use the number line above to say which is smaller (a) 1 or 4 (b) 7 or 5 (c) -6 or 8 (d) -4 or -2 (e) -7 or 6 (f) -8 or -2 (g) -10 or -3 (h)-8 or Complete the statement: If one number is larger than another it lies on the number line. 5. From the following groups, list the numbers from the highest to the lowest (i.e. in decreasing order) (i) 3, -5, 7, -3, 9. (ii) 8, -6, -2, -3, 5. (iii) -9, -7, 6, -3, -2. (iv) 4, -7, 0, -4, Which of the following temperatures are colder? (i) 8 C or 5 C (ii) -7 C or 2 C (iii) 0 C or 5 C (iv) -8 C or -5 C 6. Insert the correct symbol > or < between the following numbers. Example: 10 > 5 because 10 is bigger than 5 i) 14 5 ii) -2 5 iii) 7-3 iv) v) vi) Project Maths Development Team

21 Section C: Student Activity 2 Addition and Subtraction 1. The number line shows which gives 2 Start Forward Steps Answer Use the number lines below to show the answers to the following questions. Show your work on the number lines. i) ii) Answer iii) Answer iv) Answer v) Answer Answer 2. Find the values of each of the following i) = ii) = iii) = iv) = v) = vi) = ii) = iii) = iv) = (v) = 3. Explain how you got the answers to any one of the questions in question 2 above Project Maths Development Team

22 Section C: Student Activity 2 (continued) 4. The number line shows 2-7 which gives -5 Start Backward Steps Answer Use the number lines below to show the answers to the following questions. Show your work on the appropriate number line in each case. i) Answer ii) Answer iii) Answer iv) Answer v) Answer Project Maths Development Team

23 Section C: Student Activity 2 (continued) 5. The table below shows the temperatures in a number of cities. If the temperature in Galway is 15 C, fill in the table below to find the temperature in the various cities. CITY Warmer/Colder Temperature Galway 15 C Dublin Paris Moscow New-York Sydney Cairo Oslo 2 colder than Galway 10 warmer than Galway 20 colder than Galway 4 warmer than Moscow 25 colder than Galway 10 warmer than Paris 3 colder than Moscow 6. Find the values of each of the following. a) 2 + ( -4) + 5 Answer b) (-10) Answer c) 8 + ( - 7) + ( -6) Answer d) -2 + ( -3) + ( -3) Answer 7. Find the value of each of the following a) 11 + (-2) (-1) (-4) + (-3) Answer b) (-2) + (-12) (-7) Answer c) 10 + (-2) (-11) (-8) +12 Answer Project Maths Development Team

24 Section C: Student Activity 2 (continued) 8. The scores, compared to par, for ten players in a golf tournament are listed in the following table. (See below for definition of par.) Name Round 1 Round 2 Round 3 Round 4 Total score compared to par O Brien Level (0) McCarthy Collins Level (0) Level (0) -1 Level (0) O Connor Level (0) Gallagher Ryan +2-2 Level (0) +3 Conneely -1 Level (0) Cleary Level (0) Scanlon +1-3 Level (0) -1 Lyons Level (0) -1 Use this table to answer the following questions i) Fill the total score, compared to par, for each player into the table above. ii) Which player had the lowest score? iii) Which player had the highest score? iv) Who is the best golfer, according to the above table? Definition: Par is the number of strokes an expert golfer is expected to need to complete each individual hole, or all the holes on a golf course. 9. Mr. McKeon has E500 in his bank account. During the day he withdraws E275 from an ATM and a cheque for E370 is also debited from his account. What is the account balance at the end of the day? Project Maths Development Team

25 Section D: Student Activity 3 Two Negatives Example: Mary borrowed 20 from her brother and after doing some babysitting was able to pay back 12. How much did she owe then? 8 Write out a Mathematical Sentence to show this and illustrate the process on a number line = -8 (Owing 20 and subsequently taking away 8 of the debt) I took away 12 of the debt I borrowed 20 from my brother Use the number lines given to answer each of the following questions. In each case show your work on the number line. Write a Mathematical Sentence to illustrate your answers. 1. My sister had to borrow 100 from my Dad for her school tour. She paid him back 20 per week. How much did she owe at the end of the first week? Mathematical Sentence How many weeks did it take to pay back the full amount? 2. Joan borrowed 25 from her sister and promised to pay 30 in return. Her sister had 50 to begin with. How much did she have at the end? Mathematical Sentence Project Maths Development Team

26 Section D: Student Activity 3 (continued) 3. i) I needed 42 and had to borrow 7 from each of my 6 friends. Illustrate this using a mathematical sentence. ii) I borrowed an additional 3 from one of them. Show in steps, on the number line how I paid him back in full Maths sentence (i) Maths sentence (ii) 4. Look at the number line below. Write a story using two negatives. Indicate the direction on the number line and add to the diagram if necessary Using the same number line, write a story for a negative and a positive. Indicate the direction on the number line and add to the diagram if necessary. Project Maths Development Team

27 Section D: Student Activity 4 Multiplication of Signs Outside Brackets 1. Simplify by removing the brackets. a) - (+ 1) = b) + (-2) = c) - (-4) = d) + (-8) = e) - (-12) = f) - (+ 5) = From the above, complete the following sentences. A minus outside a bracket changes the of the number inside the bracket. A plus outside a bracket has no effect on the of the number inside the bracket. 2. Simplify each of the following by removing the brackets. Example: 5 + (-1) = 5-1 = 4 a) 4 + (-1) = b) 6 + (-2) = c) 5 - (-3) = d) 7 + (-8) = e) 12 - (-12) = f) 0 - (+ 5) = 3. Simplify each of the following. a) -3 + (-4) + 6 = b) (-3) = c) 2 + (-6) + (-8) = d) -6 + (-4) + (-1) = e) 9 - (-2) + 7 = f) 11 + (-3) + 9 = f) 13 + (-6) + 9 = g) -5 + (-5) + 3 = h) 15 + (-12) + (-5) = 4. Simplify each of the following a) 4 - (-7) (-5) = b) (-5) - 4 (-3 ) = c) (-4) - (-1) = d) (-3) - (-7) + 2 = 5. Simplify each of the following a) 7 + ( ) - (6-4) = b) (-2+ 5) - (-1-2) = c) 7 - (-2) - (2-1) = d) (5-5 ) - (- 8-8) + 3 = Project Maths Development Team

28 Section E: Student Activity 5 Multiplication of Positive and Negative Integers Use number patterns to complete the following tables. Table 1 3 Times Result 3 4 = 12 Positive Answer 3 3 = 9 Positive Answer 3 2 = 3 1 = 3 0 = (-1) = 3 (-2) = 3 (-3) = 3 (-4) = 3 (-5) = Table 2 5 Times Result 5 4 = 20 Positive Answer 5 3 = 15 Positive Answer 5 2 = 5 1 = 5 0 = (-1) = 5 (-2) = 5 (-3) = 5 (-4) = 5 (-5) = Use the completed tables to fill in the appropriate term in the following sentences. a) A positive number multiplied by a positive number gives a number. b) A positive number multiplied by a negative number gives a number. Project Maths Development Team

29 Section E: Student Activity 5 (continued) Use number patterns to complete the following tables. Table 3-2 Times Result -2 4 = -8 Negative Answer -2 3 = -6 Negative Answer -2 2 = = -2 0 = (-1) = -2 (-2) = -2 (-3) = -2 (-4) = -2 (-5) = Table 4-4 Times Result -4 4 = -16 Negative Answer -4 3 = -12 Negative Answer -4 2 = = -4 0 = (-1) = -4 (-2) = -4 (-3) = -4 (-4) = -4 (-5) = Use the completed tables to fill in the appropriate term in the following sentences. a) A negative number multiplied by a positive number gives a number. b) A negative number multiplied by a negative number gives a number. Project Maths Development Team

30 Section F: Student Activity 6 Order of Operations - BIMDAS 1. A mechanic charged a customer 45 for parts. He charged 15 per hour and it took 4 hours to fix the car. How much was the bill? 2. 4 x x 6 = 50. Add brackets, where appropriate, to make this statement correct. 3. Mike cuts 6 lawns every Saturday. He charges 8 per lawn. Two of the houses always give him a 2 tip. How much will he earn after four Saturdays? Write out a mathematical sentence to represent this. 4. In a factory, the standard rate per hour is The rate for working on Saturday is 14 per hour. Circle the following statements which correctly represent working 36 hours at the standard rate and 6 hours of Saturday work? There may be more than 1 correct answer. a) 9.50 x x 6 b) 9.50 x ( ) x 6 c) x d) (14 x 6) + (9.50 x 36) e) 23.5 x Dry Cleaners Price list Jacket Trousers 8.00 Dress 7.50 Coat A dry cleaners is trying to drum up business. The following mathematical sentence represents Mary s bill and the special offer. Write out what Mary got cleaned and the special offer. 3 x x x 15 - (2 x 7.50) 6. Use brackets, where necessary, to make to following correct. i) x 7-5 x 4 = 17 ii) x 7 5 x 4 = 680 iii) x 7 5 x 4 = 128 iv) x 7 5 x 4 = 200 Project Maths Development Team

31 Section G: Student Activity 7 Multiplying a Number of Integers Example 1: Find the value of -7 (-4) 2-7 x (-4) x x Example 2: Find the value of -1 (-3) (-2) (2) -1 x (-3) x (-2) x (2) +3 x Complete the following questions on multiplication of integers. 1. Multiply each of the following. a) 7 (-3) = b) -8 (-1) = c) 3 (-4) = d) -4 (-2) = e) -9 (-4) = f) 5 (-3) = g) (-2) (-3) = h) 5 (-5) = i) -5 (-2) = j) -6 (-3) = k) 5 (-8) = l) -5 (-6) = 2. Simplify the following. a) 5 (-1) (-3) = b) -3 (-1) 4 = c) (-3) (-4) (-4) = d) -3 (-1) (-5) = 3. Simplify the following. a) 6 (-3) (-2) (-4) = b) -2 (-1) 4 (-6) = c) -7 (-4) (-1) (-2) = d) 5 (-8) 4 (-6) = Project Maths Development Team

32 Section G: Student Activity 7(continued) Complete the multiplication table below and then answer the questions that follow. x List three patterns you see on the completed table Project Maths Development Team

33 Section H: Student Activity 8 Division of Integers x Above is the completed table from Student Activity 7. The circle and the arrows represent division, which is read as 12 4 = 3 or 12 3 = = 5 (-3) (-3) = 1 or (-3) 1 = (-3) Use the table above to complete the tables on the next page. Project Maths Development Team

34 Section H: Student Activity 8(continued) Table 1 Division Result 12 4 = 3 Positive Answer 25 5 = 5 Positive Answer -3 1 = -3 (-6) (-2) = (-10) 2 = 12 (-4) = (-8) (-2) = 15 x (-3) = (-20) 5 = 10 (-2) = Table 2 Division Result (-12) 3 = -4 Negative Answer 15 5 = Positive Answer 20 (-2) = 8 (-4) = 16 (-2) = 0 (-2) 1 = 4 4 = 6 1 = 20 (-4) = (-20) (-10) = Use the completed tables to fill in the following spaces. a) A positive number divided by a positive number gives a number. b) A negative number divided by a negative number gives a number. c) A positive number divided by a negative number gives a number. d) A negative number divided by a positive number gives a number Simplify each of the following. a) 12 3 = b) = c) = d) (-12) (-4) = e) 6-3 = f) (-24) (-6) = g) -(12 11) = e) -(-32 4) = f) (-26) 9 = Project Maths Development Team

35 Appendix 1 Class Demonstration Place an empty box or the outline of a square on the table. Ask the students what quantity is in the box/square. Answer: Nothing/Zero Place a card with +6 on it in the box. Again, ask the students what quantity is in the box. Answer: 6 or plus 6 or positive 6 +6 Remove this card and put in a different one with -6 on it. Ask the students what quantity is in the box now. Answer: Minus 6 or take away 6 or negative 6-6 Place the +6 in the box with the -6. Ask the students what quantity is in the box at this stage. Answer: Nothing/zero Project Maths Development Team

37 APPENDIX 2 Mental Maths 1. Small white boards These are small, white, laminated boards approximately 30cm x 20cm. Each student in the class is given one of these boards with a small white board marker and a cloth. The teacher calls out a question such as -4 multiplied by -2. Each student writes down his or her answer and the teacher says show me. Each student then holds up the board with his or her answer so that the teacher can scan around the room quickly and check to see who is getting the mental maths right or wrong. The teacher then says wipe and each student wipes his or her board clean. The teacher proceeds to call out more questions. This enables the teacher to identify students who are having difficulty with a particular aspect of the topic. 2. Maths walls These are useful from the point of view that they hold the students attention over a period of time. Below are two examples of five block walls, one for addition and one for multiplication. You can also have 7, 9, block walls but these sometimes take too long to complete and therefore do not fall into the mental maths category Block Addition Wall 5 Block Multiplication Wall Note: Keep the integers for the multiplication wall small as wall increases in difficulty with larger integers. Project Maths Development Team

### Teaching & Learning Plans. The Multiplication of Fractions. Junior Certificate Syllabus

Teaching & Learning Plans The Multiplication of Fractions Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes

### Teaching & Learning Plans. Quadratic Equations. Junior Certificate Syllabus

Teaching & Learning Plans Quadratic Equations Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.

### Teaching & Learning Plans. Applications of Geometric Sequences and Series. Junior Certificate Syllabus Leaving Certificate Syllabus

Teaching & Learning Plans Applications of Geometric Sequences and Series Junior Certificate Syllabus Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what

### Teaching & Learning Plans. Inequalities. Junior Certificate Syllabus

Teaching & Learning Plans Inequalities Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve. Prior Knowledge

### Teaching & Learning Plans. The Correlation Coefficient. Leaving Certificate Syllabus

Teaching & Learning Plans The Correlation Coefficient Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to

### Teaching & Learning Plans. Arithmetic Sequences. Leaving Certificate Syllabus

Teaching & Learning Plans Arithmetic Sequences Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.

### Teaching & Learning Plans. Introduction to Equations. Junior Certificate Syllabus

Teaching & Learning Plans Introduction to Equations Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.

### Math 016. Materials With Exercises

Math 06 Materials With Exercises June 00, nd version TABLE OF CONTENTS Lesson Natural numbers; Operations on natural numbers: Multiplication by powers of 0; Opposite operations; Commutative Property of

### The Crescent Primary School Calculation Policy

The Crescent Primary School Calculation Policy Examples of calculation methods for each year group and the progression between each method. January 2015 Our Calculation Policy This calculation policy has

### Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

### Teaching & Learning Plans. Geometric Sequences. Leaving Certificate Syllabus

Teaching & Learning Plans Geometric Sequences Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.

### Teaching & Learning Plans. Plan 8: Introduction to Trigonometry. Junior Certificate Syllabus

Teaching & Learning Plans Plan 8: Introduction to Trigonometry Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes

### Teaching & Learning Plans. Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus

Teaching & Learning Plans Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson,

### Eureka Lessons for 7th Grade Unit ONE ~ ADD/SUBTRACT Rational Numbers Concept 1-1

Eureka Lessons for 7th Grade Unit ONE ~ ADD/SUBTRACT Rational Numbers Concept 1-1 LESSONS 7, 8, & 9 are the FOURTH set of Eureka Lessons for Unit 1. Also Includes four fluency drills, 2 in lesson 8 and

### Teaching & Learning Plans. Plan 4: Outcomes of Coin Tosses. Junior Certificate Syllabus Leaving Certificate Syllabus

Teaching & Learning Plans Plan 4: Outcomes of Coin Tosses Junior Certificate Syllabus Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson,

### Teaching & Learning Plans. Introducing e. Leaving Certificate Syllabus Higher level

Teaching & Learning Plans Introducing e Leaving Certificate Syllabus Higher level The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.

### Teaching & Learning Plans. Plan 6: Planes and Points. Junior Certificate Syllabus

Teaching & Learning Plans Plan 6: Planes and Points Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.

### Calculations Policy. Introduction

Thousands Hundreds Tens Units Tenth Hundredth thousandth Calculations Policy Introduction This Calculations Policy has been designed to support teachers, teaching assistants and parents in the progression

### Swavesey Primary School Calculation Policy. Addition and Subtraction

Addition and Subtraction Key Objectives KS1 Foundation Stage Say and use number names in order in familiar contexts Know that a number identifies how many objects in a set Count reliably up to 10 everyday

### Addition Methods. Methods Jottings Expanded Compact Examples 8 + 7 = 15

Addition Methods Methods Jottings Expanded Compact Examples 8 + 7 = 15 48 + 36 = 84 or: Write the numbers in columns. Adding the tens first: 47 + 76 110 13 123 Adding the units first: 47 + 76 13 110 123

### Teaching & Learning Plans. Plan 7: Introduction to Angles. Junior Certificate Syllabus

Teaching & Learning Plans Plan 7: Introduction to Angles Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to

### Year 1. Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on.

Year 1 Add with numbers up to 20 Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on. +1 +1 +1 Children should: Have access to a wide

### Listen and Learn PRESENTED BY MATHEMAGICIAN Mathematics, Grade 7

Number Sense and Numeration Integers Adding and Subtracting Listen and Learn PRESENTED BY MATHEMAGICIAN Mathematics, Grade 7 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A

### c sigma & CEMTL

c sigma & CEMTL Foreword The Regional Centre for Excellence in Mathematics Teaching and Learning (CEMTL) is collaboration between the Shannon Consortium Partners: University of Limerick, Institute of Technology,

### Maths Module 1. An Introduction to Mathematics. This module covers concepts such as:

Maths Module 1 An Introduction to Mathematics This module covers concepts such as: basic arithmetic rounding order of operations mental computation strategies www.jcu.edu.au/students/learning-centre Module

### Year 1 Procedural Fluency Subtract numbers from up to 20

Year 1 Procedural Fluency Subtract numbers from up to 20 Children consolidate understanding of subtraction practically, showing subtraction on bead strings, using cubes etc. and in familiar contexts, and

### Grade 7 Mathematics. Unit 2. Integers. Estimated Time: 15 Hours

Grade 7 Mathematics Integers Estimated Time: 15 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization Grade

### All you have to do is THINK!

Mathematician s Notes BE A MATHEMATICIAN! All you have to do is THINK! Imagination is more important than knowledge. Albert Einstein We only think when confronted with a problem. John Dewey It s not that

### 100 40 5 4 = 149. how many left? what s the difference? 5 60 80 4 = 149. take away. Maths in School. minus. Subtraction in School.

100 40 5 4 = 149 0 635 735 775 780 784 1000 8 5 2 1 5 3 how many left? what s the difference? 5 60 80 4 = 149 take away 0 635 640 700 780 784 1000 Maths in School minus Subtraction in School by Kate Robinson

### OPERATIONS AND PROPERTIES

CHAPTER OPERATIONS AND PROPERTIES Jesse is fascinated by number relationships and often tries to find special mathematical properties of the five-digit number displayed on the odometer of his car. Today

### NS5-38 Remainders and NS5-39 Dividing with Remainders

:1 PAGE 89-90 NS5-38 Remainders and NS5-39 Dividing with Remainders GOALS Students will divide with remainders using pictures, number lines and skip counting. Draw: 6 3 = 2 7 3 = 2 Remainder 1 8 3 = 2

### Teaching & Learning Plans. Plan 1: Introduction to Probability. Junior Certificate Syllabus Leaving Certificate Syllabus

Teaching & Learning Plans Plan 1: Introduction to Probability Junior Certificate Syllabus Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson,

Grade 7 Integer Addition 7.N.6 Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically. 1. Explain, using concrete materials such as integer tiles

### Adding Integers on a Number Line

NS7-5 Adding Integers on a Number Line Pages 36 37 Standards: 7.NS.A.1b Goals: Students will add integers using a number line. Students will interpret addition of integers when the integers are written

WARDEN AVE P.S. Adding & Subtracting Integers Number Sense & Numeration Unit #1 Grade 7 Math 2014-2015 School Year This mini-unit will run from September 15-26 and must be handed in on Friday Sept. 26th

### Subtraction Year 1 6 2 = 4

Subtraction Year 1 Key Vocabulary Key skills for subtraction at Y1: Given a number, say one more or one less. Count to and over 100, forward and back, from any number. Represent and use subtraction facts

### Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers. with Integers Divide Integers

Page1 Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers Lesson Topic I Can 1 Ordering & Adding Create a number line to order integers Integers Identify integers Add integers 2 Subtracting

### Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

### Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW

Name Period Date 8-1 STUDENT PACKET MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW 1.1 Integer Operations: Patterns Explore the meaning of integer addition, subtraction, multiplication, and division.

### Using Proportions to Solve Percent Problems I

RP7-1 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving

### Exponents. Exponents tell us how many times to multiply a base number by itself.

Exponents Exponents tell us how many times to multiply a base number by itself. Exponential form: 5 4 exponent base number Expanded form: 5 5 5 5 25 5 5 125 5 625 To use a calculator: put in the base number,

### Adding and Subtracting Integers. Objective: 1a. The student will add and subtract integers with the aid of colored disks.

Algebra/Geometry Institute Summer 2006 Monica Reece Grenada Middle School, Grenada, MS Grade 6 Adding and Subtracting Integers Objective: 1a. The student will add and subtract integers with the aid of

### Lesson 2: Real World Positive and Negative Numbers and Zero

Lesson 2: Real World Positive and Negative Numbers and Zero Student Outcomes Students use positive and negative numbers to indicate a change (gain or loss) in elevation with a fixed reference point, temperature,

### Abercrombie Primary School Progression in Calculation 2014

Abercrombie Primary School Progression in Calculation 204 What you need to know about calculations Mathematics will be at the core of your child s schooling from the moment they start to the moment they

### Multiplying Integers. Lesson Plan

Lesson Plan Video: 12 minutes Lesson: 38 minutes Pre-viewing :00 Warm up: Write 5 + 5 + 5 + 5 = on the board. Ask students for the answer. Then write 5 x 4 = on the board. Ask the students for the answer.

### Addition Subtraction Multiplication Division. size. The children develop ways of 5s and 10s. recording calculations using pictures etc.

Rec Children are encouraged to develop Children will experience equal a mental picture of the number groups of objects. system in their heads to use for Count repeated groups of the same calculation. size.

### Counting Money and Making Change Grade Two

Ohio Standards Connection Number, Number Sense and Operations Benchmark D Determine the value of a collection of coins and dollar bills. Indicator 4 Represent and write the value of money using the sign

### Review: Addition and Subtraction of Positive and Negative Numbers

Review: Addition and Subtraction of Positive and Negative Numbers Objective To practice adding and subtracting positive and negative numbers. www.everydaymathonline.com epresentations etoolkit Algorithms

### Objectives. Key Skills Addition. Subtraction

Objectives read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs represent and use number bonds and related subtraction facts within 20 add and

### Five daily lessons. Page 23. Page 25. Page 29. Pages 31

Unit 4 Fractions and decimals Five daily lessons Year 5 Spring term Unit Objectives Year 5 Order a set of fractions, such as 2, 2¾, 1¾, 1½, and position them on a number line. Relate fractions to division

### Introduction to Signed Numbers

Worksheet 1.6 Signed Numbers Section 1 Introduction to Signed Numbers Signed numbers are positive and negative numbers. So far in the worksheets we have mainly talked about the counting numbers, which

### Repton Manor Primary School. Maths Targets

Repton Manor Primary School Maths Targets Which target is for my child? Every child at Repton Manor Primary School will have a Maths Target, which they will keep in their Maths Book. The teachers work

Overview of Mathematics Task Arcs: Mathematics Task Arcs A task arc is a set of related lessons which consists of eight tasks and their associated lesson guides. The lessons are focused on a small number

### Progression towards a standard written method of Calculation

Progression towards a standard written method of Calculation Introduction Children are introduced to the process of Calculation through practical, oral and mental activities. Through these activities they

### Change Number Stories Objective To guide children as they use change diagrams to help solve change number stories.

Number Stories Objective To guide children as they use change diagrams to help solve change number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

### Mental Math Addition and Subtraction

Mental Math Addition and Subtraction If any of your students don t know their addition and subtraction facts, teach them to add and subtract using their fingers by the methods taught below. You should

### Objectives. Key Skills Addition. Subtraction

Objectives read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs represent and use number bonds and related subtraction facts within 20 add and

### Year 2 Summer Term Oral and Mental Starter Activity Bank

Year 2 Summer Term Oral and Mental Starter Activity Bank Objectives for term Recall x2 table facts and derive division facts. Recognise multiples of 5. Recall facts in x5 table. Recall x10 table and derive

### Adding Integers Using a Number Line

Adding Integers The addition of integers can be done in a variety of ways, such as using number lines, manipulatives and a T-chart, calculators or shortcuts. Parentheses (or brackets) are often used around

### Working with whole numbers

1 CHAPTER 1 Working with whole numbers In this chapter you will revise earlier work on: addition and subtraction without a calculator multiplication and division without a calculator using positive and

### Number System Properties Grade Nine

Ohio Standards Connection: Number, Number Sense and Operations Benchmark C Apply properties of operations and the real number system, and justify when they hold for a set of numbers. Indicator 1 Identify

### or (ⴚ), to enter negative numbers

. Using negative numbers Add, subtract, multiply and divide positive and negative integers Use the sign change key to input negative numbers into a calculator Why learn this? Manipulating negativ e numbers

### EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES. Maths Level 2. Chapter 2. Working with fractions, decimals and percentages

EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES Maths Level 2 Chapter 2 Working with fractions, decimals and percentages SECTION B Types of fraction 5 2 Using a calculator for fractions 7 Fractions of

### Gap Closing. Decimal Computation. Junior / Intermediate Facilitator's Guide

Gap Closing Decimal Computation Junior / Intermediate Facilitator's Guide Module 8 Decimal Computation Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5

### Baseball Multiplication Objective To practice multiplication facts.

Baseball Multiplication Objective To practice multiplication facts. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common

### Progression in written calculations in response to the New Maths Curriculum. September 2014

Progression in written calculations in response to the New Maths Curriculum This policy has been written in response to the New National Curriculum, and aims to ensure consistency in the mathematical written

### Chapter 10 Expanding Our Number System

Chapter 10 Expanding Our Number System Thus far we have dealt only with positive numbers, and, of course, zero. Yet we use negative numbers to describe such different phenomena as cold temperatures and

### m + n < 0 94 UNCOVERING STUDENT THINKING ABOUT MATHEMATICS IN THE COMMON CORE, GRADES 6 8 Value of the Inequality 4.1

94 UNCOVERING STUDENT THINKING ABOUT MATHEMATICS IN THE COMMON CE, GRADES 6 8 Value of the Inequality 4.1 If m > 0 and n < 0, decide if each inequality is Always True, Sometimes True, Never True, or Can

### Math News! Focus Area Topic A. 3 rd Grade Math. Grade 3, Module 3, Topic A. Properties of Multiplication and Division

Grade, Module, Topic A rd Grade Math Module : Multiplication and Division with Units of 0,, 6-9, covers Multiplication and Division with Units of 0,, 6-9 Topic A. Topic A. Properties of Multiplication

CONTENTS Introduction...iv. Number Systems... 2. Algebraic Expressions.... Factorising...24 4. Solving Linear Equations...8. Solving Quadratic Equations...0 6. Simultaneous Equations.... Long Division

### Bonneygrove Primary School Calculations Policy

Bonneygrove Primary School Calculations Policy Rationale At Bonneygrove, we strongly encourage children to independently use a variety of practical resources to support their learning for each stage of

### Count back in ones on a numbered number line to take away, with numbers up to 20

SUBTRACTION Stage 1 Subtract from numbers up to 20 Children consolidate understanding of subtraction practically, showing subtraction on bead strings, using cubes etc. and in familiar contexts, and are

### ACCUPLACER Arithmetic Assessment Preparation Guide

ACCUPLACER Arithmetic Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre at George

### Multiplication Arrays

Multiplication Arrays Objective To provide opportunities to use arrays, multiplication/ division diagrams, and number models to represent multiplication number stories. www.everydaymathonline.com epresentations

### Mathematics sample unit Order of Operations Stage 3. Detail: 8 activities. Substrand: S3 NA Multiplication and Division 2 (part)

Mathematics sample unit Order of Operations Stage 3 Scope and sequence summary Substrand: S3 NA Multiplication and Division 2 (part) Duration: 2 weeks Detail: 8 activities Outcomes Key considerations Overview

### I2T2 Final Project. Addition of Integers In the Chips. Grade 7

I2T2 Final Project Addition of Integers In the Chips Grade 7 Laura Bauer December 1, 2006 1 Title Page 1 Table of Contents. 2 Overall Objectives 3 Standards, Materials and Time 4 Outline of Activities..

### HOSPITALITY Math Assessment Preparation Guide. Introduction Operations with Whole Numbers Operations with Integers 9

HOSPITALITY Math Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre at George

### Motcombe and Milton on Stour Fractions progression Developed Spring Fractions Progression

Objectives/Activities Year R Key Vocabulary fair, sharing, the same, different, whole, equal, altogether, double, half. 1. Understanding fairness Finding equal and unequal groups. Realising when two groups

### Expressions and Equations

Expressions and Equations Standard: CC.6.EE.2 Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y.

### Accentuate the Negative: Homework Examples from ACE

Accentuate the Negative: Homework Examples from ACE Investigation 1: Extending the Number System, ACE #6, 7, 12-15, 47, 49-52 Investigation 2: Adding and Subtracting Rational Numbers, ACE 18-22, 38(a),

### Maths Progressions Number and algebra

This document was created by Clevedon School staff using the NZC, Maths Standards and Numeracy Framework, with support from Cognition Education consultants. It is indicative of the maths knowledge and

### Word Problems. Simplifying Word Problems

Word Problems This sheet is designed as a review aid. If you have not previously studied this concept, or if after reviewing the contents you still don t pass, you should enroll in the appropriate math

### Mathematics Calculation and Number Fluency Policy. Curriculum MMXIV. Chacewater School. + - x

Mathematics Calculation and Number Fluency Policy Curriculum MMXIV Chacewater School + - x Autumn 2014 Introduction The purpose of this document is to build on the successes of the Calculation Policy which

### Support Booklet for. Student Name: Coach Name(s): Start Date: What does the student want to achieve from this programme?

Support Booklet for Student Name: Name(s): Start : What does the student want to achieve from this programme? Target End : Sarah Emson Page 1 Why and Who? Using Turn Tables Using Turn Tables Individual

### Teaching & Learning Plans. Introduction to Calculus. Leaving Certificate Syllabus

Teaching & Learning Plans Introduction to Calculus Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.

### Contents. Block A Understanding numbers 7. Block C Geometry 53. Block B Numerical operations 30. Page 4 Introduction Page 5 Oral and mental starters

Contents Page 4 Introduction Page 5 Oral and mental starters Block A Understanding numbers 7 Unit 1 Integers and decimals 8 Integers Rounding and approximation Large numbers Decimal numbers Adding and

### Guidance paper - The use of calculators in the teaching and learning of mathematics

Guidance paper - The use of calculators in the teaching and learning of mathematics Background and context In mathematics, the calculator can be an effective teaching and learning resource in the primary

### Teaching & Learning Plans. Complex Number Operations. Leaving Certificate Syllabus

Teaching & Learning Plans Complex Number Operations Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to achieve.

### Objective: Apply and explain alternate methods for subtracting from multiples of 100 and from numbers with zero in the tens place.

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 2 5 Lesson 18 Objective: Apply and explain alternate methods for subtracting from multiples of Suggested Lesson Structure Fluency Practice Application Problem

### Calculation strategies for subtraction

Calculation strategies for subtraction 1 Year 1 Subtract numbers up to 20. Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways

### Personal Financial Literacy

Personal Financial Literacy 7 Unit Overview Being financially literate means taking responsibility for learning how to manage your money. In this unit, you will learn about banking services that can help

### Objective. Materials. TI-73 Calculator

0. Objective To explore subtraction of integers using a number line. Activity 2 To develop strategies for subtracting integers. Materials TI-73 Calculator Integer Subtraction What s the Difference? Teacher

### TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

### III BACKGROUND KNOWLEDGE

Algebra Made Easy Grade Level: 6 th Presented by: Julia Daniely and Pat Graham, Miller Magnet School, Macon, Georgia Length of Unit: Five math lessons (10 days) I. ABSTRACT As we enter the 21 st century,

### Conceptual Understanding of Operations of Integers

Grade 7 Mathematics, Quarter 2, Unit 2.1 Conceptual Understanding of Operations of Integers Overview Number of instructional days: 10 (1 day = 45 60 minutes) Content to be learned Demonstrate conceptual

### Teaching Guidance. For. Counting and Partitioning Numbers

Teaching Guidance For Counting and Partitioning Numbers (Overcoming Barriers Moving Levels 1 to 2, 2 to 3, 3 to 4, 4 to 5) 1 of 2 The National Strategies Primary Overcoming barriers in mathematics helping

### Lesson 4: Efficiently Adding Integers and Other Rational Numbers

Lesson 4: Efficiently Adding Integers and Other Rational Numbers Student Outcomes Students understand the rules for adding integers: Add integers with the same sign by adding the absolute values and using

### COMPASS Numerical Skills/Pre-Algebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13

COMPASS Numerical Skills/Pre-Algebra Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre