Let's investigate Pablo has these digit cards. He makes three-digit numbers with the cards. Write down all the numbers he could make. 1 Write each red number in figures, words and expanded form. (A) (1000 | 2000 | 3000 | 4000 | 5000 | 6000 | 7000 | 8000 | 9000 00 | 200[ 300] 400| 500] s00| 700| 800| 900 io} 20| 30] ao] so| so| 70| s0| % 1 2{ 3] 4{[ 5] 6| 7[ s| 9 (©) (7000 | 2000 | 3000 | 4000 | 5000 | 6000 | 7000 | 8000 | 9000 yoo | 200] 300] 400] 500] 600] 700| 800| 900 io} 20{ 30] 4o| so| so| 70] 80| % 1 2} 3] 4] 5{ 6{ 7] 8] 9 2. Write each number in words. (a) 2345 (b) 3030 (c) 2901 (d) 7777 (2) 2816 (f) 9109 AGtt:0.1,2,3,4,5,6,7,8.and 9 are digits 3 Write these numbers in figures. (a) nine thousand and nine (b) four thousand and forty 4 What is the value of 4 in these numbers? (a) 6423 (b) 4623 (c) 3409 (d) 9040 (e) 1234 (f) 4321 expanded form: 4567 = 4000 + 500 + 60 + 7 partition: breaking up a number into its parts. place value: the value of a digit determined by its position. In 830, the 3 has a value of 3 tens (30) (H]\t [v) (af [o) = thousand: is a fourdigit number that is 10 times larger than a hundred. (Th H|T 1 0/0 x70 Unit 1A: Core activity 1.1 Reading, writing and partitioning numbers5 Look at these number cards. (a) Which cards have the same value as 3900? (6) Which card has the smallest value? (c) What is 10 more than 390 tens? 6 Maria writes a number. It has the digit 4 in the hundreds place and the digit 2 in the units place. Which of these numbers could Maria have written? 5426 4652 4265 5462 7 What is the largest possible number that can be written using the digits 3, 6, 3 and 4? 8 Which value is equal to 3 hundreds? 3units 30units 30tens 300 tens 9 Find the missing numbers. 3000 __8. 02 hundred less than 2 5000 __ Sone hundred more than 5 6500 8.002 thousand more than 9 980 Sone hundred less than 9 10 Write the number that is 1 more than 9999. 11 Solve these number riddles (a) ¢ | have four digits. (b) © | have four digits. e lam more than 2500. e My units digit and my e lam less than 3000. hundreds digit are the same. e My hundreds digit is 6. e lam less than 9000. e My tens digit is one less e lam greater than 8000. than my hundreds digit. e My tens digit is 4. e My units digit is 0. e My hundreds digit is two What number am I? more than my tens digit. What number am I?Ordering and rounding Let's investigate round to the nearest: to round to Ahmed writes a list of four-digit whole the nearest hundred, look at the tens digit and if it is A] Tv) numbers. The digits in each number add up to 3. ¢ <5, round down [3 | 2 | oJ , °=5or>5, round up H | T | U ) 93010 the nearest 8 3 O ) hundred, is 800. He writes the numbers in order of size, H|]T]U starting with the smallest. 418 enieg nearest Write down all the numbers that could 7 be in Ahmed’s list. Make sure you write Rounding numbers makes them easier fo use. cecal wa 4 them in order of size. 1 Write these numbers in order of size, starting with the smallest. (a) 1066 1606 1660 1060 1666 (b) 9080 8990 9009 9090 8999 2 What is the number shown by an arrow on each number line? (a) (6) l l Pititt t | | | SIE ey 8000 5500 (©) C)) ¢ >) agri] 7000 _ ___ 8000 __ 5500 3 Round these numbers to the nearest 100. (a) 1060 (b) 7225 (c) 4680 (d) 1007 (e) 885 4 Which of these numbers is closest to 1000? 1050 1039 1100 «+980 = 899 Petre eee cn ea een need5 Here are some digit cards. Use the cards to make three-digit numbers greater than 500. How many can you make? 6 Use the < and > signs to make these statements true. (a) 505 |?) 550 (b) 660 |? 606 (c) 989 |? 899 (d) 1234/7) 4321 (e) 1009/7 1010 (f)_: 1001 |?) 989 py 7 What number is halfway between 158 and 172? > Is greater than (‘s0) (7) (172) x100 Gy FF ws C210 2S 8 Here is a number calculation. 15 x 10 = 150 Write two different division calculations that use the same numbers. 9 A packet contains 500 grams of gerbil food. Aysha feeds her gerbil 10 grams of food each day. How many days does the packet of food last? 10 Here are three signs X + = Use these signs to make each calculation below correct. There may be more than one answer. (a) 60 fF] 6 (R10 = (©) 10 9] 15} 150 ~— (ce) 4507) 10 JR 45 11 Write the missing numbers. 13 20, py 510, oy 4500 10, 3 10, 1Addition (1) Let's investigate Some words that Make a route through the grid from Start to Finish. You We use for addition: can move horizontally or vertically. Add up the numbers OC, adciition, plus, on your route. Find the route that gives the lowest total, Norease, sum, Total, altogether. ° 4 = Questions that ask = 5 us to add: How many are there altogether? 7 H al | e What is the total Start 1 7 9 number of For example, 2+8+5+1+9+4+8+2=34 Use complements to 10 and 20 to help you. These are also called ‘number pairs' to Wand 20. * 1 Choose a method to solve these addition problems. (a2) 5+8+5+3=(8] (6) 44+194+124+1=2R) (©) 14+114+94+4=(% () 44+174+24+3=—2 (e-) 138+2414+5= (f) 34+1449+3=)%) Explain to your partner why you chose that method. If you think your partner could choose a better method, tell them why. 2 Copy the addition number sentences below. Then copy the list of numbers on the right. Draw arrows to complete the number sentences. The first one has been done for you. 76 + 62 = 168 28 + 34 i ee 85 65 +89 128 94+ 22= 154 17+ 68= 104 43+ 52= 95 +77 = 62 40 + 64 = 116 (err nrsnecanAll four hoops must land on a cone. There can be more than one hoop on a cone. Check your total is correct by adding together your numbers using two different methods. Of 0 oO © Number sentence stories Kasim thought up a story for the number sentence 63 + 56 = 119 Write a story for each of these number sentences: 16+8+4=28 5+4+6+5=20 49 + 37 = 86 3 Throw hoops over the cones to make the totals in the stars. show on Monday and 56 visited on Tuesday. So 119 people visited 63 people visited our art ‘our art show altogether.Subtraction (1) Let's investigate Some words that we use for Break the four-digit code to open the subtraction: subtract, subtraction, treasure chest. take, fake away, minus, decrease, fewer, leave, difference. 65 — 58 = (@) 41-2 @j=12 Questions that ask us to subtract: How many are left? How many are left over? 86 - 79 = How many more is [lj than [ij7 67 - (8 = 39 How many fewer is {il than (ij? How much more is | than [Ri]? @ 6 © @ How much less is ml than | Sarah used the ‘counting back’ method to calculate 74 — 13. 1 Solve 62 - 11 using the ‘counting back’ method 13 is a small number. | will take away 10 then 3 more.The answer is 61 1-1 +1 =10 aS, SSS. 61 62 63 64 74 Tim used ‘finding the difference’ to calculate 81 — 76. 2 Solve 62 - 58 by ‘finding the difference’ between the two numbers. 76 is quite close to 81. | will count up to find the difference between the numbers, The answer is 5 +1 +1 +1 41 41 ~~ 76 77 78 79 80 81 Unit 14: Core activity 22 Subtraction (1)Choose a method to solve these subtraction problems. (a) 45 - 43 = |? (b) 92-14=|2 (c) 36—-29=/2 (a) 89-5= (e) 52-34=B] () 42-18=8 (9) 77-68=[B] (nh) 39-35 = B Explain to your partner why you used your chosen methods. If you think your partner could choose a better method, tell them why. Fred leaves his house with 99 cents and walks to the shop. He needs 15 cents to buy a snack. But Fred has a hole in his pocket! Each time he passes a ay. Fred loses that amount of money from his. pocket. This map shows all the possible routes from his home to the shop. Find Fred a route to the shop so that he will still have enough money to buy his snack when he gets there. Number sentence stories Hayley thought up a story for 86 — 49 = 37. Write a story for each of these number sentences. 35-7 = 28 al 77 —-68=9 95 — 35 = 60 A shop had 86 loaves of bread. They sold 49 loaves, so 37 were left.Partitioning to add and subtract 228 Vocabulary partition: breaking up. a number into parts. 437 For example, 608 = 600 + 8 Let's investigate Find five pairs of numbers that add up to 900. One has been done for you. 601 672 + 228 = 900 465 900 is a multiple of 10, Look for fwo numbers that add to make a multiple of 10.We can do this by looking for number pairs to 10 in the units digits. Then choose a method to add the two numbers together. For example, 67/2) + 22/8) ... Partitioning to add 423 + 589 ~ [il 400 + 20 + 3.add 500 + 80+ 9 400 + 500 = 900 20 + 80 = 100 34+9= 12 Therefore, 423 + 589 = 1012 1 Partition each number into hundreds, tens and ones. Then calculate each answer. (a) 482 + 213 = |P) (b) 237 + 149 = (c) 821 + 546 = (d) 271 + 649 = (e) 362 + 841 () 598 + 613 = |B) Unit 1A: Core activity 2.3 Partitioning to add and subtractPartitioning to subtract 623 - 238 = [Rl 500 + 110 + 13 - 200 + 30+ 8 500 — 200 = 300 110 — 30 80 13-8 5 Therefore, 623 — 238 = 385 2. Partition each number into hundreds, tens and ones. Then calculate each answer. (a) 628 — 405 = |) (b) 972 — 813 = 3 (C) 716 — 246 = |?) If we partition 623 to 600 + 20 + 3, (d) 609 — 388 = then later we will have fo calculate = 20 - 30 and 3 ~ 8.$0, we partition itto Oe Tea 500 + 110 + 13. (f) 560 — 308 = (g) 612 - 237 = (h) 507 — 239 =|?) 3 Choose a method to solve each of these problems. Explain why you used your chosen methods: (a) | bought a television for $438 and the delivery charge was $48. How much did | pay altogether? (b) A sea journey is 657 km. So far the ship has travelled 239km. How much further does the ship have to travel? (c) | bought 350 beads. | used 124 beads to make jewellery for my friends. How many beads do | have left? (d) My tree grew 68cm one year, then 57 cm the next year, and 72cm the year after that. How much has it grown in total over the 3 years?Learning multiplication facts Let's investigate multiple: a number Try to learn multiplication facts for the 2X, 3X, 4X, that can be divided 5x, 6X, 9X and 10X tables so you can remember exactly by another them quickly. For example: number is a multiple of that number. Start at 0 X2 multiples are even numbers pee en cans X5 multiples end in O or 5 nlite iin tiiesidl X10 multiples end in 0. you will find numbers — that are multiples of Use a blank (xl: [2[s[e]s[e[7[e[*|19) the step size. multiplication riolw square like the +2 +2 +2 +2 +2 one here to look for patterns. 072346678910 So the multiples of 2 L are 2,4, 6,8, 10,12... The multiples of 3 are 3,6,9,12... zl2l-l-lele (a) Write the 1x table across the first row and down the first column. The table is symmetrical so the answers in the first column will be the same as the answers in the first row: 1 X 2 = 2 (tow) and 2 x 1 = 2 (column) (b) Repeat for other times tables such as the 2x, 5x and 10x tables (c) Look at the blank squares. Think about how you could fill them in. You could use: * Counting on or repeated addition. You already have the first two multiples of 3 (3 and 6) so keep adding 3 to give you 9, 12, 15. * Using existing answers. You already have answers for the 2x table, so multiply each answer by 2 fo give you the 4 table. Then multiply the answers to the 4x table by two to get the 8x table. Complete the rest of the multiplication grid. Unit 1A: Core activity 3.1 Learning and using multiplication facts2 Look at the spider diagrams for the 2x table. Copy the diagrams and fill in the missing boxes (a) (®) ” 2 1G E ® ES OOO FOxXe TEE ® ” : ° ’ Work with a partner to create spider diagrams for other times tables. 3 Look at the numbers in the two circles. Find pairs of numbers in the first circle that multtiply together to give an answer from inside the second circle. Find as many pairs of numbers as possible. Record both multiplications for each pair. For example: 5 x 4 = 20 and 4 x 5 = 20 Work with a partner. Draw two circles each. Choose five numbers from 1 to 9 to write in one circle. Swap circles and work out the answers to write in the second circle. Ask your partner to check your work.Using multiplication facts Let's investigate expression: numbers and signs What number goes in the circle to complete grouped to show how much something is. For example, 4 + 2is an expression for 6, and 3 x 5 is an expression for 15. product: the answer you get when you multiply numbers, 3x5 = (18) product inverse: signs that ‘undo’ each 1 Sanjiv has a collection of toy cars. eee Mutiplyand divide cre inverse signs, for example, Ge 186 a xs the puzzle? Which expressions can he use to find the total number of toy cars? 5x3 3x5 34+3+3 5x5x5 2 Which two number sentences have the same answer? 2x8= 2 2x9=2 3x7=(R) 4x4=2) 3 Use multiplication facts to help you answer these questions. (a) Sara buys 3 bunches of bananas. There are 6 bananas in each bunch. How many bananas does Sara buy altogether? (b) Ahmed paints 4 rows of animals. He paints 8 animals in each row. What is the tofal number of animals Ahmed paints? (c) Fatima has 5 packets of beads. Each packet contains 8 beads. How many beads has Fatima got? reer etn ne ent rsUse each of the digits 3, 5, 7 and 0 to complete these statements. You can only use each digit once. |? |? is a multiple of 5 greater than 50. \? |? is a multiple of 10 less than 50. Hugo is thinking of a number. He says: ‘My number is a multiple of 2 and a multiple of 3. My number is greater than 10! What is the smallest number Hugo could be thinking of? Which numbers on the grid are multiples of 5? 61 | 62 | 63 | 64 | 65 69 | 70 | 71 | 72 | 73 77 | 78 | 79 | 80 | 81 Parveen has some number cards. (a) She says: ‘If | multiply the number on my card by 5 the answer is 45! What number is on her card? (b) She chooses a different card and says: ‘If | divide the number on this card by 4 the answer is 6! What number is on her card? (c) Write some similar puzzles for your partner to try. Find the missing numbers. (a) 4x5=2 (b) 5/2 =45 (ce) |P x 3=27 Look at this list of numbers. Which ones are multiples of 3? 23 12 21 27 26 9 28 22 15 7 18 Look at your answers. Explain to your partner what you notice about them.Investigating patterns Work through these investigations with a partner. 1 These triangles are made from sticks. 7 \ Pattern number | Number of sticks 4\ 7 N ; = WN ZN Z4_S 3 9 pattem 1 — pattem 2 pattern 3 (a) How many sticks would be needed to make pattern 7? (b) How many sticks would be needed to make pattern 17? (ce) Which pattern could be made from 33 sticks? 2 These squares are made from sticks. Pattern number | Number of sticks - - 1 4 —~ vii \ 2 8 mt) tet ioe) Cos pattern pattern 2 pattern 3 (a) How many sticks would be needed to make pattern 9? (b) How many sticks would be needed to make pattern 15? (ce) Which pattern could be made from 48 sticks? How do you know? Explain to your partner how you worked out the answer. Prerreeerrre nnn tnt3 Look at these stair patterns. a lle, lll pattern 1 pattern 2 pattern 3 It takes 2 steps IHakes 4 stey It takes 6 steps togoupanddown. — to goup and down, to go up and down, (a) How many steps would it take to go up and down the 8th pattern of stairs? (b) How do you know? Explain your method to your partner. (c) How many steps would it take to go up and down the 10th pattern of stairs? (d) How many steps would it take to go up and down the 100th pattern of stairs? 4 Look at these squares made on a pinboard. square 1 square 2 square 3 Ittouches 4 pins, Ittouches 8 pins, Ittouches 12 pins (a) How many pins should the 7th square touch? (6) Explain to your partner how to work out the answer without drawing a diagram What have you noticed in all these investigations? What has your partner noticed?Vocabulary Let's investigate double: twice as many; multiply by 2. What is the missing number? What rule connects 4,3. and 247 Does that rule work for 7.2.and 28? Use the rule to find the missing number. 1 Double these numbers. (a) 58 = (b)71_—s (ec) 36 (A) 9B 2. The rule for these number sequences is to double the previous number. What are the missing numbers? (a) 3,6,12, (b) 5, 10, 20, 3 Copy these tables. Use doubling to complete these table patterns. Number | 1 2 3 4 5 6 7 8 9 | 10 2x 2|4 8 12 18 | 20 4x 12 32 | 36 8x 40 56 72 Number | 1 2 3 4 5 6 7 8 9 | 10 3x 3 6 12 18 27 | 30 6x 18 48 | 54 12x 60 84 108 4 Use doubling to complete this pattern: 1X13 =13 2X13 = 26 4x13= ee eee5 Copy and complete the tables for these number machines. Input _| Output 4 9 18 32 = \f- Je0e Input | Output Eee) = B _ 1 45 6 Here are some triangle numbers. 1 3 6 10 If you double a triangle number, you can make a rectangle. Here, the fourth triangle number (10) has been doubled. (a) What is special about the length and width of the rectangle? (b) Double the other triangle numbers and then complete the sentence: When | double a triangle number 7 Asequence starts 2, 3,5, 9,17 Explain to your partner the rule for the sequence. 8 Find two examples to show that the following rule is true: Any odd number is double a number and then add 1.Multiplying Let's investigate The number in each square is the product of mutliplying together the two circles on either side. For example, Mx®@-4 Find the missing numbers. 1 Use a number line to show how to calculate 23 x 4 using repeated addition. +23 a 0 23 2 Abdul calculates 23 x 5 using partitioning. 23 x 5 = (20 X 5) + (3X 5) = 100 +15 =115 Work out the value of these expressions using partitioning: (a) 42x 3 (b) 37x 4 (©) 46x5 3. Estimate the value of these expressions. Then calculate the value. (a) 47x 5 (6) 29x 4 (©) 89x 3 (d) 74x 4 te cee Vocabulary grid method: a method of multiplication that uses a grid. For example, 27 x 4 = 108 ( 20 | 7) La [20 [ 28} 80 + 28 = 1084 Sultan uses the grid method to answer some calculations, but then spills ink on his work. What numbers are under the ink smudges? (@) 47x 3 (b) 93 x 4 “ ew 141 ge Bevin (c) 51x (a) 87 x4 x|s 0 yf x 7 - + 255 320 + 28 = * 5 re <« 4/320 28 - 5 Multiply together the numbers in the circles to calculate the products in the squares between them. Copy the diagrams and fill in the missing numbers. os fa 6 Pencils are sold in packs of five. Each pack costs 95 cents. Fatima buys four packs of pencils. How much does she spend? 7 Use the digits 2,3 and 4 to make the expression with the greatest product. Bax What is the product?