Number Smash
1
Numbers Rule
or roll some numbers:
Add some numbers below, then drag one onto another to smash them
๐Ÿ“œ Working
Whole numbers, fractions (3/4, 1 1/2) or decimals (0.25), from โˆ’9999 to 9999. Press Enter to add.

Investigation questions

63 questions. Work through these with the tool above. Set it up puts the right counters on the board for you (on an empty board, so nothing you have made is lost), and Show on board puts the question on screen, full size.

โ†‘ Back to the tool

First experiments
6 questions

  1. Drag the 3 onto the 5 and choose +. What appears, and where does it land? Press โ†ฉ to undo, then drag the 5 onto the 3 instead. Is the answer the same? Is it in the same place?

    Teacher notes

    8 both times. The answer lands where the target counter was, so it moves when you swap. Addition is commutative: 3 + 5 = 5 + 3.

  2. Drag the 8 towards the 2 but don’t let go yet: the dark label shows the order the numbers will be used in. Predict 8 โˆ’ 2, then choose โˆ’. Undo, and this time drag the 2 onto the 8. Predict first again.

    Teacher notes

    8 โˆ’ 2 = 6 and 2 โˆ’ 8 = โˆ’6. The counter you move always comes first. The two answers are opposites, the start of seeing that a โˆ’ b = โˆ’(b โˆ’ a).

  3. Predict all four answers for 6 and 4 before you smash: 6 + 4, 6 โˆ’ 4, 6 ร— 4 and 6 รท 4. Then drag the 6 onto the 4 and press ๐Ÿ‘ Answers in the box to check. Which is biggest? Which isn’t a whole number?

    Teacher notes

    10, 2, 24 and 1ยฝ. ร— gives the biggest answer here, but not always: with 6 and ยฝ, 6 รท ยฝ = 12 beats 6 ร— ยฝ = 3.

  4. Smash 2 ร— 3, then smash the 6 with the 5 using +. Read the calculation under the answer. Now press โฎ (twice) to go back to the start, and this time smash 3 + 5 first, then 2 ร— 8. Same numbers, same operations: why is the answer different?

    Teacher notes

    2 ร— 3 + 5 = 11 but 2 ร— (3 + 5) = 16. The calculation under each counter shows where the brackets go: which pair you smash first is exactly what brackets record.

  5. What colour is each counter? Smash 7 + (โˆ’3), predicting the colour of the answer first. Undo and try 7 โˆ’ (โˆ’3) (drag the 7 onto the โˆ’3). What decides the colour?

    Teacher notes

    Blue is positive, red is negative and grey is zero. 7 + (โˆ’3) = 4 and 7 โˆ’ (โˆ’3) = 10, both blue. The colour shows the sign of the answer, whatever the signs of the numbers that made it.

  6. No dragging this time: tap the 5, then tap the 4. Which number comes first in the box? Press โ‡„ Swap and look again before you choose โˆ’. What did Swap change?

    Teacher notes

    The counter you tap first comes first, so it starts as 5 โˆ’ 4 = 1. After โ‡„ Swap it is 4 โˆ’ 5 = โˆ’1. Tapping is often easier than dragging on a whiteboard or a phone.

Does order matter?
6 questions

  1. Using 4 and 7, smash with + both ways round (4 onto 7, then undo and 7 onto 4). Then do the same with ร—. What do you notice?

    Teacher notes

    4 + 7 = 7 + 4 = 11 and 4 ร— 7 = 7 ร— 4 = 28. Addition and multiplication are commutative: the order of the two numbers doesn’t matter.

  2. Now try โˆ’ both ways round with 4 and 7. Predict both answers first. How are the two answers related?

    Teacher notes

    4 โˆ’ 7 = โˆ’3 and 7 โˆ’ 4 = 3: the same size, opposite signs. Subtraction is not commutative, but swapping always gives the negative of the answer.

  3. Try รท both ways round with 12 and 3. One answer is a whole number and one is a fraction. How are they related?

    Teacher notes

    12 รท 3 = 4 and 3 รท 12 = ยผ. Swapping a division gives the reciprocal of the answer: 4 ร— ยผ = 1.

  4. Smash 5 with 5 in all four ways (duplicate the counters with โง‰ if you need more). For which operations does the order matter now?

    Teacher notes

    10, 0, 25 and 1. When the two numbers are equal the order never matters, because swapping them changes nothing. Subtracting gives 0 and dividing gives 1 for any non-zero number.

  5. Is subtraction associative? Make (8 โˆ’ 4) โˆ’ 2 by smashing 8 โˆ’ 4 first, then the result โˆ’ 2. Press โฎ to start again and make 8 โˆ’ (4 โˆ’ 2). Then try the same two groupings with รท.

    Teacher notes

    (8 โˆ’ 4) โˆ’ 2 = 2 but 8 โˆ’ (4 โˆ’ 2) = 6. With division, (8 รท 4) รท 2 = 1 but 8 รท (4 รท 2) = 4. Grouping matters for โˆ’ and รท.

  6. Now group the same numbers both ways with +, then with ร—: (8 + 4) + 2 and 8 + (4 + 2). Look at the calculations under the answers. Why does the tool write no brackets for these?

    Teacher notes

    Both groupings give 14 for + and 64 for ร—. Addition and multiplication are associative, so brackets would change nothing and the tool leaves them out. It only writes brackets that change the answer.

Brackets and the order of operations
6 questions

  1. Make 3 + 4 ร— 5 by smashing 4 ร— 5 first, then adding the 3. What calculation is written under it? Now start again and make (3 + 4) ร— 5. Which needs brackets, and why?

    Teacher notes

    3 + 4 ร— 5 = 23 needs no brackets because ร— is done before + anyway. (3 + 4) ร— 5 = 35 needs them. A basic calculator that works left to right gives 35 for 3 + 4 ร— 5, a common slip.

  2. Make 10 โˆ’ 6 โˆ’ 2 by smashing 10 โˆ’ 6 first. Then undo and smash 6 โˆ’ 2 first, then 10 โˆ’ 4. Which of the two calculations needs brackets?

    Teacher notes

    (10 โˆ’ 6) โˆ’ 2 = 2 is written 10 โˆ’ 6 โˆ’ 2, because โˆ’ is worked left to right. 10 โˆ’ (6 โˆ’ 2) = 6 needs the brackets.

  3. Predict 12 รท 6 ร— 2. Make it by smashing 12 รท 6 first. Then make 12 รท (6 ร— 2). Many students think ร— always comes before รท. What does the tool show?

    Teacher notes

    12 รท 6 ร— 2 = 4, worked left to right, and 12 รท (6 ร— 2) = 1. ร— and รท have equal priority: BIDMAS lists D before M, but they are done in order from left to right.

  4. Using 2, 3 and 4 with one + and one ร—, how many different answers can you make? Read the calculation under each one before you go back to the start.

    Teacher notes

    5 different answers: (2 + 3) ร— 4 = 20, (2 + 4) ร— 3 = 18, (3 + 4) ร— 2 = 14, 2 ร— 3 + 4 = 10 and 2 ร— 4 + 3 = 11. 3 ร— 4 + 2 also gives 14.

  5. Use one 2, the 3 and the 4 on the top row to make 2 ร— (3 + 4). Use the other four counters to make 2 ร— 3 + 2 ร— 4. Compare the answers and the calculations.

    Teacher notes

    Both are 14: 2 ร— (3 + 4) = 2 ร— 3 + 2 ร— 4. Multiplication distributes over addition. This is what expanding brackets in algebra relies on.

  6. Make 8 โˆ’ 4 + 2 in two ways: smash 8 โˆ’ 4 first, or smash 4 + 2 first and then 8 โˆ’ 6. Read both calculations. What happens to the + when it ends up inside a bracket after a minus?

    Teacher notes

    (8 โˆ’ 4) + 2 = 6, written 8 โˆ’ 4 + 2. 8 โˆ’ (4 + 2) = 2. Subtracting a bracket subtracts everything in it: 8 โˆ’ (4 + 2) = 8 โˆ’ 4 โˆ’ 2.

Fractions
7 questions

  1. Predict, then smash: ยฝ + ยฝ, then โ…“ + โ…“, then ยผ + ยผ. What happens to the numerator and the denominator when you add a fraction to itself?

    Teacher notes

    1, โ…” and ยฝ. Adding a fraction to itself doubles the numerator and keeps the denominator. Watch for ยฝ + ยฝ = 2/4, which adds the denominators too.

  2. A common wrong answer for ยฝ + โ…“ is 2/5. Predict, then smash. How can you tell straight away that 2/5 can’t be right? Then try ยฝ โˆ’ โ…“.

    Teacher notes

    ยฝ + โ…“ = 5/6. 2/5 is less than ยฝ, and adding โ…“ must make the answer bigger than ยฝ. ยฝ โˆ’ โ…“ = 1/6.

  3. Smash โ…” ร— ยพ. Does the tool simplify the answer? Then undo and try โ…” รท ยพ (drag the โ…” onto the ยพ). Is the answer bigger or smaller than โ…”?

    Teacher notes

    โ…” ร— ยพ = ยฝ (6/12 simplified), and โ…” รท ยพ = 8/9. Dividing by a number less than 1 makes the answer bigger than the number you started with.

  4. Smash ยฝ รท 2, then undo and smash ยฝ ร— 2. A student says “dividing by 2 is the same as multiplying by ยฝ.” Use the 6 to test the claim.

    Teacher notes

    ยฝ รท 2 = ยผ and ยฝ ร— 2 = 1. The claim is true: 6 รท 2 = 6 ร— ยฝ = 3. Dividing by a number is the same as multiplying by its reciprocal.

  5. Smash ยฝ + โ…“, then add the โ…™. What do you get? Use a pen to write the calculation with a common denominator.

    Teacher notes

    ยฝ + โ…“ = 5/6, and 5/6 + โ…™ = 1. In sixths it is 3/6 + 2/6 + 1/6 = 6/6.

  6. Smash 1 รท 2, then the answer รท 2, and keep going. Predict each answer before you see it. How many divisions does it take to get below 1/100?

    Teacher notes

    ยฝ, ยผ, โ…›, 1/16, 1/32, 1/64, 1/128: seven divisions, because 2โท = 128 is the first power of 2 above 100. Each answer is half the one before.

  7. Add 1ยฝ + 2ยผ. Then press Improper under Show as. What does the answer become, and how could you work that out without the tool?

    Teacher notes

    3ยพ, which is 15/4 as an improper fraction: 3 wholes are 12 quarters, plus 3 more quarters.

Decimals and recurring decimals
6 questions

  1. Smash 0.1 + 0.2. Many computer programs give 0.30000000000000004 for this. What does Number Smash give, and why?

    Teacher notes

    Exactly 0.3. The tool stores 0.1 and 0.2 as the fractions 1/10 and 2/10, so there is no rounding at all.

  2. Smash 1 รท 3 with Show as set to Decimals. What does the dot over the digit mean? Now multiply the answer by 3. Were you expecting 0.9999โ€ฆ?

    Teacher notes

    1 รท 3 = 0.3ฬ‡: the dot means the 3 repeats for ever. 0.3ฬ‡ ร— 3 = 1 exactly, which is another way of seeing that 0.9ฬ‡ = 1.

  3. Smash 1 รท 7, 2 รท 7 and 3 รท 7 (duplicate the 7s if you need more). Look at the dots. What do you notice about the repeating digits?

    Teacher notes

    1/7 = 0.1ฬ‡42857ฬ‡, 2/7 = 0.2ฬ‡85714ฬ‡ and 3/7 = 0.4ฬ‡28571ฬ‡. The same six digits repeat in the same cycle, starting at a different place. Dots go over the first and last repeating digit.

  4. Smash 0.25 โˆ’ ยผ. What do you get? Now type 2/4 into the box and add it. What does the counter show? Switch between Fractions and Decimals.

    Teacher notes

    0.25 โˆ’ ยผ = 0, because they are the same number. Typing 2/4 gives ยฝ straight away: the tool always simplifies. ยฝ and 0.5 are one counter shown two ways.

  5. Smash 1 รท 6 and 1 รท 9 as decimals, then 1 รท 8. Which ones stop and which ones repeat? Can you predict, from the denominator, whether a fraction will stop?

    Teacher notes

    1/6 = 0.16ฬ‡, 1/9 = 0.1ฬ‡ and 1/8 = 0.125. A fraction in its simplest form stops only when its denominator has no prime factors other than 2 and 5.

  6. Smash 100 รท 7, then multiply the answer by 7. Do you get exactly 100 back? What would a calculator that rounds 100 รท 7 to 14.2857 give?

    Teacher notes

    100 รท 7 = 14.2ฬ‡85714ฬ‡ and ร— 7 gives exactly 100, because the tool keeps it as 100/7. 14.2857 ร— 7 = 99.9999: rounding part-way through loses accuracy.

Negative numbers
6 questions

  1. Smash 5 + (โˆ’3). Then undo and smash 5 + (โˆ’8). How can you predict the sign of the answer when you add a positive and a negative?

    Teacher notes

    5 + (โˆ’3) = 2 and 5 + (โˆ’8) = โˆ’3. The answer takes the sign of the number further from zero.

  2. With โˆ’4 and โˆ’6, predict then try: โˆ’4 + (โˆ’6), โˆ’4 ร— (โˆ’6), โˆ’4 โˆ’ (โˆ’6) and โˆ’6 โˆ’ (โˆ’4). Which give a positive answer?

    Teacher notes

    โˆ’10, 24, 2 and โˆ’2. The product is always positive. The subtraction is positive one way round and negative the other.

  3. Try all four operations with 3 and โˆ’3, dragging the 3 onto the โˆ’3. Then try โˆ’3 รท 3. Which operation gives zero?

    Teacher notes

    3 + (โˆ’3) = 0, 3 โˆ’ (โˆ’3) = 6, 3 ร— (โˆ’3) = โˆ’9, 3 รท (โˆ’3) = โˆ’1 and โˆ’3 รท 3 = โˆ’1. A number plus its negative is always zero.

  4. A student says: “Two negatives make a positive.” Test โˆ’2 ร— (โˆ’5) and โˆ’3 ร— (โˆ’4). Then multiply the answer to โˆ’2 ร— (โˆ’5) by โˆ’3. Is the student always right?

    Teacher notes

    โˆ’2 ร— (โˆ’5) = 10 and โˆ’3 ร— (โˆ’4) = 12, the same as 2 ร— 5 and 3 ร— 4. But โˆ’2 ร— (โˆ’5) ร— (โˆ’3) = โˆ’30: an odd number of negative factors gives a negative product. And โˆ’2 + (โˆ’5) is โˆ’7, not positive.

  5. Smash โˆ’8 รท 2, then undo and smash 2 รท (โˆ’8). Then try โˆ’8 รท (โˆ’2). State the sign rules for division.

    Teacher notes

    โˆ’8 รท 2 = โˆ’4, 2 รท (โˆ’8) = โˆ’ยผ and โˆ’8 รท (โˆ’2) = 4. Division follows the same sign rules as multiplication: same signs give a positive, different signs a negative.

  6. Smash โˆ’3 ร— (โˆ’3) with ๐Ÿท Calculations on. A calculator given โˆ’3ยฒ usually says โˆ’9. Why do the two disagree?

    Teacher notes

    โˆ’3 ร— (โˆ’3) = 9. A calculator reads โˆ’3ยฒ as โˆ’(3ยฒ) = โˆ’9, because powers come before the minus sign. To square โˆ’3 you need brackets: (โˆ’3)ยฒ.

Zero, one and inverses
6 questions

  1. Smash 7 + 0, 7 โˆ’ 0, 7 ร— 0 and 0 โˆ’ 7 (undo between each). For which operation does 0 change nothing? For which does it take over?

    Teacher notes

    7 + 0 = 7 and 7 โˆ’ 0 = 7, so adding or subtracting zero changes nothing. 7 ร— 0 = 0 whatever the other number. 0 โˆ’ 7 = โˆ’7.

  2. Try 7 รท 0 (drag the 7 onto a 0). What does the box say? Then try 0 รท 7, and 0 รท 0. Why is one of these fine and the other two not?

    Teacher notes

    7 รท 0 has no answer, because no number ร— 0 makes 7. 0 รท 7 = 0. 0 รท 0 has no single answer, because every number ร— 0 makes 0. Both divisions by zero are undefined.

  3. Smash 8 ร— 1 and 8 รท 1, then 8 ร— (โˆ’1) and 8 รท (โˆ’1). What does multiplying by โˆ’1 do? Test it on a fraction and a negative number too.

    Teacher notes

    8 ร— 1 = 8 รท 1 = 8: 1 is the identity for ร— and รท. 8 ร— (โˆ’1) = 8 รท (โˆ’1) = โˆ’8. Multiplying by โˆ’1 always flips the sign: ยพ ร— (โˆ’1) = โˆ’ยพ and โˆ’5 ร— (โˆ’1) = 5.

  4. Multiply each number by the one next to it: 3 ร— โ…“, 4 ร— ยผ and โ…” ร— 3/2. What do you notice? What is the name for a pair like this? Then try 3 + โ…“.

    Teacher notes

    Every product is 1: the numbers are reciprocals of each other. 3 + โ…“ = 3โ…“, which is nothing special.

  5. Make 2 ร— 2 = 4. Duplicate the 4 (long-press, or โง‰) and multiply the two 4s. Keep squaring: how far can you get before the box says too big? Then start again from 3.

    Teacher notes

    2, 4, 16, 256, then 256 ร— 256 = 65536 is too big for the board (over 9999). From 3: 9, 81, 6561. Each squaring roughly doubles the number of digits.

  6. Smash 6 ร— 4, then multiply or divide the answer to get back to 6. Then smash 6 โˆ’ 3 and get back to 6 again. Which operation undoes which?

    Teacher notes

    6 ร— 4 = 24 and 24 รท 4 = 6. 6 โˆ’ 3 = 3 and 3 + 3 = 6. รท undoes ร—, and + undoes โˆ’: they are inverse operations.

Predictions and misconceptions
6 questions

  1. “Multiplying always makes a number bigger.” With ๐Ÿ™ˆ on, predict 6 ร— ยฝ and 6 รท ยฝ, then tap each answer to reveal it.

    Teacher notes

    6 ร— ยฝ = 3 and 6 รท ยฝ = 12. Multiplying by a number between 0 and 1 makes it smaller, and dividing by one makes it bigger.

  2. Many students say 5 รท ยฝ = 2ยฝ. Predict, then reveal. Explain the answer as “how many halves fit into 5?”

    Teacher notes

    5 รท ยฝ = 10: there are 10 halves in 5. 2ยฝ is 5 ร— ยฝ or 5 รท 2.

  3. “Subtracting always makes a number smaller.” Predict 10 โˆ’ (โˆ’2), then reveal it.

    Teacher notes

    10 โˆ’ (โˆ’2) = 12. Subtracting a negative makes the number bigger: taking away a debt of 2 leaves you 2 better off.

  4. Predict ยพ รท ยผ before you reveal it. Common wrong answers are 3/16 and ยพ.

    Teacher notes

    ยพ รท ยผ = 3, because ยผ fits into ยพ three times. 3/16 is ยพ ร— ยผ.

  5. Predict 0.5 ร— 0.5 and 0.6 รท 0.2 with decimals showing, then reveal them. Popular wrong answers are 2.5 and 0.3.

    Teacher notes

    0.5 ร— 0.5 = 0.25 (a half of a half is a quarter), and 0.6 รท 0.2 = 3 (0.2 fits into 0.6 three times).

  6. Predict โˆ’5 + 3, then reveal it. Some students give โˆ’8. What mistake leads to that?

    Teacher notes

    โˆ’5 + 3 = โˆ’2. โˆ’8 comes from adding the sizes and keeping the minus sign. On a number line, start at โˆ’5 and move 3 to the right.

Challenge mode
9 questions

  1. Make each target using all of 1, 2, 3 and 4. A target only counts when one counter is left. What happens if you make 10 after two smashes, with a counter still unused?

    Teacher notes

    With four numbers it takes exactly three smashes to use them all, and only then does a target count. 10 = 1 + 2 + 3 + 4 and 24 = 1 ร— 2 ร— 3 ร— 4. One way for each of the others: 7 = (2 โˆ’ 1) ร— (3 + 4), โˆ’5 = 4 โˆ’ 3 ร— (1 + 2), ยฝ = 3 รท (4 + 1 ร— 2).

  2. Press ๐ŸŽฒ 1 to 10. Before you start, predict which of the five targets will be hardest for you. Then try them. Were the labels right for you?

    Teacher notes

    The labels come from the simplest route the tool finds: + scores 1, โˆ’ and ร— score 2, รท scores 4, plus extra for negative or fraction steps. Students often find a “Hard” target easy because they spot a different route.

  3. Make 24 with 3, 5, 7 and 8. Work backwards: what could the last smash be? 3 ร— 8? 4 ร— 6? 21 + 3? Then look for ways to make the numbers you need.

    Teacher notes

    One way: 3 ร— 7 + 8 โˆ’ 5 = 24 (21 + 3). Working backwards from a likely last step is a good strategy for any target.

  4. Make 24 with 8, 3, 8 and 3, using all four. This one is famous for being hard. Tap the target only when you have tried for a while.

    Teacher notes

    8 รท (3 โˆ’ 8 รท 3) = 24, because 3 โˆ’ 8/3 = 1/3 and 8 รท 1/3 = 24. Whole-number thinking won’t find it: it needs a fraction on the way.

  5. Make 24 with 1, 5, 5 and 5. Hint: you may need a fraction along the way.

    Teacher notes

    5 ร— (5 โˆ’ 1 รท 5) = 24, because 5 โˆ’ โ…• = 4โ…˜ and 5 ร— 4โ…˜ = 24.

  6. Press ๐Ÿ“Š What can be made? for 1, 2, 3 and 4. Predict how many of the whole numbers from 1 to 100 can be made, then tap cells to check, or reveal them all.

    Teacher notes

    31 of them: every number from 1 to 28, plus 30, 32 and 36. 29 is the smallest that can’t be made, and 36 = (1 + 2) ร— 3 ร— 4 is the largest.

  7. Open ๐Ÿ“Š What can be made? for 3, 5, 7 and 8 and count how many of 1 to 100 can be made. Then press โœŽ Change numbers, choose Use any of them and make the targets again. How many more can be made now? Why?

    Teacher notes

    65 using all four, and 83 using any of them. Being allowed to leave numbers out can only add targets, never remove them.

  8. With 2, 3, 4 and 5, type your own targets into the Own target box: try 100, 119 and 120. Predict which can be made before you tap each one.

    Teacher notes

    100 = (2 + 3) ร— 4 ร— 5 and 120 = 2 ร— 3 ร— 4 ร— 5 can be made, but 119 can’t. 120 is the largest number these four can make.

  9. Make the targets for any four numbers, then press ๐Ÿ–จ to print a sheet of six puzzles like it, with answers on a separate page. Swap sheets with a partner. Did you find the same solutions as the answer page?

    Teacher notes

    The answer page shows one way to make each target; there are often several. Comparing routes is a good discussion: which used fewer or easier steps?

Open investigations
5 questions

  1. Using four 1s and all three smashes, how many different answers can you make? Not just whole numbers: use รท and โˆ’ too. Work systematically and keep a list.

    Teacher notes

    11 different answers: โˆ’2, โˆ’1, โˆ’ยฝ, 0, โ…“, ยฝ, 1, 1ยฝ, 2, 3 and 4. For example โ…“ = 1 รท (1 + 1 + 1) and 1ยฝ = 1 + 1 รท (1 + 1).

  2. With four 2s, which whole numbers from 1 to 10 can you make using all of them? Predict which are impossible, then check with ๐Ÿ“Š What can be made?.

    Teacher notes

    Every number from 1 to 10 except 7 and 9. From 1 to 100, only 1, 2, 3, 4, 5, 6, 8, 10, 12 and 16 can be made.

  3. Which four numbers from 1 to 10 make the most whole numbers from 1 to 100? Try a few sets with ๐Ÿ“Š What can be made?. Which sets are worst?

    Teacher notes

    The best sets make 78 of the 100, for example 2, 3, 8, 9 and 5, 6, 7, 10. Four 1s are the worst, with only 4. Sets with very different numbers tend to do best.

  4. A student claims: “If you double the first number, the answer doubles.” Test it for all four operations, using 3 and 6 as the first number and 5 as the second.

    Teacher notes

    It is true for ร— and รท (3 ร— 5 = 15, 6 ร— 5 = 30; 3 รท 5 = โ…—, 6 รท 5 = 1โ…•) and false for + and โˆ’ (3 + 5 = 8 but 6 + 5 = 11; 3 โˆ’ 5 = โˆ’2 but 6 โˆ’ 5 = 1).

  5. Design your own Number Smash investigation. Choose the mode, the starting numbers and three questions for a partner, and test them yourself first. Use ๐Ÿ”— to share the set-up as a link.

    Teacher notes

    Good student investigations usually change one thing at a time (one number, or one operation) and ask for a prediction first. The link opens the tool with the same numbers.