Question

multiply by 2s
skip count by 2s.
0 → 2 → 4 → → 8 → 10 → 12 → 14 → 16 → 18 → 20
complete the input/output table.
input 2 6 8 3 7 10 5 1 0 4
output
rule: multiply by 2
write the number missing from each fact family.
compare. <, >, or =
2×3 8
2×7 2×9
20 2×10
2×6 2×5
what fact is shown by the illustration?

Explanation:

Step1: Complete skip - counting

The sequence is skip - counting by 2s. After 4, the next number is 6.

Step2: Complete input/output table

Multiply each input number by 2.
For input 2, output is \(2\times2 = 4\); for input 6, output is \(6\times2=12\); for input 8, output is \(8\times2 = 16\); for input 3, output is \(3\times2=6\); for input 7, output is \(7\times2 = 14\); for input 10, output is \(10\times2=20\); for input 5, output is \(5\times2 = 10\); for input 1, output is \(1\times2=2\); for input 0, output is \(0\times2 = 0\); for input 4, output is \(4\times2=8\).

Step3: Find missing numbers in fact - families

For the first triangle with sides 7, 2, and 12, assume the operation is addition or subtraction. \(7 + 2=9
eq12\), \(7\times2 = 14
eq12\), \(12-7 = 5
eq2\), \(12 - 2=10
eq7\). If we consider multiplication - related fact - families, there is an error in this triangle's setup.
For the second triangle with sides 5, 2, assume the missing number \(x\) and if we consider addition \(5 + 2=7\), if multiplication \(5\times2 = 10\). Since no operation is clearly defined, if we assume multiplication, the number could be 10.
For the third triangle with sides 12, 6, if we assume division or multiplication, \(12\div6=2\) or \(6\times2 = 12\), the missing number is 2.

Step4: Compare

For \(2\times3=6\), so \(2\times3<8\); for \(2\times7 = 14\) and \(2\times9=18\), so \(2\times7<2\times9\); for \(2\times10 = 20\), so \(20 = 2\times10\); for \(2\times6=12\) and \(2\times5 = 10\), so \(2\times6>2\times5\).

Step5: Analyze illustration

The illustration shows 4 pentagons with 2 dots in each, so the fact is \(4\times2=8\).

Answer:

Skip - counting: 6
Input/Output table: 4, 12, 16, 6, 14, 20, 10, 2, 0, 8
Missing numbers in fact - families: (error in first triangle), 10 (assuming multiplication), 2
Comparisons: <, <, =, >
Illustration fact: \(4\times2 = 8\)