MacGill | LEA Symbols - Good-Lite® Charts - Good-Lite® Cabinets ... - Free Printable
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Step-by-step solution for: MacGill | LEA Symbols - Good-Lite® Charts - Good-Lite® Cabinets ...
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Show Answer Key & Explanations
Step-by-step solution for: MacGill | LEA Symbols - Good-Lite® Charts - Good-Lite® Cabinets ...
- The top row has 4 symbols: heart, circle, house, square.
- The second row has the same 4 symbols but in a different order: house, square, heart, circle.
- The third row has the same 4 symbols again, reordered: heart, circle, square, house.
- The fourth row is incomplete and shows: circle, heart, [blank], [blank].
- Comparing the pattern, each row contains the same set of 4 unique symbols, just rearranged.
- Looking at the sequence of positions:
- Row 1: H C Hs S
- Row 2: Hs S H C
- Row 3: H C S Hs
- Row 4: C H ? ?
- Notice that Row 2 is Row 1 shifted left by two positions (Hs S H C).
- Row 3 is not a simple shift of Row 2; instead, it appears to be Row 1 with the last two symbols swapped: H C S Hs.
- Alternatively, observe the position of each symbol across rows:
- Heart: pos1 → pos3 → pos1 → pos2
- Circle: pos2 → pos4 → pos2 → pos1
- House: pos3 → pos1 → pos4 → ?
- Square: pos4 → pos2 → pos3 → ?
- Another approach: look at the pattern of the first two symbols in each row:
- Row1: H C
- Row2: Hs S
- Row3: H C
- Row4: C H
- It seems Row3 repeats Row1’s first two symbols, and Row4 starts with the reverse of Row1’s first two.
- But perhaps the simplest consistent pattern is that each row is a cyclic shift or permutation.
- Let’s consider the order of appearance per column:
- Col1: H, Hs, H, C
- Col2: C, S, C, H
- Col3: Hs, H, S, ?
- Col4: S, C, Hs, ?
- In col3: Hs → H → S → ?
- If we follow the sequence: Hs, H, S — these are the 3rd, 1st, 4th symbols from row1.
- Not obvious.
- Try this: Each row uses all 4 symbols. Row4 already has circle and heart, so missing are house and square.
- Now, what order? Look at the last two rows:
- Row3 ends with S, Hs
- Row4 starts with C, H
- Perhaps the pattern is that row n+1 is row n shifted right by 1, wrapping around.
- Row1: H C Hs S
- Shift right: S H C Hs → but row2 is Hs S H C — not matching.
- Shift left by 2: H C Hs S → Hs S H C — matches row2.
- Row2: Hs S H C → shift left by 2: H C Hs S — but row3 is H C S Hs — not matching.
- Row3: H C S Hs — if we shift row2 left by 2: Hs S H C → H C Hs S — doesn’t match row3.
- Another idea: maybe the pattern is alternating between two arrangements.
- Row1: H C Hs S
- Row2: Hs S H C (which is row1 reversed? No, reverse would be S Hs C H)
- Row3: H C S Hs — similar to row1 but last two swapped.
- Let’s look at the fourth row: it starts with C H, which are the first two of row3 but in reverse order.
- Row3 starts with H C, row4 starts with C H — reverse.
- Then perhaps row4 should end with the reverse of row3’s last two: row3 ends with S Hs, so reverse is Hs S.
- So row4: C H Hs S
- Check if that makes sense: symbols are C, H, Hs, S — all present, no duplicates.
- Also, compare to row2: Hs S H C — which is different.
- But let’s see if there’s a column pattern:
- Col1: H, Hs, H, C
- Col2: C, S, C, H
- Col3: Hs, H, S, Hs
- Col4: S, C, Hs, S
- Col3: Hs, H, S, Hs — repeats Hs?
- Col4: S, C, Hs, S — repeats S?
- That might be acceptable if it’s a pattern.
- Alternatively, perhaps the intended pattern is that each row is a rotation.
- Let’s try assigning numbers: let H=1, C=2, Hs=3, S=4.
- Row1: 1 2 3 4
- Row2: 3 4 1 2
- Row3: 1 2 4 3
- Row4: 2 1 ? ?
- Row2 is row1 +2 mod 4 (with 1-based indexing: 1→3, 2→4, 3→1, 4→2)
- Row3 is row1 with last two swapped: 1 2 4 3
- Row4 starts with 2 1, which is swap of first two of row1.
- Then perhaps row4 should be swap of first two and swap of last two of row1: so 2 1 4 3
- That would be C H S Hs
- But earlier I thought Hs S.
- Let’s see which one fits better.
- If row4 is C H S Hs, then:
- Col1: 1,3,1,2
- Col2: 2,4,2,1
- Col3: 3,1,4,4 — duplicate 4
- Col4: 4,2,3,3 — duplicate 3
- If row4 is C H Hs S, then:
- Col1: 1,3,1,2
- Col2: 2,4,2,1
- Col3: 3,1,4,3 — duplicate 3
- Col4: 4,2,3,4 — duplicate 4
- Both have duplicates in columns, which is fine since no rule says columns must be unique.
- But perhaps there's a better pattern.
- Look at the image: the fourth row has two blanks after C H.
- Now, notice that in row3, the symbols are H C S Hs.
- Row4 starts with C H, which is the reverse of the first two of row3.
- If we reverse the entire row3: Hs S C H — but row4 starts with C H, not Hs S.
- Another idea: perhaps the pattern is that row n and row n+2 are related.
- Row1 and row3: both start with H C.
- Row2 and row4: row2 starts with Hs S, row4 starts with C H — not obviously related.
- Let’s consider the possibility that the pattern is simply that each row contains all four symbols, and the arrangement is arbitrary except for the given ones.
- But that can't be, because we need to fill the blanks.
- Perhaps the key is in the lower part of the image, but the user said not to describe the image, and the task is likely for the top part.
- Re-examining: the fourth row is "circle, heart, [blank], [blank]".
- And the only symbols are heart, circle, house, square.
- So the missing two are house and square.
- Now, what order? Let's look at the sequence of the last two symbols in each row:
- Row1: house, square
- Row2: heart, circle
- Row3: square, house
- Row4: ?, ?
- Row1 last two: Hs S
- Row2 last two: H C
- Row3 last two: S Hs
- So it's like Hs S, then H C, then S Hs.
- Not clear.
- Notice that row3 last two are the reverse of row1 last two.
- Row2 last two are the first two of row1.
- For row4, if we follow row2 last two = row1 first two, then row4 last two might be row3 first two, which are H C.
- But row4 already has C H as first two, so last two would be H C — but that would make the row C H H C — duplicate symbols, not allowed.
- So not that.
- Perhaps the pattern is that the row is determined by shifting the previous row.
- From row1 to row2: H C Hs S -> Hs S H C — this is a left shift by 2.
- From row2 to row3: Hs S H C -> H C S Hs — this is not a simple shift.
- Hs S H C to H C S Hs: position 1: Hs->H, 2:S->C, 3:H->S, 4:C->Hs.
- It's like swapping 1 and 3, and 2 and 4? Hs and H swap, S and C swap? But Hs and H are different.
- Let's list the changes:
- Pos1: Hs -> H
- Pos2: S -> C
- Pos3: H -> S
- Pos4: C -> Hs
- So it's a cycle: Hs->H->S->C->Hs? Let's see: Hs at pos1 goes to pos3 in row3? No, in row3 pos1 is H.
- Perhaps it's a different pattern.
- Given the time, and since the most reasonable guess is that the fourth row should have the remaining two symbols, and based on the first two being C H, and to avoid duplication, the last two should be Hs and S.
- Now, which order? Let's assume that the pattern is that the row is sorted or something, but not.
- Another idea: look at the very bottom of the image, but the user said not to describe the image, and the task is likely self-contained in the top part.
- Perhaps the answer is house and square in that order, or square and house.
- Let's try to see if there's a mathematical pattern.
- Assign values: H=1, C=2, Hs=3, S=4.
- Row1: 1,2,3,4 sum=10
- Row2: 3,4,1,2 sum=10
- Row3: 1,2,4,3 sum=10
- Row4: 2,1,?,? sum must be 10, so ?+? =7, and the only pair from {3,4} is 3+4=7, so Hs and S.
- So the last two are 3 and 4, i.e., house and square.
- Now, which order? The row is 2,1,3,4 or 2,1,4,3.
- In row3, it was 1,2,4,3 — so last two are 4,3.
- In row1, last two are 3,4.
- In row2, last two are 1,2.
- No clear pattern for order.
- But in row4, if we put 3,4, then it's C H Hs S.
- If we put 4,3, then C H S Hs.
- Now, look at the column for position 3:
- Row1: 3
- Row2: 1
- Row3: 4
- Row4: ?
- 3,1,4 — perhaps next is 2, but 2 is already used in row4 pos2.
- Or 3,1,4,2 — but 2 is not available for pos3.
- Similarly, position 4: 4,2,3,? — could be 1, but 1 is used.
- So no help.
- Perhaps the intended answer is to continue the pattern of row3.
- Row3 is H C S Hs.
- Row4 starts with C H, which is the reverse of the first two of row3.
- Then perhaps the last two should be the reverse of the last two of row3: row3 last two are S Hs, reverse is Hs S.
- So row4: C H Hs S.
- This seems plausible.
- Moreover, in the image, the fourth row has two blanks, and if we put house then square, it might be correct.
- I think that's the best guess.
- So the missing symbols are house and square, in that order.
- Therefore, the answer is house, square.
- The second row has the same 4 symbols but in a different order: house, square, heart, circle.
- The third row has the same 4 symbols again, reordered: heart, circle, square, house.
- The fourth row is incomplete and shows: circle, heart, [blank], [blank].
- Comparing the pattern, each row contains the same set of 4 unique symbols, just rearranged.
- Looking at the sequence of positions:
- Row 1: H C Hs S
- Row 2: Hs S H C
- Row 3: H C S Hs
- Row 4: C H ? ?
- Notice that Row 2 is Row 1 shifted left by two positions (Hs S H C).
- Row 3 is not a simple shift of Row 2; instead, it appears to be Row 1 with the last two symbols swapped: H C S Hs.
- Alternatively, observe the position of each symbol across rows:
- Heart: pos1 → pos3 → pos1 → pos2
- Circle: pos2 → pos4 → pos2 → pos1
- House: pos3 → pos1 → pos4 → ?
- Square: pos4 → pos2 → pos3 → ?
- Another approach: look at the pattern of the first two symbols in each row:
- Row1: H C
- Row2: Hs S
- Row3: H C
- Row4: C H
- It seems Row3 repeats Row1’s first two symbols, and Row4 starts with the reverse of Row1’s first two.
- But perhaps the simplest consistent pattern is that each row is a cyclic shift or permutation.
- Let’s consider the order of appearance per column:
- Col1: H, Hs, H, C
- Col2: C, S, C, H
- Col3: Hs, H, S, ?
- Col4: S, C, Hs, ?
- In col3: Hs → H → S → ?
- If we follow the sequence: Hs, H, S — these are the 3rd, 1st, 4th symbols from row1.
- Not obvious.
- Try this: Each row uses all 4 symbols. Row4 already has circle and heart, so missing are house and square.
- Now, what order? Look at the last two rows:
- Row3 ends with S, Hs
- Row4 starts with C, H
- Perhaps the pattern is that row n+1 is row n shifted right by 1, wrapping around.
- Row1: H C Hs S
- Shift right: S H C Hs → but row2 is Hs S H C — not matching.
- Shift left by 2: H C Hs S → Hs S H C — matches row2.
- Row2: Hs S H C → shift left by 2: H C Hs S — but row3 is H C S Hs — not matching.
- Row3: H C S Hs — if we shift row2 left by 2: Hs S H C → H C Hs S — doesn’t match row3.
- Another idea: maybe the pattern is alternating between two arrangements.
- Row1: H C Hs S
- Row2: Hs S H C (which is row1 reversed? No, reverse would be S Hs C H)
- Row3: H C S Hs — similar to row1 but last two swapped.
- Let’s look at the fourth row: it starts with C H, which are the first two of row3 but in reverse order.
- Row3 starts with H C, row4 starts with C H — reverse.
- Then perhaps row4 should end with the reverse of row3’s last two: row3 ends with S Hs, so reverse is Hs S.
- So row4: C H Hs S
- Check if that makes sense: symbols are C, H, Hs, S — all present, no duplicates.
- Also, compare to row2: Hs S H C — which is different.
- But let’s see if there’s a column pattern:
- Col1: H, Hs, H, C
- Col2: C, S, C, H
- Col3: Hs, H, S, Hs
- Col4: S, C, Hs, S
- Col3: Hs, H, S, Hs — repeats Hs?
- Col4: S, C, Hs, S — repeats S?
- That might be acceptable if it’s a pattern.
- Alternatively, perhaps the intended pattern is that each row is a rotation.
- Let’s try assigning numbers: let H=1, C=2, Hs=3, S=4.
- Row1: 1 2 3 4
- Row2: 3 4 1 2
- Row3: 1 2 4 3
- Row4: 2 1 ? ?
- Row2 is row1 +2 mod 4 (with 1-based indexing: 1→3, 2→4, 3→1, 4→2)
- Row3 is row1 with last two swapped: 1 2 4 3
- Row4 starts with 2 1, which is swap of first two of row1.
- Then perhaps row4 should be swap of first two and swap of last two of row1: so 2 1 4 3
- That would be C H S Hs
- But earlier I thought Hs S.
- Let’s see which one fits better.
- If row4 is C H S Hs, then:
- Col1: 1,3,1,2
- Col2: 2,4,2,1
- Col3: 3,1,4,4 — duplicate 4
- Col4: 4,2,3,3 — duplicate 3
- If row4 is C H Hs S, then:
- Col1: 1,3,1,2
- Col2: 2,4,2,1
- Col3: 3,1,4,3 — duplicate 3
- Col4: 4,2,3,4 — duplicate 4
- Both have duplicates in columns, which is fine since no rule says columns must be unique.
- But perhaps there's a better pattern.
- Look at the image: the fourth row has two blanks after C H.
- Now, notice that in row3, the symbols are H C S Hs.
- Row4 starts with C H, which is the reverse of the first two of row3.
- If we reverse the entire row3: Hs S C H — but row4 starts with C H, not Hs S.
- Another idea: perhaps the pattern is that row n and row n+2 are related.
- Row1 and row3: both start with H C.
- Row2 and row4: row2 starts with Hs S, row4 starts with C H — not obviously related.
- Let’s consider the possibility that the pattern is simply that each row contains all four symbols, and the arrangement is arbitrary except for the given ones.
- But that can't be, because we need to fill the blanks.
- Perhaps the key is in the lower part of the image, but the user said not to describe the image, and the task is likely for the top part.
- Re-examining: the fourth row is "circle, heart, [blank], [blank]".
- And the only symbols are heart, circle, house, square.
- So the missing two are house and square.
- Now, what order? Let's look at the sequence of the last two symbols in each row:
- Row1: house, square
- Row2: heart, circle
- Row3: square, house
- Row4: ?, ?
- Row1 last two: Hs S
- Row2 last two: H C
- Row3 last two: S Hs
- So it's like Hs S, then H C, then S Hs.
- Not clear.
- Notice that row3 last two are the reverse of row1 last two.
- Row2 last two are the first two of row1.
- For row4, if we follow row2 last two = row1 first two, then row4 last two might be row3 first two, which are H C.
- But row4 already has C H as first two, so last two would be H C — but that would make the row C H H C — duplicate symbols, not allowed.
- So not that.
- Perhaps the pattern is that the row is determined by shifting the previous row.
- From row1 to row2: H C Hs S -> Hs S H C — this is a left shift by 2.
- From row2 to row3: Hs S H C -> H C S Hs — this is not a simple shift.
- Hs S H C to H C S Hs: position 1: Hs->H, 2:S->C, 3:H->S, 4:C->Hs.
- It's like swapping 1 and 3, and 2 and 4? Hs and H swap, S and C swap? But Hs and H are different.
- Let's list the changes:
- Pos1: Hs -> H
- Pos2: S -> C
- Pos3: H -> S
- Pos4: C -> Hs
- So it's a cycle: Hs->H->S->C->Hs? Let's see: Hs at pos1 goes to pos3 in row3? No, in row3 pos1 is H.
- Perhaps it's a different pattern.
- Given the time, and since the most reasonable guess is that the fourth row should have the remaining two symbols, and based on the first two being C H, and to avoid duplication, the last two should be Hs and S.
- Now, which order? Let's assume that the pattern is that the row is sorted or something, but not.
- Another idea: look at the very bottom of the image, but the user said not to describe the image, and the task is likely self-contained in the top part.
- Perhaps the answer is house and square in that order, or square and house.
- Let's try to see if there's a mathematical pattern.
- Assign values: H=1, C=2, Hs=3, S=4.
- Row1: 1,2,3,4 sum=10
- Row2: 3,4,1,2 sum=10
- Row3: 1,2,4,3 sum=10
- Row4: 2,1,?,? sum must be 10, so ?+? =7, and the only pair from {3,4} is 3+4=7, so Hs and S.
- So the last two are 3 and 4, i.e., house and square.
- Now, which order? The row is 2,1,3,4 or 2,1,4,3.
- In row3, it was 1,2,4,3 — so last two are 4,3.
- In row1, last two are 3,4.
- In row2, last two are 1,2.
- No clear pattern for order.
- But in row4, if we put 3,4, then it's C H Hs S.
- If we put 4,3, then C H S Hs.
- Now, look at the column for position 3:
- Row1: 3
- Row2: 1
- Row3: 4
- Row4: ?
- 3,1,4 — perhaps next is 2, but 2 is already used in row4 pos2.
- Or 3,1,4,2 — but 2 is not available for pos3.
- Similarly, position 4: 4,2,3,? — could be 1, but 1 is used.
- So no help.
- Perhaps the intended answer is to continue the pattern of row3.
- Row3 is H C S Hs.
- Row4 starts with C H, which is the reverse of the first two of row3.
- Then perhaps the last two should be the reverse of the last two of row3: row3 last two are S Hs, reverse is Hs S.
- So row4: C H Hs S.
- This seems plausible.
- Moreover, in the image, the fourth row has two blanks, and if we put house then square, it might be correct.
- I think that's the best guess.
- So the missing symbols are house and square, in that order.
- Therefore, the answer is house, square.
Parent Tip: Review the logic above to help your child master the concept of lea eye chart printable.