Multiplying together three numbers - Master The Curriculum - Free Printable
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Step-by-step solution for: Multiplying together three numbers - Master The Curriculum
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Show Answer Key & Explanations
Step-by-step solution for: Multiplying together three numbers - Master The Curriculum
Let’s work through each part of the worksheet step by step.
---
Top Left Box (Green Squares):
We see 3 groups of green squares. Each group has 8 squares (2 rows × 4 columns).
So:
→ I have 3 lots of 8, 3 times? Wait — that doesn’t make sense. Let’s read carefully.
Actually, looking at the structure:
The sentence says: “I have ___ lots of ___, 3 times.”
But visually, we have 3 separate groups, and each group has 8 squares.
That means: We are multiplying 8 (per group) by 3 (number of groups). But the phrasing is tricky.
Wait — let’s look at the equation below:
“__ x __ x __ = ____”
and then “8 x 3 = ____”
Ah! So they’re breaking it down as:
First, count how many in one group → 8
Then, how many groups → 3
So total = 8 × 3 = 24
But the first blank says: “I have ___ lots of ___, 3 times.”
This seems to be saying: You have some number of items, and you repeat that set 3 times.
Looking again: There are 3 identical sets. Each set has 8 squares.
So perhaps it should be:
“I have 8 lots of 1, 3 times”? No, that’s not right.
Wait — maybe it’s misphrased. Let’s think differently.
Perhaps it’s meant to say:
“I have [number of groups] lots of [items per group], repeated [how many times?]”
But the “3 times” likely refers to the number of groups.
Actually, re-reading:
“I have ___ lots of ___, 3 times.”
Maybe it’s: You take a certain amount, and do it 3 times.
In this case, each “lot” is 8 squares, and you do it 3 times → so 3 lots of 8.
But the sentence says “___ lots of ___, 3 times” — which might mean: you have X lots of Y, and you repeat that whole thing 3 times? That would be overcomplicating.
Alternatively, perhaps it’s a typo or poor phrasing, and it should be:
“I have 3 lots of 8.”
Because there are 3 groups, each with 8.
And then the multiplication is 8 × 3 = 24.
Similarly, for the next box.
Let me check the second box to compare.
---
Top Right Box (Green Squares – Different Arrangement):
There are 2 groups. Each group has 12 squares (3 rows × 4 columns).
Sentence: “I have ___ lots of ___, 2 times.”
Again, probably means: 2 groups of 12.
Equation: “__ x __ x __ = ____” and then “___ x 2 = ____”
So likely: 12 × 2 = 24
Same answer as before? Interesting.
Wait — top left was 3 groups of 8 = 24
Top right is 2 groups of 12 = 24
Okay, consistent.
Now back to top left:
If we fill:
“I have 3 lots of 8, 3 times.” — but that would imply 3 × 8 × 3 = 72, which is wrong.
No — I think the “3 times” is redundant or misplaced. Probably it should just be “I have 3 lots of 8.”
But since the worksheet says “3 times”, maybe it’s trying to say: you have a set of 8, and you have it 3 times → so 3 lots of 8.
Yes, that makes sense.
So:
“I have 3 lots of 8” — and the “3 times” might be emphasizing repetition, but it’s already included in “3 lots”.
To avoid confusion, let’s follow the pattern from the equations.
For top left:
They give “8 x 3 = ___” → so 24
And the triple multiplication: probably 1 x 8 x 3 = 24? Or 8 x 1 x 3? Doesn't matter order.
But typically, we write: number of groups × size of each group.
So for top left: 3 groups × 8 per group = 24
But the blank is “__ x __ x __” — three blanks. Why three?
Oh! Because the objective is “multiplying together three numbers”.
So perhaps they want us to break it into three factors.
For example, in top left: each group is 8, which is 2×4, so maybe 2 × 4 × 3 = 24
Similarly, top right: each group is 12, which is 3×4, so 3 × 4 × 2 = 24
That makes sense!
Let me verify.
Top left:
Groups: 3
Each group: 2 rows × 4 columns = 8
So total: 2 × 4 × 3 = 24
Yes.
Top right:
Groups: 2
Each group: 3 rows × 4 columns = 12
So 3 × 4 × 2 = 24
Perfect.
Now middle row.
---
Middle Left (Blue Circles):
There are 5 groups. Each group has 4 circles (arranged in a cross or something — actually, looking: each cluster has 4 dots).
Count: yes, 5 clusters, each with 4 dots.
Sentence: “I have ___ lots of ___, 5 times.”
Probably: 5 lots of 4.
Triple multiplication: 4 can be broken? 4 is 2×2, so 2 × 2 × 5 = 20
Given equation: “4 x 5 = ___” → 20
So triple: 2 × 2 × 5 = 20
Or 4 × 1 × 5, but better to use factors.
Since 4 = 2×2, use that.
---
Middle Right (Yellow Dots):
3 groups. Each group has 6 dots? Let's count.
Each yellow group: looks like 2 rows of 3? Or arranged differently.
Actually, counting: each group has 6 dots (e.g., triangle shape with 3 on bottom, 2 middle, 1 top? Wait no — in image, it seems each group has 6 dots.
Confirm: first group: 3 on top row, 2 middle, 1 bottom? That’s 6. Yes.
So 3 groups of 6.
Sentence: “I have ___ lots of ___, 3 times.” → 3 lots of 6.
Triple multiplication: 6 = 2×3, so 2 × 3 × 3 = 18
Given: “___ x 3 = ___” → 6 × 3 = 18
Good.
---
Bottom Left (Pink Stars):
2 groups. Each group has 9 stars (3×3 grid).
Sentence: “I have ___ lots of ___, 2 times.” → 2 lots of 9.
Triple multiplication: 9 = 3×3, so 3 × 3 × 2 = 18
Given: “9 x 2 = ___” → 18
---
Bottom Right (Red Hearts):
4 groups. Each group has 4 hearts (2×2).
Sentence: “I have __ lots of __, 4 times.” → 4 lots of 4.
Triple multiplication: 4 = 2×2, so 2 × 2 × 4 = 16
Given: “___ x 4 = ___” → 4 × 4 = 16
---
Now, filling all blanks.
Start with Top Left:
- I have 3 lots of 8, 3 times. → But wait, if we say "3 lots of 8", the "3 times" is redundant. Perhaps it's a mistake, or perhaps it's "I have 1 lot of 8, 3 times" meaning you take 8 three times.
Actually, rereading the sentence: “I have ___ lots of ___, 3 times.”
This is ambiguous. But given that later it says “8 x 3”, and the triple multiplication, I think the intended meaning is:
You have a quantity, and you repeat it 3 times.
In top left, each "lot" is 8, and you have it 3 times → so 3 lots of 8.
But the phrase "___ lots of ___, 3 times" might mean: the number of lots is X, each lot has Y items, and you do this X times? Confusing.
Alternative interpretation: Perhaps "I have A lots of B, C times" means A * B * C.
But in top left, if A=3, B=8, C=3, then 3*8*3=72, but actual total is 24, so no.
I think the "3 times" is meant to indicate the number of groups, so it's poorly worded.
Looking at the bottom right: “I have __ lots of __, 4 times.” and there are 4 groups, each with 4 hearts, so likely "4 lots of 4".
Similarly, top left: 3 groups of 8 → "3 lots of 8"
But why say "3 times"? Maybe it's a template error.
Perhaps "times" here means "groups", so "I have 3 lots of 8" and the "3 times" is extra.
To resolve, let's look at the triple multiplication blank.
For top left: they expect three numbers multiplied to get 24.
As I thought earlier: 2 × 4 × 3 = 24, since each group is 2x4=8, and 3 groups.
Similarly, for the sentence, perhaps it's "I have 3 lots of (2x4)", but that's not helping.
Another idea: perhaps the first blank is the number of repetitions, second is the size of each repetition.
So "I have 3 lots of 8" — and the "3 times" is redundant or emphasizes.
I think for consistency, we'll go with:
Top Left:
- I have 3 lots of 8
- Triple: 2 x 4 x 3 = 24 (since 8=2x4)
- 8 x 3 = 24
But the sentence has "3 times" at the end, so if we put 3 and 8, it becomes "I have 3 lots of 8, 3 times" which is odd.
Perhaps it's "I have 1 lot of 8, 3 times" meaning you start with 8 and add it 3 times.
That could work: 1 lot of 8, repeated 3 times → total 24.
Then triple multiplication: 1 x 8 x 3 = 24
Similarly for others.
Let me test with top right.
Top right: 2 groups of 12.
If "I have 1 lot of 12, 2 times" → 1x12x2=24
Triple: 3x4x2=24 (since 12=3x4)
Yes.
Middle left: 5 groups of 4.
"I have 1 lot of 4, 5 times" → 1x4x5=20
Triple: 2x2x5=20 (4=2x2)
Middle right: 3 groups of 6.
"I have 1 lot of 6, 3 times" → 1x6x3=18
Triple: 2x3x3=18 (6=2x3)
Bottom left: 2 groups of 9.
"I have 1 lot of 9, 2 times" → 1x9x2=18
Triple: 3x3x2=18 (9=3x3)
Bottom right: 4 groups of 4.
"I have 1 lot of 4, 4 times" → 1x4x4=16
Triple: 2x2x4=16 (4=2x2)
This makes sense! The "lots of" is singular in the sense that you have one unit of that size, repeated multiple times.
So the first blank is always 1, because you're taking one group of that size, and repeating it the specified number of times.
In the sentence: "I have ___ lots of ___, N times." — the "N times" is the repetition count, and "lots of" might be misleading, but if we put 1 in the first blank, it works.
For example, "I have 1 lot of 8, 3 times" means you have a single set of 8, and you have it 3 times → total 24.
Yes.
Whereas if you put 3 in the first blank, "I have 3 lots of 8, 3 times" would be 3*8*3=72, wrong.
So definitely, first blank should be 1.
Confirming with the given equations.
In top left, they have "8 x 3 = ___" which is correct for 8 per group times 3 groups.
And triple multiplication is additional factorization.
So for all, the "I have" sentence should have 1 in the first blank.
Now, writing answers.
---
Final Answers per box:
Top Left:
- I have 1 lots of 8, 3 times.
- 2 x 4 x 3 = 24 (or any order, but 2,4,3 since 8=2x4)
- 8 x 3 = 24
Top Right:
- I have 1 lots of 12, 2 times.
- 3 x 4 x 2 = 24 (12=3x4)
- 12 x 2 = 24 (since the blank is before x2)
The equation is "__ x 2 = ___", so first blank is 12.
Middle Left:
- I have 1 lots of 4, 5 times.
- 2 x 2 x 5 = 20 (4=2x2)
- 4 x 5 = 20
Middle Right:
- I have 1 lots of 6, 3 times.
- 2 x 3 x 3 = 18 (6=2x3)
- 6 x 3 = 18
Bottom Left:
- I have 1 lots of 9, 2 times.
- 3 x 3 x 2 = 18 (9=3x3)
- 9 x 2 = 18
Bottom Right:
- I have 1 lots of 4, 4 times.
- 2 x 2 x 4 = 16 (4=2x2)
- 4 x 4 = 16
All totals match.
Note: In the triple multiplication, the order might vary, but as long as the product is correct and factors make sense, it's fine. I chose to factor the group size into two numbers and multiply by the number of groups.
Also, in "I have ___ lots of ___", I put 1 and the group size, assuming "lots" means instances, and "of" specifies the content.
This resolves the ambiguity.
Now, compiling final answer as per format.
Since ExplainAnswer and TeachTopic are false, and GeneratePractice is false, we only provide Final Answer with all filled values.
But the instruction says: "Provide only the final correct answer — this should come AFTER all explanations and reasoning."
And since no options are true, we just output the completed worksheet values.
But to present clearly, I'll list each section.
Final Answer should contain all the filled blanks.
So:
For Top Left:
- First sentence: 1, 8
- Triple: 2, 4, 3, 24
- Last: 24
Similarly for others.
To save space, I'll write it compactly.
──────────────────────────────────────
Final Answer:
Top Left:
I have 1 lots of 8, 3 times.
2 x 4 x 3 = 24
8 x 3 = 24
Top Right:
I have 1 lots of 12, 2 times.
3 x 4 x 2 = 24
12 x 2 = 24
Middle Left:
I have 1 lots of 4, 5 times.
2 x 2 x 5 = 20
4 x 5 = 20
Middle Right:
I have 1 lots of 6, 3 times.
2 x 3 x 3 = 18
6 x 3 = 18
Bottom Left:
I have 1 lots of 9, 2 times.
3 x 3 x 2 = 18
9 x 2 = 18
Bottom Right:
I have 1 lots of 4, 4 times.
2 x 2 x 4 = 16
4 x 4 = 16
---
Top Left Box (Green Squares):
We see 3 groups of green squares. Each group has 8 squares (2 rows × 4 columns).
So:
→ I have 3 lots of 8, 3 times? Wait — that doesn’t make sense. Let’s read carefully.
Actually, looking at the structure:
The sentence says: “I have ___ lots of ___, 3 times.”
But visually, we have 3 separate groups, and each group has 8 squares.
That means: We are multiplying 8 (per group) by 3 (number of groups). But the phrasing is tricky.
Wait — let’s look at the equation below:
“__ x __ x __ = ____”
and then “8 x 3 = ____”
Ah! So they’re breaking it down as:
First, count how many in one group → 8
Then, how many groups → 3
So total = 8 × 3 = 24
But the first blank says: “I have ___ lots of ___, 3 times.”
This seems to be saying: You have some number of items, and you repeat that set 3 times.
Looking again: There are 3 identical sets. Each set has 8 squares.
So perhaps it should be:
“I have 8 lots of 1, 3 times”? No, that’s not right.
Wait — maybe it’s misphrased. Let’s think differently.
Perhaps it’s meant to say:
“I have [number of groups] lots of [items per group], repeated [how many times?]”
But the “3 times” likely refers to the number of groups.
Actually, re-reading:
“I have ___ lots of ___, 3 times.”
Maybe it’s: You take a certain amount, and do it 3 times.
In this case, each “lot” is 8 squares, and you do it 3 times → so 3 lots of 8.
But the sentence says “___ lots of ___, 3 times” — which might mean: you have X lots of Y, and you repeat that whole thing 3 times? That would be overcomplicating.
Alternatively, perhaps it’s a typo or poor phrasing, and it should be:
“I have 3 lots of 8.”
Because there are 3 groups, each with 8.
And then the multiplication is 8 × 3 = 24.
Similarly, for the next box.
Let me check the second box to compare.
---
Top Right Box (Green Squares – Different Arrangement):
There are 2 groups. Each group has 12 squares (3 rows × 4 columns).
Sentence: “I have ___ lots of ___, 2 times.”
Again, probably means: 2 groups of 12.
Equation: “__ x __ x __ = ____” and then “___ x 2 = ____”
So likely: 12 × 2 = 24
Same answer as before? Interesting.
Wait — top left was 3 groups of 8 = 24
Top right is 2 groups of 12 = 24
Okay, consistent.
Now back to top left:
If we fill:
“I have 3 lots of 8, 3 times.” — but that would imply 3 × 8 × 3 = 72, which is wrong.
No — I think the “3 times” is redundant or misplaced. Probably it should just be “I have 3 lots of 8.”
But since the worksheet says “3 times”, maybe it’s trying to say: you have a set of 8, and you have it 3 times → so 3 lots of 8.
Yes, that makes sense.
So:
“I have 3 lots of 8” — and the “3 times” might be emphasizing repetition, but it’s already included in “3 lots”.
To avoid confusion, let’s follow the pattern from the equations.
For top left:
They give “8 x 3 = ___” → so 24
And the triple multiplication: probably 1 x 8 x 3 = 24? Or 8 x 1 x 3? Doesn't matter order.
But typically, we write: number of groups × size of each group.
So for top left: 3 groups × 8 per group = 24
But the blank is “__ x __ x __” — three blanks. Why three?
Oh! Because the objective is “multiplying together three numbers”.
So perhaps they want us to break it into three factors.
For example, in top left: each group is 8, which is 2×4, so maybe 2 × 4 × 3 = 24
Similarly, top right: each group is 12, which is 3×4, so 3 × 4 × 2 = 24
That makes sense!
Let me verify.
Top left:
Groups: 3
Each group: 2 rows × 4 columns = 8
So total: 2 × 4 × 3 = 24
Yes.
Top right:
Groups: 2
Each group: 3 rows × 4 columns = 12
So 3 × 4 × 2 = 24
Perfect.
Now middle row.
---
Middle Left (Blue Circles):
There are 5 groups. Each group has 4 circles (arranged in a cross or something — actually, looking: each cluster has 4 dots).
Count: yes, 5 clusters, each with 4 dots.
Sentence: “I have ___ lots of ___, 5 times.”
Probably: 5 lots of 4.
Triple multiplication: 4 can be broken? 4 is 2×2, so 2 × 2 × 5 = 20
Given equation: “4 x 5 = ___” → 20
So triple: 2 × 2 × 5 = 20
Or 4 × 1 × 5, but better to use factors.
Since 4 = 2×2, use that.
---
Middle Right (Yellow Dots):
3 groups. Each group has 6 dots? Let's count.
Each yellow group: looks like 2 rows of 3? Or arranged differently.
Actually, counting: each group has 6 dots (e.g., triangle shape with 3 on bottom, 2 middle, 1 top? Wait no — in image, it seems each group has 6 dots.
Confirm: first group: 3 on top row, 2 middle, 1 bottom? That’s 6. Yes.
So 3 groups of 6.
Sentence: “I have ___ lots of ___, 3 times.” → 3 lots of 6.
Triple multiplication: 6 = 2×3, so 2 × 3 × 3 = 18
Given: “___ x 3 = ___” → 6 × 3 = 18
Good.
---
Bottom Left (Pink Stars):
2 groups. Each group has 9 stars (3×3 grid).
Sentence: “I have ___ lots of ___, 2 times.” → 2 lots of 9.
Triple multiplication: 9 = 3×3, so 3 × 3 × 2 = 18
Given: “9 x 2 = ___” → 18
---
Bottom Right (Red Hearts):
4 groups. Each group has 4 hearts (2×2).
Sentence: “I have __ lots of __, 4 times.” → 4 lots of 4.
Triple multiplication: 4 = 2×2, so 2 × 2 × 4 = 16
Given: “___ x 4 = ___” → 4 × 4 = 16
---
Now, filling all blanks.
Start with Top Left:
- I have 3 lots of 8, 3 times. → But wait, if we say "3 lots of 8", the "3 times" is redundant. Perhaps it's a mistake, or perhaps it's "I have 1 lot of 8, 3 times" meaning you take 8 three times.
Actually, rereading the sentence: “I have ___ lots of ___, 3 times.”
This is ambiguous. But given that later it says “8 x 3”, and the triple multiplication, I think the intended meaning is:
You have a quantity, and you repeat it 3 times.
In top left, each "lot" is 8, and you have it 3 times → so 3 lots of 8.
But the phrase "___ lots of ___, 3 times" might mean: the number of lots is X, each lot has Y items, and you do this X times? Confusing.
Alternative interpretation: Perhaps "I have A lots of B, C times" means A * B * C.
But in top left, if A=3, B=8, C=3, then 3*8*3=72, but actual total is 24, so no.
I think the "3 times" is meant to indicate the number of groups, so it's poorly worded.
Looking at the bottom right: “I have __ lots of __, 4 times.” and there are 4 groups, each with 4 hearts, so likely "4 lots of 4".
Similarly, top left: 3 groups of 8 → "3 lots of 8"
But why say "3 times"? Maybe it's a template error.
Perhaps "times" here means "groups", so "I have 3 lots of 8" and the "3 times" is extra.
To resolve, let's look at the triple multiplication blank.
For top left: they expect three numbers multiplied to get 24.
As I thought earlier: 2 × 4 × 3 = 24, since each group is 2x4=8, and 3 groups.
Similarly, for the sentence, perhaps it's "I have 3 lots of (2x4)", but that's not helping.
Another idea: perhaps the first blank is the number of repetitions, second is the size of each repetition.
So "I have 3 lots of 8" — and the "3 times" is redundant or emphasizes.
I think for consistency, we'll go with:
Top Left:
- I have 3 lots of 8
- Triple: 2 x 4 x 3 = 24 (since 8=2x4)
- 8 x 3 = 24
But the sentence has "3 times" at the end, so if we put 3 and 8, it becomes "I have 3 lots of 8, 3 times" which is odd.
Perhaps it's "I have 1 lot of 8, 3 times" meaning you start with 8 and add it 3 times.
That could work: 1 lot of 8, repeated 3 times → total 24.
Then triple multiplication: 1 x 8 x 3 = 24
Similarly for others.
Let me test with top right.
Top right: 2 groups of 12.
If "I have 1 lot of 12, 2 times" → 1x12x2=24
Triple: 3x4x2=24 (since 12=3x4)
Yes.
Middle left: 5 groups of 4.
"I have 1 lot of 4, 5 times" → 1x4x5=20
Triple: 2x2x5=20 (4=2x2)
Middle right: 3 groups of 6.
"I have 1 lot of 6, 3 times" → 1x6x3=18
Triple: 2x3x3=18 (6=2x3)
Bottom left: 2 groups of 9.
"I have 1 lot of 9, 2 times" → 1x9x2=18
Triple: 3x3x2=18 (9=3x3)
Bottom right: 4 groups of 4.
"I have 1 lot of 4, 4 times" → 1x4x4=16
Triple: 2x2x4=16 (4=2x2)
This makes sense! The "lots of" is singular in the sense that you have one unit of that size, repeated multiple times.
So the first blank is always 1, because you're taking one group of that size, and repeating it the specified number of times.
In the sentence: "I have ___ lots of ___, N times." — the "N times" is the repetition count, and "lots of" might be misleading, but if we put 1 in the first blank, it works.
For example, "I have 1 lot of 8, 3 times" means you have a single set of 8, and you have it 3 times → total 24.
Yes.
Whereas if you put 3 in the first blank, "I have 3 lots of 8, 3 times" would be 3*8*3=72, wrong.
So definitely, first blank should be 1.
Confirming with the given equations.
In top left, they have "8 x 3 = ___" which is correct for 8 per group times 3 groups.
And triple multiplication is additional factorization.
So for all, the "I have" sentence should have 1 in the first blank.
Now, writing answers.
---
Final Answers per box:
Top Left:
- I have 1 lots of 8, 3 times.
- 2 x 4 x 3 = 24 (or any order, but 2,4,3 since 8=2x4)
- 8 x 3 = 24
Top Right:
- I have 1 lots of 12, 2 times.
- 3 x 4 x 2 = 24 (12=3x4)
- 12 x 2 = 24 (since the blank is before x2)
The equation is "__ x 2 = ___", so first blank is 12.
Middle Left:
- I have 1 lots of 4, 5 times.
- 2 x 2 x 5 = 20 (4=2x2)
- 4 x 5 = 20
Middle Right:
- I have 1 lots of 6, 3 times.
- 2 x 3 x 3 = 18 (6=2x3)
- 6 x 3 = 18
Bottom Left:
- I have 1 lots of 9, 2 times.
- 3 x 3 x 2 = 18 (9=3x3)
- 9 x 2 = 18
Bottom Right:
- I have 1 lots of 4, 4 times.
- 2 x 2 x 4 = 16 (4=2x2)
- 4 x 4 = 16
All totals match.
Note: In the triple multiplication, the order might vary, but as long as the product is correct and factors make sense, it's fine. I chose to factor the group size into two numbers and multiply by the number of groups.
Also, in "I have ___ lots of ___", I put 1 and the group size, assuming "lots" means instances, and "of" specifies the content.
This resolves the ambiguity.
Now, compiling final answer as per format.
Since ExplainAnswer and TeachTopic are false, and GeneratePractice is false, we only provide Final Answer with all filled values.
But the instruction says: "Provide only the final correct answer — this should come AFTER all explanations and reasoning."
And since no options are true, we just output the completed worksheet values.
But to present clearly, I'll list each section.
Final Answer should contain all the filled blanks.
So:
For Top Left:
- First sentence: 1, 8
- Triple: 2, 4, 3, 24
- Last: 24
Similarly for others.
To save space, I'll write it compactly.
──────────────────────────────────────
Final Answer:
Top Left:
I have 1 lots of 8, 3 times.
2 x 4 x 3 = 24
8 x 3 = 24
Top Right:
I have 1 lots of 12, 2 times.
3 x 4 x 2 = 24
12 x 2 = 24
Middle Left:
I have 1 lots of 4, 5 times.
2 x 2 x 5 = 20
4 x 5 = 20
Middle Right:
I have 1 lots of 6, 3 times.
2 x 3 x 3 = 18
6 x 3 = 18
Bottom Left:
I have 1 lots of 9, 2 times.
3 x 3 x 2 = 18
9 x 2 = 18
Bottom Right:
I have 1 lots of 4, 4 times.
2 x 2 x 4 = 16
4 x 4 = 16
Parent Tip: Review the logic above to help your child master the concept of multiplying with 3 factors worksheet.