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Let’s solve this step by step.

We are given a list of words with missing letters, and we need to fill in the blanks using one of these vowel sounds:
UE, O, E, OO, U, UI

Each word has a blank (or blanks) where we must insert the correct letter(s) to make a real English word that matches the sound pattern shown at the top.

Also, next to each incomplete word is a jumbled string of letters — that’s our “letter bank” for that row. We must pick the right letters from that bank to complete the word correctly.

Let’s go row by row:

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1. n__west → letter bank: `n e w e s t k v e t e e s t n w e s t`
We know the word is “newest”. So we need to fill in “e” and “w”? Wait — actually, it’s “n _ _ west”, so two blanks? But looking at the example above: “r u ler” → ruler, so sometimes it’s one letter per blank. Let’s check the format.

Actually, looking again:
The first line says:
Spell the oo sound → UE O E OO U UI
Then examples:
r_u_ler → ruler (so ‘u’ fills the blank)
bl_u_e → blue (‘u’)
outgr_e_w → outgrew (‘e’)
continu_e → continue (‘e’)
co_u_gar → cougar (‘u’)
thr_e_w → threw (‘e’)

So each underscore represents ONE missing letter. And we choose from the vowel sounds listed.

But in the main table, some words have multiple underscores — like “sc__ping” — which probably means two letters missing? Or maybe it’s just formatting? Let’s look at the letter banks.

Wait — actually, looking closely at the worksheet design:
Each row has:
- A partially spelled word with underscores (each underscore = 1 missing letter)
- Then a long string of letters — that’s the pool we can use to pick the correct letters to fill the blanks.

And we’re supposed to circle or write the correct completed word using letters from the bank.

But since we’re solving it, let’s reconstruct each word correctly.

Let me go row by row and figure out the correct spelling, then verify if those letters exist in the bank.

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Row 1: n__west → should be “newest” → so missing letters: e, w? But “n_e_west” would be 3 letters? No — “newest” is N-E-W-E-S-T → so if it’s written as “n__west”, that’s 2 blanks between n and west → so positions 2 and 3: e and w.

Letter bank: `n e w e s t k v e t e e s t n w e s t` → yes, has e and w.

✔ Correct word: newest

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Row 2: sc__ping → likely “scooping” → s-c-o-o-p-i-n-g → so blanks are o,o

Letter bank: `i n d o s c o o p i n g s o o p i n g` → has o,o

✔ Correct word: scooping

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Row 3: appr__ved → “approved” → a-p-p-r-o-v-e-d → so blank is o? Wait — “appr__ved” — that’s two blanks after r? Actually, “approved” is spelled A-P-P-R-O-V-E-D → so between R and V is O, then E? But here it’s “appr__ved” — so two letters missing: O and V? No — V is already there? Wait no: “appr__ved” — let’s count:

A P P R _ _ V E D → that’s 9 letters. Approved is 8 letters: A-P-P-R-O-V-E-D → so perhaps it’s “appr_o_ved”? Maybe typo in spacing.

Looking at letter bank: `r o p p i r z v a p p r o v e d r o d` → contains “approved”

So likely the word is “approved”, missing letter is O (after R), and maybe the second blank is part of “ved”? Hmm.

Actually, standard spelling: approved → so if it’s “appr__ved”, probably meant to be “appr_o_ved” — but written with two underscores by mistake? Or perhaps it’s “approv_ed” — still confusing.

Wait — look at the example above: “continu_e” → continue → so last letter e is filled. Similarly, “appr__ved” might be “approved” with O and... wait, no — “approved” has only one vowel between R and V: O.

Perhaps it’s “appr_o_ved” — meaning one blank? But it shows two underscores.

Looking at the letter bank: it includes “a p p r o v e d” — so we can form “approved”.

I think it’s safe to say the intended word is approved, and the missing letter is o (and maybe the second underscore is a formatting error).

But let’s check other rows for consistency.

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Row 4: grad__ated → “graduated” → g-r-a-d-u-a-t-e-d → so between D and A is U? “grad_u_ated” → so one blank? But it shows two underscores.

Letter bank: `x g r a d u a t e d a e u p d a v t` → has u,a,t,e,d etc.

“Graduated” → so missing letter is U.

Again, probably one blank, but written as two.

This seems to be a formatting issue — many words show two underscores but only need one letter.

Let’s assume each underscore represents one missing letter, and we’ll find the correct spelling.

To save time and avoid confusion, I’ll list the correct completed word for each row based on common English words and the letter banks provided.

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Let me go through all rows systematically:

1. n__west → newest (missing: e, w) — but “newest” is n-e-w-e-s-t → so if “n__west”, blanks are position 2 and 3: e and w. Letter bank has them. ✔

2. sc__ping → scooping (missing: o, o) ✔

3. appr__ved → approved (missing: o) — even though two underscores, likely only one letter needed. Letter bank has “o”. ✔

4. grad__ated → graduated (missing: u) ✔

5. j__ciest → juiciest (missing: u, i) — j-u-i-c-i-e-s-t → so blanks are u and i. Letter bank: `x r y i g i j u i c i e s t i q d j s` → has u,i ✔

6. bl__bird → bluebird (missing: u, e) — b-l-u-e-b-i-r-d → so blanks u,e. Letter bank: `d n b l u e b i r d i b l e b i r d e` → has u,e ✔

7. n__w → naouk? No — likely “now” but that doesn’t fit. Wait — letter bank: `n a o u k v x n s n a g d e w n e w` → possible words: “new”, “now”, “naow”? Not making sense.

Wait — perhaps “n__w” is “new”? But “new” is n-e-w → so blank is e. But it shows two underscores? “n__w” — three letters total? That would be n _ _ w — four letters? Confusing.

Look at letter bank: has “n e w” — so probably “new”, and the two underscores are a mistake — should be one blank: n_e_w → new.

Similarly, later we have “m_ver” → “mover” or “mover”? Letter bank has m,y,o,v,e,r — so “mover”.

I think for consistency, we should interpret each underscore as one missing letter, and the word length may vary.

For “n__w” — if it’s three characters: n, _, _, w — that’s four letters? No — “n__w” likely means n followed by two blanks then w — so four-letter word? Like “know”? But k not in bank.

Letter bank: `n a o u k v x n s n a g d e w n e w` — has “new” — n,e,w — so perhaps it’s “n_e_w” with one blank, but written as two.

This is messy. Let’s look at the answer key implied by the letter banks.

Notice that in each row, the letter bank contains the full correct word scrambled.

For example, row 1: letter bank contains “newest” — n,e,w,e,s,t

Row 2: contains “scooping”

Row 3: contains “approved”

Row 4: contains “graduated”

Row 5: contains “juiciest”

Row 6: contains “bluebird”

Row 7: n__w — letter bank has “new” — so word is “new”

Row 8: impr__ved — “improved” — letter bank has “improved”

Row 9: grad__ation — “graduation” — letter bank has “graduation”

Row 10: stat__ — “statue” — letter bank has “statue”

Row 11: j__ce — “juice” — letter bank has “juice”

Row 12: fr__ps — “froops”? No — “troops”? Letter bank: `o t r o u p s t r o o p s x r s b t r` — has “troops” — so word is “troops”, missing r,o? “fr__ps” — f,r,_,_,p,s — not matching.

“fr__ps” — if it’s “frogs”? No. “drops”? No.

Letter bank has “troops” — t,r,o,o,p,s — so perhaps the word is “troops”, and “fr__ps” is a misprint — should be “tr__ps”?

That makes sense! Probably a typo — “tr__ps” → “troops”

Similarly, row 13: rescu_d — “rescued” — letter bank has “rescued”

Row 14: j_ne — “june” — letter bank has “june”

Row 15: m_ver — “mover” — letter bank has “mover”

Row 16: l_ses — “loses” — letter bank has “loses”

Row 17: j_weler — “jeweler” — letter bank has “jeweller” or “jeweler” — US spelling “jeweler”

Row 18: sol__tion — “solution” — letter bank has “solution”

Row 19: t_nes — “stones” — letter bank has “stones”

Row 20: thr_w — “threw” — letter bank has “threw”

Now, for the blanks:

We need to fill in the missing letters using the vowel sounds: UE, O, E, OO, U, UI

But actually, from the examples, it’s about choosing the correct vowel sound to complete the word.

Since the letter banks contain the full words, we can deduce the missing letters.

Let’s list each word with its missing letters:

1. newest → missing: e, w — but w is consonant, so perhaps only vowels matter? The instruction is “spell the oo sound” but then lists UE,O,E,OO,U,UI — so it’s about vowel combinations.

In “newest”, the ‘e’ is the vowel sound.

But for simplicity, since the task is to complete the word, and the letter bank provides the letters, I think the expected answer is to write the completed word.

However, the user asked to “solve the problem”, and the problem is to fill in the blanks.

Given the complexity and potential typos, I’ll provide the completed word for each row, as that’s what the exercise intends.

Final decision: For each row, the correct completed word is:

1. newest
2. scooping
3. approved
4. graduated
5. juiciest
6. bluebird
7. new
8. improved
9. graduation
10. statue
11. juice
12. troops (assuming "tr__ps" was meant)
13. rescued
14. june
15. mover
16. loses
17. jeweler
18. solution
19. stones
20. threw

Now, to match the format, perhaps we need to specify the missing letters.

But since the question is to solve the homework, and the homework is to complete the words, I'll provide the completed words.

For the Final Answer, since it's a list, I'll write them in order.

But let's confirm row 12: "fr__ps" — if we force it, with letter bank having "troops", it must be a typo, and it's "tr__ps" → "troops".

Similarly, row 7: "n__w" → "new" — so missing 'e' (and perhaps another letter, but "new" is three letters, so "n_e_w" with one blank).

I think it's best to output the completed words.

So here is the solution:

──────────────────────────────────────

Final Answer:
1. newest
2. scooping
3. approved
4. graduated
5. juiciest
6. bluebird
7. new
8. improved
9. graduation
10. statue
11. juice
12. troops
13. rescued
14. june
15. mover
16. loses
17. jeweler
18. solution
19. stones
20. threw