Texas Grab-and-Go Substitute Packet · Teacher Answer Key
Answer Key: Fractions and Decimals: Compare and Combine
Grade: 4
Subject: Mathematics
For teacher use only
Math
How to use this key
Answers are grouped by section and question number, with full worked steps. Accept any correct method that reaches the right value — a picture, a number line, or a decimal check are all fine where they apply. Watch-for notes flag common misconceptions. A basic calculator is allowed, so grade the reasoning and steps, not just the arithmetic. This is a Grade 4 packet, so every add/subtract uses the same (like) denominator. Estimated grading time: ~4–6 min per packet.
Start Warm-Up ~1 min
1 Name the shaded fraction of the bar.
3/4. The bar has 4 equal parts and 3 are shaded. Accept an
equivalent that is clearly justified, but 3/4 is the intended reading. Alternate: a
student who also writes 0.75 has connected 3/4 to its decimal — that is beyond the required
answer, so give full credit as long as 3/4 is shown.
2 Which is bigger, 3/4 or 1/4?
3/4 is bigger. Both are fourths (same size parts), and 3 shaded
parts is more than 1 shaded part, so 3/4 > 1/4. Full credit for choosing 3/4 and
a same-size-parts reason. Watch-for: a student who thinks the bottom "4" makes it big
should be reminded that when the bottoms match, the bigger top wins.
Build Study the Math ~1 min
3 Add 1/5 + 3/5.
Same bottom (fifths). Add the tops: 1 + 3 = 4. Keep the bottom: 5.
So 1/5 + 3/5 = 4/5. Alternate: a number line from 0 to 1 in fifths landing on
4/5, or a bar of 5 parts with 4 shaded. As a decimal, 4/5 = 8/10 = 0.8 (beyond the required
answer — do not deduct if omitted).
4 Equal fraction: 1/2 = ?/4.
1/2 = 2/4. Multiply top and bottom by 2 (1×2 = 2, 2×2 = 4). The
missing number is 2. Alternate: a picture — cut a half-bar into two equal
pieces and you see 2 of 4 parts. Full credit for 2 with any correct reason.
Apply Use What You Know ~2–3 min
5 Compare 2/8 and 5/8.
2/8 < 5/8. Both are eighths (same size parts), so compare the
tops: 2 < 5, so 2/8 < 5/8. Full credit for the correct symbol and a
same-bottom reason. Watch-for: the </> symbol pointed the wrong way — the
small end points to the smaller number, 2/8.
6 Ribbon: 7/8 m − 3/8 m cut off.
Same bottom (eighths). Subtract the tops: 7 − 3 = 4. Keep the
bottom: 8. So 7/8 − 3/8 = 4/8 of a meter is left. Alternate: 4/8 also equals
1/2 — accept either 4/8 or the simplified 1/2. Note: simplifying is not required in
Grade 4, so do not deduct for leaving 4/8.
7 Match fraction to decimal.
3/10 = 0.3 (three tenths); 7/10 = 0.7 (seven tenths);
3/100 = 0.03 (three hundredths).
Watch-for: a student who matches 3/100 to 0.3 has misread the place value — 3/100 is three hundredths, written 0.03. Full credit for all three correct matches.
Watch-for: a student who matches 3/100 to 0.3 has misread the place value — 3/100 is three hundredths, written 0.03. Full credit for all three correct matches.
8 Error analysis: 2/5 + 1/5 = 3/10 (student added the bottoms).
The mistake: The student added the denominators (5 + 5 = 10). When the
bottoms are already the same, you do not add them — the bottom tells the size
of the parts, and that size does not change. You add only the tops and keep the bottom.
Correct work: Same bottom (fifths). Add the tops: 2 + 1 = 3. Keep the bottom: 5. So 2/5 + 1/5 = 3/5.
Sanity check: 3/10 (the student's answer) is smaller than 2/5 alone, which cannot be right when you add a positive amount. Full credit requires (1) naming the "added the bottoms" error and (2) the correct 3/5.
Correct work: Same bottom (fifths). Add the tops: 2 + 1 = 3. Keep the bottom: 5. So 2/5 + 1/5 = 3/5.
Sanity check: 3/10 (the student's answer) is smaller than 2/5 alone, which cannot be right when you add a positive amount. Full credit requires (1) naming the "added the bottoms" error and (2) the correct 3/5.
Explain Justify Your Thinking (Q9) ~1–2 min
9 Why keep the bottom the same (2/5 + 1/5).
Model answer. Answer: the correct sum is 3/5.
Model or numbers: the bottoms are both 5, so the parts are the same size; add the
tops 2 + 1 = 3 and keep the bottom 5.
Why: The denominator names the size of each part (fifths). Both fractions
are already fifths, so joining them just counts how many fifths there are in all — the
size of a fifth does not change. Adding the bottoms would change the parts to tenths,
which is why 3/10 is wrong. Full credit requires the correct sum (3/5) and a reason that
the bottom stays the same because the parts are already the same size.
Justification scoring rubric (3 points)
| Score | Answer | Model or numbers used | Why (reasoning) |
|---|---|---|---|
| 3 | Correct sum 3/5. | Shows the bottoms are the same and adds the tops (2 + 1 = 3, keep 5). | Clearly explains the bottom stays the same because the parts are already the same size. |
| 2 | Correct sum 3/5. | Some work shown, or a minor slip. | Reasoning present but incomplete (e.g., "keep the bottom" without saying why). |
| 1 | Answer attempted, may be incorrect. | Little or no work shown. | Weak or missing reasoning. |
| 0 | No/incorrect answer. | No work. | No reasoning. |
Close ACE ~1 min
ACE Articulate / Connect / Extend.
Articulate: Accept any plain-language version of: "the bottom number stays the
same; you add only the tops."
Connect: Valid items where a like-denominator add/subtract happened include Q3, Q6, or Q8 (and the worked example). Any correctly named item earns credit.
Extend: Any correct fraction–decimal pair not in the packet — e.g., 1/10 = 0.1, 6/10 = 0.6, 9/10 = 0.9, 25/100 = 0.25, 50/100 = 0.5. More than one answer is defensible; check the pair is truly equal (tenths → one decimal place, hundredths → two decimal places).
Connect: Valid items where a like-denominator add/subtract happened include Q3, Q6, or Q8 (and the worked example). Any correctly named item earns credit.
Extend: Any correct fraction–decimal pair not in the packet — e.g., 1/10 = 0.1, 6/10 = 0.6, 9/10 = 0.9, 25/100 = 0.25, 50/100 = 0.5. More than one answer is defensible; check the pair is truly equal (tenths → one decimal place, hundredths → two decimal places).
Challenge Early Finisher (optional)
EF Draw a model for 4/6.
A correct area model shows a bar split into 6 equal parts with 4 shaded,
labeled 4/6; or a number line from 0 to 1 in sixths with a point/jump at 4/6. Full credit
for a labeled model that clearly shows 4 of 6 equal parts. Alternate: a student who
notices 4/6 = 2/3 (each pair of sixths grouped) has gone beyond the task — accept it if
the picture still shows 4 of 6 parts.
Watch Common misconceptions
- Adding the denominators. The Q8 error: 2/5 + 1/5 = 3/10. Students add both tops and both bottoms. Reinforce that with a like denominator you add only the tops and keep the bottom — the size of the part does not change. A quick sanity check helps: the sum must be bigger than 2/5, but 3/10 is smaller.
- Bigger denominator = bigger fraction. In Q2 and Q5, some students think a bigger bottom number means a bigger fraction, or compare only the bottoms. When the bottoms match, the bigger top wins (3/4 > 1/4; 5/8 > 2/8). A quick bar picture makes the same-size parts visible.
- 0.3 vs 0.03. In Q7, students may match 3/100 to 0.3. Three tenths (3/10 = 0.3) is ten times larger than three hundredths (3/100 = 0.03). Anchor the place-value names: tenths fill one decimal place, hundredths fill two.
- Forgetting the fraction is "how many equal parts are shaded." In Q1, a student who writes 3/1 or counts only shaded-vs-unshaded (3/1 or 3 to 1) needs the reminder that the bottom is the total equal parts (4) and the top is the shaded parts (3).
Teacher follow-up based on likely errors
If many students miss Q8, do a quick 5-minute bar picture of 2/5 + 1/5 so they see the parts stay the same size and you just count more fifths. If Q2 or Q5 show "bigger bottom = bigger," compare two same-bottom bars side by side and count shaded parts. If Q7 shows 0.3/0.03 mix-ups, practice reading tenths and hundredths aloud with a place-value chart. The Q9 justifications reveal who understands why the bottom stays the same — a good discussion starter next class. The separate student packet has all methods printed; this key is for the teacher only.
G04_MATH_FractionsDecimals_01 — Fractions and Decimals: Compare and Combine
Teacher Answer Key