Texas Grab-and-Go Substitute Packet · Teacher Answer Key
Answer Key: Fractions and Decimals in Everyday Problems
Grade: 5
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 — alternate strategies (a larger common denominator, a picture, or a decimal check) are noted where they apply. Watch-for notes flag common misconceptions. A basic calculator is allowed, so grade the reasoning and steps, not just the arithmetic. Estimated grading time: ~4–6 min per packet.
Start Warm-Up ~1 min
1 Compare 0.7 and 0.68.
0.7 > 0.68. Line up by place value: write 0.7 as 0.70, then
compare tenths first — 7 tenths > 6 tenths, so 0.70 > 0.68. Full credit for the
correct symbol and a place-value reason. Watch-for: students who say 0.68 is
bigger "because it has more digits" have the length-vs-place-value misconception.
2 Name the shaded fraction of the bar.
3/5. The bar has 5 equal parts and 3 are shaded. Accept an
equivalent that is clearly justified, but 3/5 is the intended reading. Alternate: a
student who writes 0.6 has also correctly connected 3/5 to its decimal — give full credit
if the fraction reasoning is shown.
Build Study the Math ~1 min
3 Add 1/2 + 1/4.
Common denominator: 4 (since 2 divides into 4). Rename 1/2 = 2/4.
Then 2/4 + 1/4 = 3/4. Alternate: using 2 × 4 = 8 gives 4/8 + 2/8 = 6/8, which
simplifies to 3/4 — accept either the 4ths or the 8ths form. As a decimal, 3/4 = 0.75.
Apply Use What You Know ~2–3 min
4 Recipe: 1/2 cup raisins + 1/3 cup almonds.
Common denominator: 6. Rename 1/2 = 3/6 and 1/3 = 2/6. Add the
tops: 3/6 + 2/6 = 5/6 cup in all. Alternate: any common multiple of 2 and 3
(such as 12: 6/12 + 4/12 = 10/12 = 5/6) is fine. This mirrors the worked example, so many
students can reuse those steps.
5 Money: notebook $3.45, pen $1.60, pays with $10.00.
5a. $3.45 + $1.60 = $5.05 (line up the decimal points: 45 hundredths + 60
hundredths = 105 hundredths = $1.05, carry the dollar).
5b. $10.00 − $5.05 = $4.95 change.
Watch-for: a student who writes $3.45 + $1.6 and lines up the last digits (getting $3.51 or similar) has lined up by digits, not place value. Remind them $1.60 = $1.60.
5b. $10.00 − $5.05 = $4.95 change.
Watch-for: a student who writes $3.45 + $1.6 and lines up the last digits (getting $3.51 or similar) has lined up by digits, not place value. Remind them $1.60 = $1.60.
6 Error analysis: 1/4 + 1/2 = 2/6 (student added tops and bottoms).
The mistake: The student added the denominators (4 + 2 = 6). You cannot add
the bottoms — the bottom tells the size of the parts, and you must make the parts
the same size first with a common denominator.
Correct work: Common denominator 4. Rename 1/2 = 2/4. Then 1/4 + 2/4 = 3/4.
Sanity check: 1/2 alone is already 2/4, so the sum must be more than 1/2 — but the student's 2/6 (= 1/3) is less than 1/2, which shows the answer cannot be right. Full credit requires (1) naming the "added the denominators" error and (2) the correct 3/4.
Correct work: Common denominator 4. Rename 1/2 = 2/4. Then 1/4 + 2/4 = 3/4.
Sanity check: 1/2 alone is already 2/4, so the sum must be more than 1/2 — but the student's 2/6 (= 1/3) is less than 1/2, which shows the answer cannot be right. Full credit requires (1) naming the "added the denominators" error and (2) the correct 3/4.
7 Which operation: 3/4 L + 1/2 L drunk from a 2 L bottle.
7a. "In all" → add. Common denominator 4. Rename 1/2 = 2/4. Then
3/4 + 2/4 = 5/4 = 1 1/4 liters (one and one-quarter liters). Accept the improper
form 5/4 or the mixed number 1 1/4.
7b. The phrase "in all" (combining both amounts) tells you to add. Accept any answer that points to "in all" or the idea of joining the two amounts.
Note: The 2-liter capacity is extra information; some students may check that 1 1/4 L is less than 2 L, which is good reasoning.
7b. The phrase "in all" (combining both amounts) tells you to add. Accept any answer that points to "in all" or the idea of joining the two amounts.
Note: The 2-liter capacity is extra information; some students may check that 1 1/4 L is less than 2 L, which is good reasoning.
Explain Justify Your Thinking (Q8) ~1–2 min
8 Why you cannot add tops and bottoms (1/4 + 1/2).
Model answer. Answer: the correct sum is 3/4.
Numbers I used: common denominator 4; 1/2 renamed as 2/4; 1/4 + 2/4 = 3/4.
Why: The denominator names the size of each part. Fourths and halves are
different sizes, so you cannot combine them until you rename them as the same-size parts
(fourths). Adding the bottoms would change the size of the parts, which is why 2/6 is
wrong. Full credit requires the correct sum (3/4) and a reason that fractions must have
the same-size parts (a common denominator) before adding.
Justification scoring rubric (3 points)
| Score | Answer | Numbers used | Why (reasoning) |
|---|---|---|---|
| 3 | Correct sum 3/4. | Shows common denominator 4 and the rename 1/2 = 2/4. | Clearly explains that parts must be the same size, so you cannot add the denominators. |
| 2 | Correct sum 3/4. | Some renaming shown, or a minor slip. | Reasoning present but incomplete (e.g., says "make bottoms match" 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: "a common denominator is a shared
bottom number so the parts are the same size; you need it so the fractions can be
combined."
Connect: Valid items where a common denominator was found include Q3, Q4, Q6, or Q7a. Any correctly named item earns credit.
Extend: Any correct fraction–decimal pair not in the packet — e.g., 1/5 = 2/10 = 0.2, 1/4 = 25/100 = 0.25, 3/10 = 0.3, 1/10 = 0.1. More than one answer is defensible; check the pair is truly equal.
Connect: Valid items where a common denominator was found include Q3, Q4, Q6, or Q7a. Any correctly named item earns credit.
Extend: Any correct fraction–decimal pair not in the packet — e.g., 1/5 = 2/10 = 0.2, 1/4 = 25/100 = 0.25, 3/10 = 0.3, 1/10 = 0.1. More than one answer is defensible; check the pair is truly equal.
Challenge Early Finisher (optional)
EF Draw a model for 1/3 + 1/6.
Common denominator: 6. Rename 1/3 = 2/6; 1/6 stays 1/6. Then 2/6 + 1/6 =
3/6 = 1/2. A correct area model shows a bar in sixths with 3 of 6 parts shaded, or
a number line from 0 to 1 in sixths with a jump ending at 3/6. As a decimal, 1/2 = 0.5.
Full credit for a labeled model that matches 3/6 (or the simplified 1/2). Accept the
unsimplified 3/6.
Watch Common misconceptions
- Adding the denominators. The Q6 error: 1/4 + 1/2 = 2/6. Students add both tops and both bottoms. Reinforce that only the tops are added, and only after the bottoms match (same-size parts). A quick sanity check helps: the sum must be bigger than 1/2, but 2/6 is smaller.
- Lining up decimals by digits, not place value. In Q5, $1.60 must line up as 1.60, not "1.6" pushed to the right. Comparing 0.7 and 0.68 (Q1) trips students who think "more digits = larger." Rewrite with matching decimal places (0.70 vs 0.68).
- 1/2 vs 0.2. Students may write 1/2 = 0.2. Model that 1/2 = 5/10 = 0.5 (one half of ten tenths is five tenths). 0.2 is 2/10 = 1/5.
- Forgetting to rename before adding. Some find a common denominator but forget to change the numerators too (e.g., leaving 1/2 as 1/6 instead of 2/6). Both top and bottom multiply by the same number.
- Choosing the wrong operation. In Q7, "in all" signals addition; watch for students who subtract. Anchor the key words ("in all," "left," "how much more").
Teacher follow-up based on likely errors
If many students miss Q6, do a quick 5-minute picture of 1/4 + 1/2 with an area model so they see the parts must match before adding. If Q1 or Q5 show digit-lining, practice writing decimals with equal places (0.70, 1.60) and comparing tenths first. If Q3/Q4 show a missing rename, model multiplying top and bottom by the same number. The Q8 justifications reveal who understands why a common denominator is needed — a good discussion starter next class. The separate student packet has all methods printed; this key is for the teacher only.
G05_MATH_FractionsDecimals_01 — Fractions and Decimals in Everyday Problems
Teacher Answer Key