Texas Grab-and-Go Substitute Packet

Fractions and Decimals in Everyday Problems

Grade: 5 Subject: Mathematics Time: ~45 min core + ~15 min extension Math

Overview

This is a self-contained, low-tech substitute packet in which Grade 5 students practice comparing decimals to the thousandths, adding and subtracting fractions with unlike denominators, and connecting a fraction to its decimal. Working alone with a pencil (a basic calculator is allowed but not required), students compare two decimals and name a fraction of a picture, study a worked example that adds 1/2 + 1/3 with a common denominator, and then apply the ideas to a recipe, a money problem, an error to find and fix, and a multi-step "which operation" problem. They finish by explaining why you cannot add the denominators.

At a glance

Grade: 5

Subject: Mathematics

Time: about 45 minutes core plus a 15-minute optional extension

Materials: printed packet and a pencil; a basic calculator is allowed but not required (no computer, internet, or physical manipulatives)

Work mode: independent

Standards (provisional): 19 TAC §111.7 (Grade 5 Mathematics) — comparing/ordering decimals to the thousandths using place value, and adding/subtracting fractions with unlike denominators using equivalent fractions. Provisional — pending educator verification against the current official TAC source. Standards are paraphrased, not quoted.

Accessible version of the student activity

The full student activity is reproduced below in plain, screen-reader-friendly HTML. It reflows on phones and at 200% zoom. Write your answers on the printed packet, and show your work.

Start (5 minutes) — Warm-up

Compare two decimals: write <, >, or = between 0.7 and 0.68, and tell in one sentence how you knew.
Name the fraction: a bar is cut into 5 equal parts and 3 parts are shaded. Write the fraction of the whole bar that is shaded. (The shaded amount is three of the five equal parts.)

Build (5–10 minutes) — Study the math

To compare decimals to the thousandths, line the numbers up by place value, not by how many digits they have; add zeros so both have the same number of decimal places, then compare tenths, hundredths, and thousandths from left to right (0.70 > 0.68). To add or subtract fractions with unlike denominators, first find a common denominator (a number both bottoms divide into; multiplying the two bottoms always works), rename each fraction as an equal fraction with that bottom, then add or subtract only the tops. To connect a fraction to its decimal, rename it with a bottom of 10, 100, or 1000 and read the decimal (1/2 = 5/10 = 0.5; 3/4 = 75/100 = 0.75). Careful: 1/2 is 0.5, not 0.2.

Worked example — adding fractions with unlike denominators

Add 1/2 + 1/3. Step 1, common denominator: 2 × 3 = 6. Step 2, rename: 1/2 = 3/6 and 1/3 = 2/6. Step 3, add the tops: 3/6 + 2/6 = 5/6.

Figure 2 description and numbers. A grayscale area model of 1/2 + 1/3. Three equal-length bars are stacked. The top bar is split into two equal parts with one half shaded (a diagonal-line pattern), labeled 1/2 = 3/6. The middle bar is split into three equal parts with one third shaded (a dotted pattern), labeled 1/3 = 2/6. The bottom bar is split into six equal parts; five of the six are shaded — three with the diagonal pattern and two with the dotted pattern — labeled 5/6. Below the bars, a number line from 0 to 1 marked in sixths (0, 1/6, 2/6, 3/6, 4/6, 5/6, 1) has an arrow starting at 0 and ending at 5/6. The model shows that renaming both fractions into sixths makes the parts the same size, so 3/6 + 2/6 = 5/6. In the printed packet this is a labeled black-and-white figure that reads clearly in grayscale.

Using the worked example as a guide, add 1/2 + 1/4. Rename to a common denominator first, then add the tops. Show each step.

Apply (20–25 minutes) — Use what you know

Recipe (adding fractions): a snack uses 1/2 cup of raisins and 1/3 cup of almonds. How many cups are there in all? Find a common denominator, rename, and add.
Money (decimals): Maya buys a notebook for $3.45 and a pen for $1.60.
- 5a. How much does she spend in all? Line up the decimal points and add.
- 5b. She pays with a $10.00 bill. How much change does she get back?
Find and fix the error: a student wrote 1/4 + 1/2 = (1 + 1)/(4 + 2) = 2/6. Find the mistake, explain it, and give the correct sum.
Which operation (multi-step): a 2-liter bottle; José drinks 3/4 liter in the morning and 1/2 liter at lunch.
- 7a. How much has he drunk in all? Decide the operation, find a common denominator, and add.
- 7b. In one sentence, tell which words told you to add.

Explain (5–10 minutes) — Justify your thinking (Answer, Numbers, Why)

Question 8. In problem 6 a student wrote 1/4 + 1/2 = 2/6. Explain why you cannot add the tops and add the bottoms. Write your Answer (the correct sum), the Numbers you used, and Why your way is correct.

Sentence starters you may use: "The correct sum is ___ because…"; "First I found a common denominator by…"; "I renamed 1/4 as ___ and 1/2 as ___…"; "You cannot add the bottoms because the parts must be…".

Close (5 minutes) — ACE

Articulate: explain in your own words what a common denominator is and why you need one to add fractions.
Connect: name one packet item where you found a common denominator.
Extend: write a fraction and its matching decimal that was not used in this packet.

Continue (optional, ~15 minutes) — Early finisher

Draw your own model: add 1/3 + 1/6. Find a common denominator, then draw an area model or a number line to show the sum, label the parts, and write the final answer as a fraction (and, if you can, as a decimal).

Turn in

Hand in the whole packet with your name, class period, and date, with questions 1–8 and the ACE box answered and your work shown. Include the optional challenge if you did it.

G05_MATH_FractionsDecimals_01 — Fractions and Decimals in Everyday Problems Accessible landing page