All packets
Texas Grab-and-Go Substitute Packet

Fractions and Decimals: Compare and Combine

Grade: 4 Subject: Mathematics Time: ~45 min core + ~15 min extension Math

Overview

This is a self-contained, low-tech substitute packet in which Grade 4 students practice equivalent fractions, comparing fractions with the same denominator, adding and subtracting fractions with like (equal) denominators, and relating tenths and hundredths to their decimals. Working alone with a pencil (a basic calculator is allowed but not required), students name a fraction of a picture and pick the larger of 3/4 and 1/4, study a worked example that adds 2/6 + 3/6 by keeping the bottom the same, and then apply the ideas to a compare item, a ribbon subtraction story, a fraction–decimal match, and an error to find and fix. They finish by explaining why the bottom stays the same when the denominators are equal.

At a glance

Grade: 4

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 §111.6 (Grade 4 Mathematics) — equivalent fractions and comparing fractions with the same denominator using a model, adding/subtracting fractions with like denominators, and relating fractions with denominators of 10 or 100 to decimals. Provisional — pending educator verification against the current official TAC source. Standards are paraphrased, not quoted; this is not a claim of TEKS alignment.

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

  1. Name the fraction: a bar is cut into 4 equal parts and 3 parts are shaded. Write the fraction of the whole bar that is shaded. (The shaded amount is three of the four equal parts.)
  2. Which is bigger, 3/4 or 1/4? Circle the larger fraction and finish the sentence telling how you knew. (Both are fourths — the same size parts.)

Build (5–10 minutes) — Study the math

Equivalent fractions: two fractions can name the same amount; multiply the top and bottom by the same number (1/2 = 2/4). Comparing fractions with the same bottom: when the denominators match, the fraction with the bigger top is bigger (3/4 > 1/4). Adding and subtracting fractions with the same bottom: the parts are already the same size, so add or subtract only the tops and keep the bottom (1/5 + 2/5 = 3/5; 4/6 − 1/6 = 3/6). Fractions and decimals: a fraction with a bottom of 10 is written in the tenths place, and a bottom of 100 is written in the hundredths place (3/10 = 0.3; 3/100 = 0.03). Careful: you never add the bottoms, and 0.3 is much bigger than 0.03.

Worked example — adding fractions with the same bottom

Add 2/6 + 3/6. Step 1: the bottoms are the same (both sixths), so the parts are the same size. Step 2, add the tops: 2 + 3 = 5. Step 3, keep the bottom: 6. So 2/6 + 3/6 = 5/6.

Area model and number line showing two sixths plus three sixths equals five sixths. Two stacked equal-length bars split into six equal parts: the first has two of six shaded (two sixths); the second has five of six shaded (five sixths). Below the bars, a number line from 0 to 1 marked in sixths has an arrow from 0 ending at five sixths.
Figure 2 description and numbers. A grayscale area model of 2/6 + 3/6. Two equal-length bars are stacked, each split into six equal parts. The top bar has two of the six parts shaded (a diagonal-line pattern), labeled 2/6. The bottom bar has five of the six parts shaded — two with the diagonal pattern and three with a 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 because the bottoms are already the same, you add only the tops (2 + 3 = 5) and keep the bottom (6), so 2/6 + 3/6 = 5/6. In the printed packet this is a labeled black-and-white figure that reads clearly in grayscale.
  1. Using the worked example as a guide, add 1/5 + 3/5. Add the tops and keep the bottom the same. Show each step.
  2. Fill in the missing number to make an equal fraction: 1/2 = ?/4. Explain how you knew.

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

  1. Compare two fractions: write <, >, or = between 2/8 and 5/8, and tell in one sentence how you knew. (Both are eighths.)
  2. Ribbon (story problem): Ana has a ribbon 7/8 of a meter long and cuts off 3/8 of a meter. How much is left? Subtract the tops and keep the bottom.
  3. Match the fraction to its decimal: 3/10, 7/10, and 3/100 to 0.3, 0.7, and 0.03. Write each fraction next to the decimal that equals it.
  4. Find and fix the error: a student wrote 2/5 + 1/5 = (2 + 1)/(5 + 5) = 3/10. Find the mistake, explain it, and give the correct sum.

Explain (5–10 minutes) — Justify your thinking (Answer, Model or numbers, Why)

Question 9. In problem 8 a student wrote 2/5 + 1/5 = 3/10. Explain why you keep the bottom the same when the bottoms are equal. Write your Answer (the correct sum), the Model or numbers you used, and Why your way is correct.

Sentence starters you may use: "The correct sum is ___ because…"; "The bottoms are both ___, so the parts are the same…"; "I add only the tops: ___ + ___ = ___…"; "You cannot add the bottoms because that would change…".

Close (5 minutes) — ACE

Continue (optional, ~15 minutes) — Early finisher

Draw your own model: show the fraction 4/6. Split a bar into 6 equal parts and shade 4 of them (or use a number line), label the parts, and write the fraction under your picture.

Turn in

Hand in the whole packet with your name, class period, and date, with questions 1–9 and the ACE box answered and your work shown. Include the optional challenge if you did it.

G04_MATH_FractionsDecimals_01 — Fractions and Decimals: Compare and Combine Accessible landing page