step 1 of 6
A school trip costs $280. Families have already paid 3/4 of the cost.
First look at the fraction 3/4. What does the bottom number 4 mean?
به انگلیسی
Moving between situations, diagrams and equations
Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents
کارهایی که یادگیرنده بعد از این درس می‌تواند انجام دهد
- Write an equation with three-digit numbers to match a measurement or money word problem
- Draw a bar model to represent a fraction problem and use it to solve
- Explain how a number line diagram relates to the quantities in a word problem
۱ · بخوان
You know how to check a story by matching its picture and its number sentence. That check helps with bigger stories too, like money for a trip. You can draw a bar cut into equal parts. You can jump along a number line. Or you can write an equation with numbers and a fraction. All three show the same amounts in different forms.
Tap to shade 3 of the 4 parts.
Try it together
A school trip costs $280. Parents have already paid 3/4 of that. Split $280 into 4 equal parts: 280 ÷ 4 = 70. Then take 3 of those parts: 3 × 70 = 210. Parents paid $210, and the bar model shows it as 3 shaded parts out of 4.
Tap to shade 3 of the 4 parts.
Try it together
The same $280 fits on a number line. Start at 0, and the whole cost sits at 280. Four equal hops of $70 reach it, and 3 hops land on $210. A number line also shows taking away: start at the amount you had and hop back by what you spend. Where you land is what is left.
When you switch between a picture, a number line, and an equation, check that they agree. If your bar is cut into 4 equal parts, your equation uses fourths and your number line hops in fourths too. Two pictures that cut the same amount into different-sized parts are not showing the same thing.
A diagram, a number line, and an equation can all show the same fraction problem, and when they match, you know your answer is right.
The rewritten readings were written for this dataset.
برای خواندن بیشتر
Write a story with numbers
A pencil costs 125p. A rubber costs 75p. To find their total cost, write 125 + 75 = ?. The question mark means the amount you need to find. This number sentence matches the shopping story. Writing it before you calculate helps you choose what to do.
Reasoning about equations with tape diagrams
Tape diagrams draw numbers as bars, and bar models work the same way. A fraction problem becomes a bar split into equal parts, with shading showing the fraction. The picture and the equation must tell the same story. If the bar shows 3 parts with 2 shaded, the equation must use 2/3.
Key ideas: compare non-unit fractions less than 1 with the same numerator by using tape diagrams
Diagrams make fractions visible. Draw a bar, split it into equal parts and shade some to show the fraction. Two bars side by side let you compare fractions fairly. Number lines do a similar job for adding: each jump stands for a quantity in the story, and landing points show the running total. Pictures, bars and lines all describe the same maths.
Show the same total in different ways
You sell 234 apples today and 156 tomorrow. Write 234 + 156 = ? to find how many you sell altogether. On a number line, begin at 234 and move forward by 156. A bar model can show the amounts too. Each way must show the same total. Matching them helps you understand.
کاوش بیشتر
۲ · ببین
به انگلیسی۳ · بازی
به انگلیسیبه انگلیسی
Try it yourself
Shade parts of the bar and watch the fraction change.
دور از صفحه‌نمایش
چاپ کاربرگکاغذ A4، با یک صفحهٔ جواب‌ها برای بزرگ‌ترها. بدون صفحه‌نمایش، بدون اینترنت.
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سپس تمرین
۳۳ سؤال پشت این درس منتظرند، هر کدام با پاسخ توضیح‌داده‌شده. هر پاسخ آسمان را پر می‌کند: ستاره‌ها هنگام یادگیری روشن می‌شوند و وقتی زمان برگشتن است کمرنگ می‌شوند.