Generalising from repeated reasoning
Recognise and use repeated reasoning to generalise: extend patterns in times tables and equivalent fractions, derive unknown facts from known facts efficiently, describe general rules
کارهایی که یادگیرنده بعد از این درس می‌تواند انجام دهد
- Notice that all fractions equivalent to 1/2 have a numerator that is half the denominator
- Use the pattern 3×4=12, 3×40=120, 3×400=1200 and explain the generalisation
- Derive 8×7 from 8×5=40 plus 8×2=16 and describe the strategy as a general approach
۱ · بخوان
You already know lots of times-table facts. Patterns hide inside them. Look at 3 × 4 = 12, 3 × 40 = 120, and 3 × 400 = 1200. When one factor gets 10 times bigger, the answer gets 10 times bigger too. One extra zero in gives one extra zero out. Say this rule aloud and use it for facts you have not learned by heart.
Mo needs 8×7 but only remembers 8×5 and 8×2. He splits it: 8×5=40 and 8×2=16. Then he adds them: 40+16=56. So 8×7=56, and Mo used the same splitting trick to solve a fact he had not memorized.
Equivalent fractions follow a rule too. 3 out of 6 shaded is the same amount as 1 out of 2. Look at the numbers: 3 is half of 6. Any fraction equal to 1/2 has a top number that is exactly half the bottom number, so 6/12 works and 5/11 does not.
Spot the pattern, say the rule in your own words, then use it to work out any new fact.
Retained academy, math-design and problems records are credited per item. x8-x10 are original P17 authoring with null license; publisher terms for retained corpus records were not independently verified.
۲ · ببین
به انگلیسیدور از صفحه‌نمایش
جایگاه این موضوع
اول این‌ها را یاد بگیر
پیوندهای اختیاری
این موضوع راه این‌ها را باز می‌کند
این موضوع به کجا می‌رسد
شغل‌هایی که بر این مهارت تکیه دارند. دنبال کردن یکی برای دیدن همهٔ چیزهایی که بر آن‌ها بنا شده است.
۱۸ 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.