eduKate · English · Ages 8–10
Choose your next learning step
Start with a precise question, select the relevant information, then explain the answer.
Understand the ideas
Clarify meanings and language choices.2 · Chapters 3–6
Learn the word cards
Read the 20 linked definitions and examples.3 · Chapter 7
Connect through a story
Follow the same story in all four languages.4 · Chapters 8–9
Practise and plan
Explain your reasoning and use a flexible plan.5 · Chapters 10–12
Support and move forward
Choose a helpful next step and check progress.
Chapter contents · Worked example: correct totals, wrong feature · Practise the reasoning, not just the answer · Vocabulary articles
These 20 vocabulary words help children aged about 8–10 ask a precise question, gather relevant information and explain an answer. Evidence is information that helps judge a particular claim; confidence alone is not evidence. Begin with the question ‘What do we need to find out?’ and connect each new word to a small, visible task.
All four editions share word numbers, the original story and the same worked example. Learn one meaning in a familiar language, then use that word’s links to compare English, Mandarin, Hindi or Russian. Keep the question and the objects unchanged while changing the language. Children do not need to memorise every translation or read all four scripts independently.
The envelope counts below are invented teaching data, not results collected from real children. Paper drawings are enough to study them. For a fresh prediction task, use a different hidden set and record the prediction before revealing its contents; a known answer is no longer a prediction. Ages 8–10 are a flexible guide, and pointing or oral explanation is welcome.
Chapter contents
1–4 · Build an answer from relevant evidence
5–8 · Clues, reasons and sources: words 11–15
9–12 · A flexible seven-day plan
A useful answer connects three parts: the question, the relevant information and the reason. In our example, the question asks which envelope contains more triangle cards. A has three circles and two triangles; B has one circle and four triangles. Both contain five cards altogether, but that total answers a different question. For triangle count, compare two with four.
Worked example: correct totals, wrong feature
Worked correction: ‘They are equal because each has five’ uses a correct total for the wrong feature. Keep the accurate counting, return to the word triangle in the question, sort by shape and compare the triangle column. Then say, ‘B has more triangles because four is greater than two; the difference is two.’ The repair targets the changed meaning, rather than asking the child to recount everything without a purpose.
This is a check of hidden contents, not an experiment showing why the contents differ. It also does not establish a rule about envelope colour or width. Good reasoning includes a boundary: these counts answer this question for these two unchanged sets. If the contents change, check again. If we ask a new question, choose the information relevant to that question.
Use the table as a concept map, then read definitions and examples on the cards. Several words overlap in daily speech: notice may begin an observation, and test and check can both describe examining an idea. Here test names the planned attempt, while check emphasises verifying the count or record. This is a useful distinction for the activity, not a claim that the words never overlap.
Evidence is used here for relevant supporting or challenging information, rather than a guarantee that every claim is settled. Mandarin 证据, Hindi प्रमाण and Russian свидетельства should be read with that definition. English evidence is normally uncountable; the Russian heading uses a plural form. Translate the meaning in the whole sentence instead of copying grammar word for word.
Mandarin pinyin includes tone marks. Hindi and Russian Roman guides are approximate reading prompts; Russian stress marks in headings are learning aids usually absent from ordinary text. A learner can understand the reasoning before recalling a translated label. If that happens, supply the label and preserve the successful explanation, then practise recall separately.
1. question · 问题
English: question
Something you ask because you want information or understanding. A useful question names what you want to find out. ‘Which envelope has more triangle cards?’ is clearer than ‘Which is more?’.
Our question is about triangle cards, not all cards.
简体中文·普通话: 问题 (wèntí)
为了获取信息或理解而提出的话。有效问题说清想知道什么。“哪个信封的三角形卡更多”比“哪个更多”清楚。
我们的问题问三角形卡，不是所有卡。
हिन्दी: प्रश्न (praśn)
जानकारी या समझ पाने के लिए पूछी बात। उपयोगी प्रश्न बताता है क्या जानना है। ‘किस लिफाफे में अधिक त्रिभुज कार्ड हैं?’ केवल ‘कौन अधिक?’ से स्पष्ट है।
हमारा प्रश्न त्रिभुज कार्डों पर है, सभी कार्डों पर नहीं।
Русский: вопро́с (vopros)
То, что спрашивают ради сведений или понимания. Уточняйте предмет вопроса: «В каком конверте больше треугольных карточек?» яснее, чем «Где больше?».
Наш вопрос о треугольных карточках, а не обо всех карточках.
Rewrite ‘Which has more?’ to name the two sets and the feature being counted. Use the word triangle so a partner knows exactly what to check.
2. answer · 回答
English: answer
A response to a question. An answer can be brief, but it should address what was asked. Saying the total number of cards does not answer a question about how many are triangles.
The answer names envelope B and gives the counts.
简体中文·普通话: 回答 (huídá)
对问题的回应。回答可以简短，但应针对所问内容。说出总卡数，并没有回答三角形卡有多少。
回答指出信封B，并给出数量。
हिन्दी: उत्तर (uttar)
प्रश्न का जवाब। छोटा हो सकता है, पर पूछी बात का होना चाहिए। कुल कार्ड गिनना त्रिभुजों की संख्या वाले प्रश्न का उत्तर नहीं।
उत्तर लिफाफा B बताता है और गिनती देता है।
Русский: отве́т (otvet)
Реакция на вопрос. Ответ может быть коротким, но должен относиться к спрошенному. Общее число карточек не отвечает на вопрос о числе треугольников.
Ответ называет конверт B и приводит числа.
Give a short answer to the triangle question, then add a reason. Check that neither sentence quietly switches from triangles to all cards.
3. notice · 注意到
English: notice
To become aware of a detail. Noticing may start a question, but a noticed feature is not automatically useful evidence for every question. Envelope width alone does not tell us its triangle count.
We notice that the envelopes look different.
简体中文·普通话: 注意到 (zhùyìdào)
留意到一个细节。注意到可能引发问题，但并非每个细节都能回答所有问题。信封宽度本身不能告诉我们三角形卡数。
我们注意到信封外观不同。
हिन्दी: ध्यान देना (dhyān denā)
किसी विवरण पर ध्यान जाना। इससे प्रश्न शुरू हो सकता है, लेकिन हर विवरण हर प्रश्न का प्रमाण नहीं। केवल लिफाफे की चौड़ाई त्रिभुजों की संख्या नहीं बताती।
हम ध्यान देते हैं कि लिफाफे अलग दिखते हैं।
Русский: замеча́ть (zamechat)
Обратить внимание на деталь. Она может вызвать вопрос, но не становится автоматически свидетельством для любого вывода. Ширина конверта не задаёт число треугольников.
Мы замечаем, что конверты выглядят по-разному.
Name one thing you notice about two drawn envelopes. Then ask whether that detail helps count hidden triangles. A noticeable detail can still be irrelevant.
4. observe · 观察
English: observe
To examine carefully and gather details. Observation is more than a quick guess. In this activity, look at each card’s shape and keep the two sets separate while counting.
We observe the cards after opening each envelope.
简体中文·普通话: 观察 (guānchá)
仔细查看并收集细节，不只是迅速猜测。本活动应查看每张卡形状，计数时保持两组分开。
打开每个信封后，我们观察卡片。
हिन्दी: अवलोकन करना (avalokan karnā)
ध्यान से देखना और विवरण जुटाना। अवलोकन झटपट अनुमान से अधिक है। हर कार्ड की आकृति देखें और गिनते समय दोनों सेट अलग रखें।
हर लिफाफा खोलकर हम कार्डों का अवलोकन करते हैं।
Русский: наблюда́ть (nablyudat)
Внимательно изучать и собирать детали. Это не быстрая догадка. Здесь рассматривайте форму каждой карточки и не смешивайте два набора при подсчёте.
Мы рассматриваем карточки после открытия каждого конверта.
Draw or sort the example cards into circles and triangles. Keep the A and B sets separate, and count each relevant card once.
5. compare · 比较
English: compare
To examine similarities and differences using a stated feature. Compare triangle counts with triangle counts. Comparing the total in one set with the triangles in another changes the question.
We compare two triangles in A with four triangles in B.
简体中文·普通话: 比较 (bǐjiào)
按指定特征查看相同与不同。应比较两组三角形数量，不把一组总数与另一组三角形数混比。
我们比较A的两个三角形与B的四个三角形。
हिन्दी: तुलना करना (tulnā karnā)
बताई विशेषता से समानता और अंतर देखना। त्रिभुजों को त्रिभुजों से तुलना करें; एक सेट के कुल को दूसरे के त्रिभुजों से लेना प्रश्न बदल देता है।
हम A के दो और B के चार त्रिभुजों की तुलना करते हैं।
Русский: сра́внивать (sravnivat)
Искать сходства и различия по выбранному признаку. Сопоставляйте числа треугольников, а не общее число в одном наборе с треугольниками в другом.
Мы сравниваем два треугольника в A с четырьмя в B.
Compare A’s triangle count with B’s triangle count. Then compare their total counts as a different question. Explain why both comparisons can have different answers.
6. predict · 预测
English: predict
To say what you expect to happen or find before checking. A prediction can have a reason and still differ from the result. Keep the original prediction so you can compare expectation with evidence.
Before opening the envelopes, Eva predicts that A has more triangles.
简体中文·普通话: 预测 (yùcè)
检查前说出预期会发生或发现什么。预测即使有理由，也可能与结果不同。保留原预测，才能比较预期与证据。
打开信封前，伊娃预测A有更多三角形。
हिन्दी: अनुमान लगाना (anumān lagānā)
जाँच से पहले बताना कि क्या होने या मिलने की उम्मीद है। कारण वाला अनुमान भी परिणाम से अलग हो सकता है। मूल अनुमान रखें ताकि प्रमाण से तुलना हो।
खोलने से पहले ईवा अनुमान लगाती है कि A में अधिक त्रिभुज हैं।
Русский: предска́зывать (predskazyvat)
Сказать заранее, что ожидаете произойти или обнаружить. Прогноз с причиной может не совпасть с результатом. Сохраните его для сравнения со свидетельствами.
До открытия Эва предполагает, что в A больше треугольников.
For a genuinely new hidden set, say what you expect before it is revealed. Keep that sentence unchanged beside the later result. Do not predict counts already supplied here.
7. test · 检验
English: test
To carry out a planned check of an idea or prediction. Here test is an action, not an examination mark. Opening and sorting the cards checks the hidden-content prediction; it is not a test of what caused the contents.
We test the prediction by opening, sorting and counting.
简体中文·普通话: 检验 (jiǎnyàn)
按计划检查想法或预测。本课test是动作，不是考试分数。打开并分类可检验隐藏内容的预测，并不检验内容由何原因形成。
我们通过打开、分类和计数检验预测。
हिन्दी: जाँच करना (jā̃c karnā)
विचार या अनुमान की नियोजित जाँच। यहाँ test क्रिया है, परीक्षा अंक नहीं। खोलकर छाँटना छिपी सामग्री का अनुमान जाँचता है, सामग्री का कारण नहीं।
हम खोलकर, छाँटकर और गिनकर अनुमान जाँचते हैं।
Русский: проверя́ть (proveryat)
Выполнить запланированную проверку идеи. Здесь test — действие, не экзамен. Открытие и сортировка проверяют предположение о содержимом, но не причину его появления.
Мы проверяем предположение, открывая, сортируя и считая.
Plan a check that can answer the question: open, separate by shape, count and label. Explain why looking at an envelope’s width alone is not that check.
8. result · 结果
English: result
What was found or happened in a check. A result is not the same as the earlier prediction. Record an unexpected result honestly rather than changing it to match what you hoped to find.
The result is A: two triangles; B: four triangles.
简体中文·普通话: 结果 (jiéguǒ)
检查发现或发生的情况。结果不同于先前预测。即使意外，也应如实记录，不为符合希望而改写。
结果是A两个三角形，B四个三角形。
हिन्दी: परिणाम (pariṇām)
जाँच में जो मिला या हुआ। परिणाम पहले के अनुमान जैसा शब्द नहीं। अप्रत्याशित परिणाम सच दर्ज करें, उम्मीद से मिलाने के लिए न बदलें।
परिणाम है A: दो त्रिभुज; B: चार त्रिभुज।
Русский: результа́т (rezultat)
То, что обнаружилось при проверке. Результат отличается от прежнего прогноза. Неожиданное записывают честно, не подгоняя под ожидание.
Результат: в A два треугольника, в B четыре.
Read the table’s result aloud without changing it to match a prediction. Distinguish the observed or supplied result from what somebody expected beforehand.
9. record · 记录
English: record
To preserve information in words, pictures or numbers. Here record is a verb. Label each set and each counted feature so someone else can understand what the numbers refer to.
We record circle and triangle counts in separate columns.
简体中文·普通话: 记录 (jìlù)
用文字、图或数字保存信息。本课record是动词。标明每组与计数特征，让别人知道数字指什么。
我们把圆形与三角形数记在不同栏。
हिन्दी: दर्ज करना (darj karnā)
शब्दों, चित्रों या संख्याओं में जानकारी रखना। यहाँ record क्रिया है। हर सेट और गिनी विशेषता लिखें ताकि संख्या का अर्थ समझ आए।
हम वृत्त और त्रिभुजों की संख्या अलग कॉलम में दर्ज करते हैं।
Русский: запи́сывать (zapisyvat)
Сохранять сведения словами, рисунками или числами. Здесь record — глагол. Подписывайте набор и признак, чтобы числа были понятны другому.
Мы записываем числа кругов и треугольников в разные столбцы.
Create headings for envelope, circles, triangles and total. Explain what each number means. A row of unlabelled numbers loses information a reader needs.
10. evidence · 证据
English: evidence
Information relevant to judging a claim or answering a question. Evidence may support or challenge an idea; it is not automatically complete proof. Ask how the information connects to the particular claim.
The recorded triangle counts are evidence for our answer.
简体中文·普通话: 证据 (zhèngjù)
与判断说法或回答问题有关的信息。证据可支持或质疑想法，并非自动成为完整证明。应问它与具体说法怎样联系。
记录的三角形数是回答的证据。
हिन्दी: प्रमाण (pramāṇ)
दावे को परखने या प्रश्न का उत्तर देने से संबंधित जानकारी। प्रमाण विचार का समर्थन या विरोध कर सकता है; अपने आप पूर्ण सिद्धि नहीं। खास दावे से संबंध पूछें।
दर्ज त्रिभुज गिनती हमारे उत्तर का प्रमाण है।
Русский: свиде́тельства (svidetelstva)
Сведения, относящиеся к оценке утверждения. Они могут поддерживать или оспаривать мысль и не равны автоматически полному доказательству. Уточняйте связь с вопросом.
Записанные числа треугольников служат свидетельствами для ответа.
Choose the table entries that support the triangle answer. Explain why correct but unrelated information, such as a favourite colour, cannot substitute for those counts.
11. clue · 线索
English: clue
A detail that may help you work out something or decide where to look next. A clue can be incomplete. Check whether it actually bears on the question before treating it as strong evidence.
A note saying ‘shape cards’ is a clue about what to look for, not the triangle count.
简体中文·普通话: 线索 (xiànsuǒ)
可能帮助推想或寻找下一步的细节。线索可能不完整，应先核对它是否真正有关，再当作强证据。
写着形状卡的便条提示要找什么，却没给三角形数。
हिन्दी: सुराग (surāg)
विवरण जो बात समझने या आगे कहाँ देखें बताने में मदद करे। सुराग अधूरा हो सकता है। मजबूत प्रमाण मानने से पहले प्रश्न से संबंध जाँचें।
‘आकृति कार्ड’ वाला नोट खोजने का सुराग है, त्रिभुजों की गिनती नहीं।
Русский: подска́зка (podskazka)
Деталь, помогающая разобраться или выбрать следующий поиск. Подсказка может быть неполной. Проверьте её отношение к вопросу, прежде чем считать сильным свидетельством.
Записка «карточки с фигурами» подсказывает, что искать, но не число треугольников.
Read the clue ‘shape cards’. Say what it suggests looking for and what it leaves unknown. Do not turn a partial clue into an exact count.
12. reason · 理由
English: reason
Why someone chooses or believes something. A reason can be strong or weak. ‘B has four triangles and A has two’ is relevant; ‘I like B’ does not establish which set contains more triangles.
Our reason uses the two relevant counts.
简体中文·普通话: 理由 (lǐyóu)
选择或相信某事的依据，可能强也可能弱。B四个A两个与数量有关；喜欢B并不能确定哪组更多。
我们的理由采用两个相关数量。
हिन्दी: कारण (kāraṇ)
चुनने या मानने का आधार। कारण मजबूत या कमजोर हो सकता है। ‘B में चार, A में दो’ संबंधित है; ‘B पसंद है’ अधिक त्रिभुज नहीं बताता।
हमारा कारण दोनों संबंधित गिनतियाँ लेता है।
Русский: основа́ние (osnovaniye)
Основание выбора или убеждения. Оно бывает сильным или слабым. «В B четыре, в A два» относится к вопросу; «мне нравится B» не устанавливает количество.
Наше основание использует два относящихся к вопросу числа.
Compare ‘B has four triangles and A has two’ with ‘I prefer B’. Which provides a reason about triangle quantity, and which concerns a preference?
13. explain · 解释
English: explain
To make thinking clear by showing a connection or giving a reason. In this lesson, explain how the counts support the answer. Repeating an answer more loudly does not add that connection.
We explain that four is greater than two, so B has more triangles.
简体中文·普通话: 解释 (jiěshì)
通过联系或理由让思路清楚。本课解释数量如何支持回答。把答案更大声重复，并没有增加这种联系。
我们解释四大于二，所以B有更多三角形。
हिन्दी: समझाना (samjhānā)
संबंध या कारण से सोच स्पष्ट करना। यहाँ गिनती उत्तर को कैसे सहारा देती है बताएँ। ज़ोर से उत्तर दोहराना नया संबंध नहीं देता।
हम समझाते हैं कि चार दो से अधिक है, इसलिए B में अधिक त्रिभुज हैं।
Русский: объясня́ть (obyasnyat)
Делать рассуждение понятным через связь или причину. Здесь объясняйте, как числа поддерживают ответ. Громкое повторение ответа не добавляет связи.
Мы объясняем: четыре больше двух, значит в B больше треугольников.
Complete ‘B has more triangles because…’. Include the relevant comparison, not merely another confident statement that B is the answer.
14. source · 来源
English: source
Where information comes from. A source can be a direct observation, a record, a person or a publication. Identify what the source actually provides and whether it fits the question.
For readers, the fictional table is the source of these example counts.
简体中文·普通话: 来源 (láiyuán)
信息从哪里来，可是直接观察、记录、人物或出版物。应明确来源实际提供什么，以及是否适合问题。
对读者，这些例子数量的来源是虚构表格。
हिन्दी: स्रोत (srot)
जानकारी कहाँ से आई। सीधा अवलोकन, रिकॉर्ड, व्यक्ति या प्रकाशन स्रोत हो सकता है। वह क्या देता है और प्रश्न से कैसे जुड़ता है, पहचानें।
पाठकों के लिए उदाहरण की गिनतियों का स्रोत काल्पनिक तालिका है।
Русский: исто́чник (istochnik)
Откуда пришли сведения: наблюдение, запись, человек или публикация. Установите, что именно даёт источник и подходит ли это вопросу.
Для читателя источник чисел примера — вымышленная таблица.
Name your source for the example counts. If you read them in this story, say that. If you count a new real set, label that as a different source and result.
15. fact · 事实
English: fact
Something true about a situation or the world. A factual claim is a statement that can be checked, but it may turn out false. Being checkable does not by itself make a statement true.
In the example record, B contains four triangle cards.
简体中文·普通话: 事实 (shìshí)
关于情况或世界的真实内容。可核实的事实性说法仍可能错误；能检查本身不代表真实。
在例子记录中，B有四张三角形卡。
हिन्दी: तथ्य (tathya)
स्थिति या दुनिया की सच्ची बात। तथ्यात्मक दावा जाँचा जा सकता है, लेकिन गलत भी निकल सकता है। जाँच योग्य होना अपने आप सच होना नहीं है।
उदाहरण के रिकॉर्ड में B में चार त्रिभुज कार्ड हैं।
Русский: факт (fakt)
То, что действительно верно. Проверяемое утверждение может оказаться ложным: возможность проверки сама по себе не делает его фактом.
В записи примера в B четыре треугольные карточки.
Check the factual claim ‘B has six triangles’ against the example record. Explain that a checkable statement can be false; it is not made true by confidence.
16. opinion · 看法
English: opinion
A personal view, preference or judgement. An opinion may have reasons, but a preference is not a count. A false factual claim does not become an opinion merely because somebody says it confidently.
I prefer the blue envelope is an opinion about a preference.
简体中文·普通话: 看法 (kànfǎ)
个人观点、偏好或判断。看法可以有理由，但偏好不是数量。错误事实性说法不会因说得自信就变成看法。
我更喜欢蓝信封，是表达偏好的看法。
हिन्दी: राय (rāy)
निजी विचार, पसंद या निर्णय। राय के कारण हो सकते हैं, लेकिन पसंद गिनती नहीं। गलत तथ्यात्मक दावा केवल आत्मविश्वास से राय नहीं बनता।
‘मुझे नीला लिफाफा पसंद है’ पसंद की राय है।
Русский: мне́ние (mneniye)
Личный взгляд, предпочтение или оценка. Мнение может иметь основания, но предпочтение не равно числу. Ложное проверяемое утверждение не становится мнением от уверенного тона.
«Мне больше нравится синий конверт» выражает предпочтение.
State a preference about an envelope without changing its contents. You can prefer A while concluding B contains more triangles; these answer different questions.
17. uncertain · 不确定的
English: uncertain
Not sure, or lacking enough information for confidence. Say what remains uncertain and what could help check it. Uncertainty is not a reason to invent a missing number.
Before opening, we are uncertain about the triangle counts.
简体中文·普通话: 不确定的 (bù quèdìng de)
没有把握或缺少足够信息。说清哪部分不确定，以及怎样核对，而不是编造缺少的数。
打开前，我们不确定三角形数量。
हिन्दी: अनिश्चित (aniścit)
निश्चित न होना या भरोसे के लिए पर्याप्त जानकारी न होना। क्या अनिश्चित है और कैसे जाँचें बताएँ; संख्या न गढ़ें।
खोलने से पहले त्रिभुजों की गिनती को लेकर हम अनिश्चित हैं।
Русский: неуве́ренный (neuverennyy)
Не имеющий достаточной уверенности или сведений. Укажите, что неясно и как проверить. Неопределённость не оправдывает выдуманное число.
До открытия мы не уверены в числе треугольников.
Without a record for a third envelope, say what is uncertain and propose a check. Do not borrow A’s or B’s number just to fill the gap.
18. check · 核对
English: check
To examine whether something agrees with an appropriate reference or method. Here check means recounting against the cards and matching the table to each set, not simply asking another person to agree.
Arun checks each count against the correct envelope’s cards.
简体中文·普通话: 核对 (héduì)
用合适依据或方法查看是否一致。本课指对照卡片重数、核对表格与各组，不只是叫别人同意。
阿伦对照正确信封的卡片核对每个数量。
हिन्दी: जाँचना (jā̃cnā)
उचित आधार या तरीके से मिलान जाँचना। यहाँ कार्ड फिर गिनकर तालिका से मिलाना है, केवल दूसरे से सहमति लेना नहीं।
अरुण सही लिफाफे के कार्डों से हर गिनती जाँचता है।
Русский: сверя́ть (sveryat)
Сопоставлять с подходящим основанием или способом проверки. Здесь — пересчитать карточки и сверить таблицу, а не просто получить согласие другого.
Арун сверяет каждое число с карточками нужного конверта.
Recount the triangles while matching each card to one count. Compare the written record with the correct set. Another person’s agreement alone is not the recount.
19. revise · 修正
English: revise
To change an idea or answer after thinking again or examining new information. Revising an unsupported answer is useful. Preserve the record of what was actually found rather than altering results to protect a prediction.
Eva revises her answer when the relevant counts challenge her prediction.
简体中文·普通话: 修正 (xiūzhèng)
重新思考或查看新信息后改变想法或回答。修正缺乏支持的答案是有用的；应保留真实发现，不为维护预测而改结果。
相关数量与预测不同后，伊娃修正回答。
हिन्दी: संशोधन करना (saṃśodhan karnā)
फिर सोचकर या नई जानकारी देखकर विचार या उत्तर बदलना। असमर्थित उत्तर बदलना उपयोगी है। अनुमान बचाने के लिए परिणाम न बदलें।
संबंधित गिनतियाँ अनुमान के विरुद्ध हों तो ईवा उत्तर में संशोधन करती है।
Русский: пересма́тривать (peresmatrivat)
Изменять мысль после повторного обдумывания или новых сведений. Пересмотреть ответ полезно; менять результаты ради защиты прогноза — другое.
Эва пересматривает ответ, когда нужные числа противоречат прогнозу.
Change an unsupported answer after checking. Keep the old prediction visible and the result intact, so the change in thinking can be explained.
20. conclude · 得出结论
English: conclude
To decide what the available evidence supports after examining it. Keep the conclusion within the question and the checked information. Two example envelopes do not tell us what every envelope in the world contains.
We conclude that B has two more triangles than A in this example.
简体中文·普通话: 得出结论 (déchū jiélùn)
查看证据后判断它支持什么。结论应限于问题与已核对信息，两个例子信封不能说明世界所有信封装什么。
我们得出结论：本例B比A多两个三角形。
हिन्दी: निष्कर्ष निकालना (niṣkarṣ nikālnā)
प्रमाण देखकर तय करना कि वह क्या सहारा देता है। निष्कर्ष प्रश्न और जाँची जानकारी तक रखें। दो लिफाफे दुनिया के हर लिफाफे की बात नहीं बताते।
हम निष्कर्ष निकालते हैं कि इस उदाहरण में B में A से दो अधिक त्रिभुज हैं।
Русский: де́лать вы́вод (delat vyvod)
Решить, что поддерживают рассмотренные сведения. Ограничьте вывод вопросом и проверенным материалом. Два конверта не описывают содержимое всех конвертов.
Мы делаем вывод: в этом примере в B на два треугольника больше, чем в A.
Write a conclusion limited to these two unchanged sets. Include which has more triangles and the difference. Name one new question this conclusion does not answer.
Read the invented counts as information supplied by the story. For readers, the table and text are the source; the characters in the fiction handle and count cards. Do not describe the table as a real measurement you personally made. A repeat with your own cards is a separate activity and should keep its own honest record.
The relevant comparison is B’s four triangles against A’s two. Four minus two equals two, so ‘two more’ describes the difference. It does not mean B has two triangles altogether. The equal totals of five are also valid information, but they become relevant to a question about total cards rather than triangle count.
| Envelope | Circles | Triangles | All cards |
|---|---|---|---|
| A | 3 | 2 | 5 |
| B | 1 | 4 | 5 |
English · The two envelopes
Eva and Arun found two closed envelopes, A and B, beside a note saying ‘shape cards’. Their question was precise: ‘Which envelope contains more triangle cards?’ The note was a clue about what to look for, not a record of the contents. Eva noticed that A looked wider and predicted it would have more triangles. Arun wrote that prediction before opening anything. They agreed that width alone did not establish the count.
They opened the envelopes and kept their contents separate. A contained three circle cards and two triangle cards. B contained one circle card and four triangle cards. They recorded circles, triangles and totals in labelled columns. Each envelope contained five cards altogether.
‘Equal!’ said Arun, looking at the totals. Eva pointed back to the question. ‘We asked about triangles.’ They kept the correct totals but compared the relevant column instead: two in A, four in B. Four was greater than two, with a difference of two. Arun checked by counting each triangle once against the appropriate set.
Eva revised her answer. ‘B contains two more triangle cards than A in these sets.’ She kept her first prediction visible rather than changing it to look as if she had been right all along. ‘I still prefer the look of A,’ she added. That preference could stay the same while the answer about quantity changed.
They named their source: their own count within the story. For someone reading their written record, the source would be the supplied table, not a personal observation of those cards. They did not claim that wider envelopes always held more shapes, or that a third envelope had the same contents.
Their last question was, ‘What would we need to check next?’ A useful conclusion had answered one question and left the boundary clear.
简体中文·普通话 · 两个信封
伊娃与阿伦发现两个关闭的信封A、B，旁边便条写着形状卡。他们的问题很明确：“哪个信封的三角形卡更多？”便条是寻找内容的线索，不是内容记录。伊娃注意到A较宽，预测它的三角形更多。阿伦在打开前记下预测。他们同意宽度本身并不能确定数量。
打开后，两组内容分开放。A有三张圆形卡、两张三角形卡；B有一张圆形卡、四张三角形卡。他们在标好的圆形、三角形、总数栏记录，每个信封总数都是五。
阿伦看总数说：“一样多！”伊娃指回问题：“我们问的是三角形。”他们保留正确总数，改比相关栏：A二，B四。四大于二，相差二。阿伦对照对应组逐张数三角形来核对。
伊娃修正回答：“这两组中，B比A多两张三角形卡。”她保留原预测，没有改成仿佛一直猜对。“我还是更喜欢A的外观。”偏好可以不变，而数量回答改变。
他们说明来源：故事中自己计的数。对阅读记录的人，来源是提供的表格，而非亲自观察这些卡。他们没有声称宽信封总装更多，也没说第三信封有什么。
最后问：“下一步还需要查什么？”有用结论回答一个问题，也清楚保留范围。
हिन्दी · दो लिफाफे
ईवा और अरुण को बंद लिफाफे A और B मिले। पास नोट पर ‘आकृति कार्ड’ लिखा था। उनका प्रश्न साफ था: ‘किसमें अधिक त्रिभुज कार्ड हैं?’ नोट खोजने का सुराग था, सामग्री का रिकॉर्ड नहीं। ईवा ने A चौड़ा देखकर अधिक त्रिभुज का अनुमान लगाया। अरुण ने खोलने से पहले लिखा। वे जानते थे कि चौड़ाई अकेले गिनती नहीं बताती।
उन्होंने खोलकर सेट अलग रखे। A में तीन वृत्त और दो त्रिभुज कार्ड थे। B में एक वृत्त और चार त्रिभुज कार्ड। वृत्त, त्रिभुज और कुल के नाम वाले कॉलम में दर्ज किया। दोनों में कुल पाँच कार्ड थे।
कुल देखकर अरुण बोला, ‘बराबर!’ ईवा ने प्रश्न दिखाया: ‘हमने त्रिभुज पूछे थे।’ सही कुल रखा और संबंधित कॉलम तुलना किया: A में दो, B में चार। चार दो से अधिक, अंतर दो। अरुण ने सही सेट में हर त्रिभुज एक बार फिर गिना।
ईवा ने उत्तर बदला: ‘इन सेटों में B में A से दो अधिक त्रिभुज कार्ड हैं।’ मूल अनुमान नहीं मिटाया, मानो पहले से सही था। उसने जोड़ा, ‘फिर भी मुझे A दिखने में पसंद है।’ पसंद वही रह सकती थी, मात्रा का उत्तर बदल सकता था।
उन्होंने स्रोत बताया: कहानी में अपनी गिनती। रिकॉर्ड पढ़ने वाले के लिए स्रोत दी तालिका थी, कार्डों का अपना अवलोकन नहीं। उन्होंने हर चौड़े लिफाफे या तीसरे लिफाफे की सामग्री पर दावा नहीं किया।
अंतिम प्रश्न था, ‘आगे क्या जाँचना होगा?’ उपयोगी निष्कर्ष ने एक प्रश्न का उत्तर और अपनी सीमा स्पष्ट रखी।
Русский · Два конверта
Эва и Арун нашли два закрытых конверта, A и B, рядом с запиской «карточки с фигурами». Вопрос был точным: «В каком конверте больше треугольных карточек?» Записка подсказывала, что искать, но не сообщала состав. Эва заметила, что A шире, и предположила больше треугольников. Арун записал прогноз до открытия. Они понимали, что ширины для числа недостаточно.
Конверты открыли, наборы не смешивали. В A было три круга и два треугольника; в B один круг и четыре треугольника. Дети подписали столбцы кругов, треугольников и общего числа. В каждом конверте оказалось по пять карточек.
«Поровну!» — сказал Арун, глядя на итоги. Эва показала вопрос: «Мы спрашивали о треугольниках». Верные итоги сохранили, но сравнили нужный столбец: два в A, четыре в B. Четыре больше двух, разница два. Арун проверил числа, считая каждый треугольник один раз в нужном наборе.
Эва пересмотрела ответ: «В этих наборах в B на две треугольные карточки больше». Старый прогноз оставила видимым, не переписав как изначально верный. «Но внешне мне всё ещё нравится A», — добавила она. Предпочтение могло сохраниться при изменении ответа о количестве.
Внутри рассказа источником служил их подсчёт. Для читателя записи источником была бы предоставленная таблица, не личное наблюдение карточек. Дети не заявляли ничего обо всех широких конвертах или содержимом третьего.
Последним стал вопрос: «Что нужно проверить дальше?» Полезный вывод отвечал на вопрос и ясно сохранял границы.
Try each discussion question before checking the answer guide. A short reason, a sketch or pointing to the correct column can show understanding. Explain which question the evidence answers. Some responses allow more than one reasonable checking method; assess whether the method can actually resolve the uncertainty, not whether it uses the adult’s exact wording.
1. Which envelope has more triangle cards, and how many more?
2. Why does ‘Both have five cards’ not settle the triangle question?
3. If the question changes to circle cards, what changes in the answer?
4. When should a prediction be recorded, and what if the result differs?
5. Does a wider envelope establish that it contains more triangles?
6. What is a reader’s source for the example counts?
7. Is ‘B has six triangles’ an opinion, or a factual claim to check? What does the record show?
8. Can Eva prefer A and still conclude B has more triangles?
9. What can we say about a third envelope whose contents are not supplied?
10. In the new example, C has one triangle and D has three. Which has more, and what is the difference?
Answer guide
- B has four and A has two, so B has two more. Compare the triangle column; ‘two more’ is the difference, not B’s total triangle count.
- Five is the total of circles and triangles together. The question asks for triangles alone. Keep the correct totals, but select two and four to answer the asked question.
- A has three circles and B has one, so A has two more circles. The table stays the same; the relevant column and answer change because the question changed.
- Before checking or revealing the unknown result. Keep the prediction and record the actual result separately, then revise the answer if needed. Do not rewrite the past prediction to make it match.
- No. Width is a noticed feature, but without further information it does not determine the hidden count. Opening, sorting and counting can check the contents in this activity.
- The supplied fictional table and story. The characters count within the fiction; readers should not claim those counts as their own real observations. A new physical activity has its own source and result.
- It is a factual claim. The example record shows four, so six is contradicted by that record. A false factual claim does not become a preference or opinion simply because it is wrong.
- Yes. Preference concerns what she likes; the count concerns contents. Neither answer needs to replace the other. Use the question to decide which kind of answer is relevant.
- Its count is uncertain. Obtain a suitable record or open and count it in a new activity. The A and B data do not supply its contents, and the missing answer is not automatically a matter of opinion.
- D has two more triangles, because three is greater than one and three minus one is two. The reasoning transfers even though the letters and counts differ. Keep the conclusion limited to those supplied sets.
The seven-day plan is a possible sequence, not a deadline or promise of mastery. Use brief sessions and return to an unclear connection. Change language while keeping the example stable; later change the counts while keeping the language familiar. That makes it easier to distinguish a vocabulary-recall difficulty from a problem selecting relevant information.
| Day | Words or focus | Activity | What to notice |
|---|---|---|---|
| 1 | 1–5 | State a precise question and sort the example cards. | Keep the counted feature clear. |
| 2 | 6–10 | Separate prediction, result and record. | Do not rewrite the prediction after the result. |
| 3 | 11–15 | Choose relevant evidence and name its source. | Distinguish a clue from a complete count. |
| 4 | 16–20 | Check a claim, revise and limit the conclusion. | Keep preference separate from quantity. |
| 5 | Worked story | Explain the error of comparing total cards. | Repair the feature without losing correct counts. |
| 6 | Two chosen words | Use matching links for another language. | Keep the question and data stable. |
| 7 | C and D | Apply the method to the transfer example. | Give the answer, evidence and reason. |
If the child answers using the total rather than triangles, keep the successful total and highlight the question’s counted feature. Sort once, label the columns and ask the child to point before speaking. If counting itself is uncertain, arrange the relevant cards in a line and count each once. These repairs address different difficulties and should not be replaced by more unrelated questions.
If prediction and result are confused, draw separate ‘before checking’ and ‘after checking’ spaces. Keep the initial prediction visible and place the observed result beside it. Changing a conclusion when evidence changes is useful; rewriting the old prediction as if it had always matched the result loses information. A mismatched prediction is an opportunity to examine the original reason.
For extension, ask what the same table cannot tell us. It does not show who packed the envelopes, why the shapes differ or what a third envelope contains. Name the missing information and propose a relevant source or check. Do not call every unknown statement an opinion: some are factual questions whose answers are not yet known.
Use new counts for a transfer check. For example, supply C with four circles and one triangle, and D with two circles and three triangles. Ask which has more triangles and how many more. A sound answer uses one and three, concludes D, and gives a difference of two; the equal totals of five are not the requested comparison.
Record the learner’s reasoning, not only the final letter. ‘Chose the triangle column and explained three is greater than one’ shows the connection. Then add one new demand, such as another language or a question about total cards. A hesitant translation does not erase correct reasoning; accurate pointing can be an appropriate first response.
| Envelope | Circles | Triangles | All cards |
|---|---|---|---|
| C | 4 | 1 | 5 |
| D | 2 | 3 | 5 |
CHAPTER 12 OF 12 · Support and move forward
12. Questions, sources and next reading
Do children have to learn four languages together?
No. Start with one understood idea and a familiar language. Add one expression when useful, keeping the same question and example. Matching word numbers support comparison without requiring equal fluency.
Is ages 8–10 a fixed requirement?
No. It guides the explanation level. Use fewer words, oral answers or pointing to the correct column when helpful. An older beginner can use the same cards for fuller reasoning or language comparison.
Are the envelope counts real research results?
No. They are explicitly invented teaching data. Readers learn from a supplied record. If you count your own cards, keep that separate record and use its actual results rather than copying the story’s numbers.
Does every investigation follow one fixed sequence?
No. This activity provides a simple route for practice. Real inquiry may return to a question, gather other information or change a method. The key is making the question, evidence and reasoning clear, not reciting a universal checklist.
Is an opinion the same as a false statement?
No. Preference or judgement differs from a factual claim. ‘B has six triangles’ is checkable and contradicted by this record; ‘I prefer A’ expresses a preference. Do not use opinion as a bin for every wrong or unknown answer.
What if a prediction is wrong?
Record the result honestly, examine the original reason and revise the answer if needed. A useful check can challenge an expectation. Keep the earlier prediction visible so the change in thinking can be understood.
Does checking mean asking someone else to agree?
No. Another person can help by independently counting against the actual set or examining the record. Agreement without a relevant check adds little information about whether the count is correct.
How do we know when to move to a new example?
Look for a precise question, selection of relevant counts and a short reason connecting evidence to answer. Then change one demand, such as the numbers or the language. Support the specific missing connection if the answer drifts.
Sources for further exploration
- Smithsonian National Museum of Natural History · See-Think-Wonder
- Smithsonian National Museum of Natural History · Science Process
- Science Buddies · Steps of the Scientific Method