Why Our Strategies Work
Aligned to 2.NBT.B.9 — Common Core State Standards for Mathematics.
What this lesson teaches
Adding and subtracting work because we group by tens. Ten ones make one ten, and ten tens make one hundred, so we can trade them.
Worked examples
Example 1
When 6 + 7 = 13, we have 13 ones. We trade 10 ones for 1 ten, so it becomes 1 ten and 3 ones. That is why we 'carry' a ten.
Example 2
In 52 − 8 you cannot take 8 from 2, so trade 1 ten for 10 ones. Now it is 4 tens and 12 ones: 12 − 8 = 4, so the answer is 44.
Example 3
Adding the tens first or the ones first gives the same total, because the groups do not change — only the order you count them does.
Practice questions
- Why can we add 30 + 40 by thinking 3 tens + 4 tens?
- When 8 + 5 = 13, how many tens do we trade for?
- Explain why 200 + 300 is 5 hundreds.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Por qué funcionan nuestras estrategias
Sumar y restar funcionan porque agrupamos de diez en diez. Diez unidades forman una decena, y diez decenas forman una centena, por eso podemos cambiarlas.
Ejemplo 1: Cuando 6 + 7 = 13, tenemos 13 unidades. Cambiamos 10 unidades por 1 decena, así queda 1 decena y 3 unidades. Por eso 'llevamos' una decena.
Ejemplo 2: En 52 − 8 no puedes quitarle 8 al 2, así que cambia 1 decena por 10 unidades. Ahora son 4 decenas y 12 unidades: 12 − 8 = 4, entonces la respuesta es 44.
Ejemplo 3: Sumar primero las decenas o primero las unidades da el mismo total, porque los grupos no cambian — solo cambia el orden en que los cuentas.
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