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Topic A Place Value Understanding for Whole Numbers
In topic A, students apply their understanding of place value to multiply and divide by powers of 10 and their multiples.
Prior to grade 5, students use place value understanding to round multi-digit whole numbers to any place. They compare quantities through multiplicative comparison and recognize that in a whole number, a digit in one place represents 10 times as much as what it represents in the place to the right.
The topic opens with students using place value charts to show that when two adjacent digits in a given number are the same, the digit to the left is 10 times as much as the digit to the right and the digit to the right is 10 times as small as the digit to the left. Students use dot models to understand what happens when they multiply or divide a number by 10 . Next, students apply what they learn from the dot models to conclude that when they multiply a number by 10 , it causes each digit of the number to shift one place value to the left, and when they divide a number by 10 , it causes each digit of the number to shift one place value to the right. Building on this understanding, they notice how the digits shift when they multiply or divide a number by 100 and by 1,000 .
Students find products and quotients of expressions composed only of powers of 10, such as 10,000 × 100, by using what they learn about how digits in a number shift. When students find products and quotients of expressions composed only of 10s, it gives rise to learning about exponents with a base of 10. They write powers of 10 in standard form, expanded form, and exponential form. Students extend their understanding of the shifts they notice when they multiply or divide by 10 to multiplying and dividing by 102 or 103.
Students estimate products and quotients of multi-digit numbers by rounding factors, divisors, and dividends to multiples of powers of 10 . By comparing estimates and analyzing estimation strategies, they understand what may cause an underestimate or an overestimate. Students then estimate products and quotients in real-world situations. The topic culminates with students using observations about how digits shift when they multiply by powers of 10 to convert metric measurements.
By combining multiplicative comparison language with their understanding of powers of 10 , students describe relative sizes of units of metric length, weight, and capacity. They convert between units and express larger units in terms of smaller units by using powers of 10 . Students solve multi-step word problems involving metric conversions and apply their estimation skills from previous lessons to determine whether answers are reasonable.
In topic B, students apply their understanding of place value to multiply multi-digit whole numbers.
