Partial Products and the Standard Algorithm

10 min

Narrative

This Number Talk routine encourages students to think about decomposing factors by place value to multiply multi-digit numbers by one-digit numbers. As students look for and make use of structure, they may notice that multiplying the ones place has a result in the pattern of 5, 10, and 15. Students may use the partial products equations to multiply. 

This routine helps students pay attention to the value of the digits when multiplying. This is important for setting up the conversation about the standard algorithm, in which students will find partial products mentally and use what they know about the value of the digits to condense the number of steps to multiply by multi-digit numbers.

Launch

  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategy.
  • Keep expression and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 5×1015 \times 101
  • 5×1025 \times 102
  • 5×2035 \times 203
  • 5×4045 \times 404

Sample Response

  • 505: 5×100=5005 \times 100 = 500 and 5×1=55 \times 1 = 5, and 500+5=505500 + 5 = 505.
  • 510: 5×1025 \times 102 is 5 more than 5×1015 \times 101, so it is 5 more than 505, which is 510.
  • 1,015: 5×2005 \times 200 is 1,000 and 5×35 \times 3 is 15, so 5×2035 \times 203 is 1,015.
  • 2,020: 404 is 4 times 101, 5×4045 \times 404 is 4 times 5×1015 \times 101 or 4×5054 \times 505, which is 2,020.
Activity Synthesis (Teacher Notes)
  • “What connections or relationships do you see between each expression?” (Each problem involves one more group of 5 or sets or 100 more.)
Standards
Addressing
  • 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
  • 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

20 min

15 min