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.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Fourth graders multiply a number with up to four digits by a one-digit number (such as 3,146 × 7) and a two-digit number by another two-digit number (such as 36 × 24). The standard does not require the traditional algorithm yet; that comes in fifth grade. Instead, students use strategies built on place value and the properties of operations, especially the distributive property.
The area model is the key picture. To find 36 × 24, students split each factor by place value (30 + 6 and 20 + 4) and draw a rectangle divided into four parts: 30 × 20, 30 × 4, 6 × 20 and 6 × 4. Adding the four partial products, 600 + 120 + 120 + 24, gives 864. Writing the same work as equations or as a column of partial products helps students see that every digit is multiplied by every other digit with its full place value.
Computing 36 × 24 as 3 × 2 and 6 × 4 to get 624 misses two of the four partial products. The area model shows all four rectangles must be included.
Students who treat the 3 in 36 as 3 instead of 30 write partial products that are ten times too small. Labeling each side of the area model with its full value prevents this.
Even with correct partial products, errors creep in when they are added. Lining them up in a column by place value makes the final sum reliable.
Use an area model to find 36 × 24.
Answer: 36 × 24 = 864.
Move from base-ten blocks to sketched area models to open area models where the rectangle is not drawn to scale. Then show the partial products method side by side so students see the same four numbers in both.
Assessment items frequently ask which expression matches an area model or which partial products are missing, not just the final answer. Practice reading and completing models as well as computing.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 864
30 × 20 = 600, 30 × 4 = 120, 6 × 20 = 120, 6 × 4 = 24. The total is 864.
Answer: 9268 (also accepted: 9,268)
2,000 × 4 = 8,000, 300 × 4 = 1,200, 10 × 4 = 40, 7 × 4 = 28. Add: 8,000 + 1,200 + 40 + 28 = 9,268.
Answer: B) (40 × 10) + (40 × 3) + (7 × 10) + (7 × 3)
Each part of 47 (40 and 7) must be multiplied by each part of 13 (10 and 3), giving four partial products.
Answer: C) 3,654
50 × 60 = 3,000, 50 × 3 = 150, 8 × 60 = 480, 8 × 3 = 24. Add: 3,000 + 150 + 480 + 24 = 3,654.
Answer: 980 (also accepted: 980 seats)
20 × 30 = 600, 20 × 5 = 100, 8 × 30 = 240, 8 × 5 = 40. The total is 600 + 100 + 240 + 40 = 980.
Answer: 9630 (also accepted: 9,630)
1,000 × 6 = 6,000, 600 × 6 = 3,600, 5 × 6 = 30. Add: 6,000 + 3,600 + 30 = 9,630.
A full lesson with slides, activities and an exit ticket on multi-digit multiplication, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.NBT.B.5 with an answer key, ready in about a minute.
Make a worksheet →Turn multi-digit multiplication into a quiz students answer online that marks itself, with a class summary for you.
Build a test →No. 4.NBT.B.5 asks for place value strategies such as area models and partial products. Fluency with the standard algorithm is a fifth grade expectation (5.NBT.B.5).
It is the product of one part of a factor with one part of the other factor, such as 30 × 4 in 36 × 24. Adding all the partial products gives the full product.