Multi-Digit Multiplication — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
In a Grade 5 lattice for 423 times 6, you draw a 2-by-2 grid.
Corrected: In a Grade 5 lattice for 423 times 6, you draw a 3-by-1 grid.
423 has 3 digits and 6 has 1 digit, so the lattice for Grade 5 students is 3 columns by 1 row, with diagonals inside each cell.
2. Fix the sentence:
After filling cells, Grade 5 learners adds the diagonals from left to right.
Corrected: After filling cells, Grade 5 learners add the diagonals from right to left.
Lattice diagonals are summed from the bottom-right toward the top-left so place value lines up, with regrouping carried into the next diagonal.
3. Fix the sentence:
Each cell of the lattice holds one partial products from a digit pair.
Corrected: Each cell of the lattice holds one partial product from a digit pair.
Grade 5 lattice cells store the single partial product of one digit from the top factor times one digit from the side factor, split by the diagonal.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. For Grade 5 lattice 312 times 4, the grid has 3 columns and 1 row.
The factor 4 has one digit, so the lattice has a single row across, with three columns matching the digits of 312.
2. In Grade 5 lattice work, each cell is split by one diagonal line.
Every lattice cell uses one diagonal so the tens digit of the partial product sits above and the ones digit sits below for clean adding.
3. If 7 times 8 equals 56, the cell shows 5 above and 6 below the diagonal.
Grade 5 lattice rules place the tens digit above the diagonal and the ones digit below, so 56 is recorded as a 5 over a 6.
4. Grade 5 learners read the final lattice answer starting at the top-left and moving down around the edge.
After diagonal sums are written along the lattice border, the answer is read top-left, down the left side, then across the bottom to give the full product.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Use the lattice method to multiply 234 times 6 and explain the diagonal sums in Grade 5 language.
Sample answer: I draw a 3-by-1 lattice. Cells hold 1 over 2, 1 over 8, and 2 over 4 for 12, 18, and 24. Adding diagonals from the right gives 4, 10, 3, 1, with one regrouping. The product is 1404.
The lattice keeps each partial product organized, and right-to-left diagonal addition with regrouping reproduces the standard product 1404 for Grade 5 learners.
2. Why is the lattice method helpful for Grade 5 students learning 3-digit by 1-digit multiplication?
Sample answer: The lattice splits the work into small one-digit times one-digit facts inside cells. The diagonals handle place value automatically, so I do not lose track of regrouping. It makes each step visible and easy to check.
Lattice multiplication breaks a 3-digit by 1-digit problem into known facts, then organizes regrouping along diagonals, supporting Grade 5 understanding of place value and magnitude.