The Number Sentence as an Object

A number sentence is a description. One hundred and seventeen chocolates are shared among fourteen people, each gets eight, and five are left over. Fourteen times eight is the chocolates that were handed out; plus five is the ones that were not; and the total is one hundred and seventeen. Every part of the sentence stands for a part of the story. That is how you check a sentence someone else has written: read it back as a story. Fourteen plus eight times five has a value, but it describes nothing that happened here.

The same number can be written as many different sentences. Twelve times three is ten times three plus two times three, because you can split the twelve into ten and two and multiply each part — that is the area model written as a sentence. It is also ten times three plus six, because two times three is six. Seventeen times six is ten sixes plus seven sixes, or twenty sixes minus three sixes, or seventeen fives plus one more seventeen. When a question asks which sentence has the same value, work each option out; the distractor is usually a split where one part forgot to be multiplied — ten times three plus two is thirty-two, not thirty-six.

An equals sign means the two sides are the same number, whatever is written on them. Sixty-seven minus triangle equals thirty-two plus seventeen: the right side looks busy, but it is just forty-nine. So sixty-seven minus triangle is forty-nine, and triangle is eighteen. The trap is to read the equals sign as an arrow that says the answer comes next, look only at sixty-seven minus triangle equals thirty-two, and answer thirty-five. Simplify the side without the box first, and every one of these becomes a single step.

Going the other way — from a story to a sentence — is the same reading skill. Three boxes of twenty-four eggs, seven broken: boxes of means multiply, broken means take away, so three times twenty-four minus seven, which is sixty-five. Five packs of twelve and four loose is five times twelve plus four. Six friends get seven each and three are left is six times seven plus three. Write the sentence first, then the answer, and then read the sentence back as the story to be sure it matches.

The test format is to give the story and four or five sentences, and ask which one describes it. Five packs of twelve stickers and four loose. Five plus twelve times four leaves the packs unmultiplied. Five times twelve minus four takes the loose stickers away. Five times sixteen adds the four to every pack. Five times twelve plus four is the one that tells the story: packs times stickers, plus the loose ones. Read each option back as a story, and use the value as a second check — only the right sentence makes sixty-four. Quiz and exercises now.