Maths Ratio and Proportion Year One Maths Year

Maths Ratio and Proportion Year One Maths | Year 6 | Ratio and Proportion | Solving Ratio Problems | Lesson 5 of 5: Ratio Reasoning

Aim • I can solve reasoning questions about ratio, calculating a missing amount. Success Criteria • I can break down complex problems into smaller steps. • I can use mathematical language to explain solutions to problems.

Ratio Reasoning 1 a ratio 3: 1 ? kg + ? kg = 20 kg Read this reasoning question carefully. A mother dog is three times the weight of her puppy. If they weigh 20 kg in total, how much does the mother dog weigh? First, let’s highlight the important information and key vocabulary in the question to show we understand the question:

Ratio Reasoning 1 a ratio 3: 1 ? kg + ? kg = 20 kg Read this reasoning question carefully. A mother dog is three times the weight of her puppy. If they weigh 20 kg in total, how much does the mother dog weigh? Next, let’s think The ratio is 3: 1, this means Tofind three parts, To one part, the that the total weight the puppy’s weight about what weto beis 20 kg needs dividedtointo parts – needs be four multiplied already know in divided by four. the mother dog has three by three. This order us out This of to thehelp four parts gives the and gives the mother the puppy hasquestion one out of answer the puppy’s weight. dog’s weight. the four parts. correctly.

Ratio Reasoning 1 a Now we are ready to apply our learning to solve the question. ratio 3: 1 ? kg + ? kg = 20 kg one part (puppy’s weight) = 20 kg ÷ 4 = 5 kg. X A mother dog is three times the weight of her three parts (mother’s weight) = 5 kghow × 3 much = 15 kg puppy. If they weigh 20 kg in total, does the mother dog weigh? Question

Ratio Reasoning 1 a Now we are ready to apply our learning to solve the question. ratio 3: 1 15 kg ? kg ++ ? 5 kg kg = 20 kg X Mother’s weight = 15 kg A mother dog is three times the weight of her Puppy’s weight = 5 kg puppy. If they weigh 20 kg in total, how much does the mother dog weigh? Question

Ratio Reasoning 1 a ratio 3: 1 15 kg + 5 kg = 20 kg Puppy’s weight = 5 kg X A mother dog is three times the weight of her Mother’s weight = 5 kg × 3 = 15 kg puppy. If they weigh 20 kg in total, how much Combined weight 5 kg + 15 kg = 20 kg does the mother dog= weigh? Question Finally, let’s check our answer with the information and key vocabulary in the question to check we have answered the question fully:

Scale Factor Reasoning 1 b Working with a partner, use your ratio reasoning skills to solve the first question on your Scale Factor Talk Partner Activity Sheet. Total weight is split into five parts. one part = 10 kg ÷ 5 = 2 kg Mother sheep has four parts so 2 kg × 4 = 8 kg A mother sheep is four times the weight of her lamb. If they weigh 10 kg in total, how much does the lamb weigh? Mother sheep weighs 8 kg. Answer

Ratio Reasoning 2 a weight 2: 3 cat 3 kg dog ? kg Read this reasoning question carefully. Jamie has a cat and a dog. The ratio of the cat’s weight to the dog’s is 2: 3. If the cat weighs 3 kg, what is the weight of his dog? First, let’s highlight the important information and key vocabulary in the question to show we understand the question:

Ratio Reasoning 2 a weight 2: 3 cat 3 kg dog ? kg Read this reasoning question carefully. Jamie has a cat and a dog. The ratio of the cat’s weight to the dog’s is 2: 3. If the cat weighs 3 kg, what is the weight of his dog? Next, let’s think about what The cat has we two parts ratio is 2: 3, already in of theknow combined so order to help usfive weight and the dog weight is in answer the question has three parts. correctly.

Ratio Reasoning 2 a weight 2: 3 cat 3 kg dog ? kg X Cat’s weight = 3 kg Jamie has a cat and a dog. The ratio of the 3 kg ÷ 2 = 1. 5 kg cat’s weight to the dog’s is 2: 3. If the cat weighs the weight of hisisdog? So one 3 kg, part what of theiscombined weight 1. 5 kg. Question The cat has two Now we are ready to parts of the apply our learning combined weight, to solve the so to find out question. what one part is, we need to divide the cat’s weight by two.

Ratio Reasoning 2 a weight 2: 3 cat 3 kg dog ? kg X Dog’s weight = 1. 5 kg × 3 = 4. 5 kg Jamie has a cat and a dog. The ratio of the cat’s weight to the dog’s is 2: 3. If the cat weighs 3 kg, what is the weight of his dog? Question The dog has three parts of the combined weight, so we need to multiply the amount for one part by three to find out his weight.

Ratio Reasoning 2 a weight 2: 3 cat 3 kg dog 4. 5 kg Finally, let’s check our answer with the information and key vocabulary in the question to check we have answered the question fully: X Combined weight is split into five parts. Jamie has a cat and a dog. The ratio of the Cat has two parts, so to find one part 3 kg ÷ 2 = 1. 5 kg cat’s weight to the dog’s is 2: 3. If the cat weighs what is the weight× of dog? Dog has 3 kg, three parts, so 1. 5 kg 3 =his 4. 5 kg Question

Ratio Reasoning 2 a weight 2: 3 cat 3 kg dog 4. 5 kg Add together the cat and the dog’s weight: 3 kg + 4. 5 kg = 7. 5 kg The combined weight has five parts. X One part = 7. 5 kg ÷ 5 = 1. 5 kg Jamie has a cat and a dog. The ratio of the Cat’s share = 1. 5 kg × 2 = 3 kg cat’s weight to the dog’s is 2: 3. If the cat weighs 3 kg, what is × the 3 weight Dog’s share = 1. 5 kg = 4. 5 kgof his dog? Question

Scale Factor Reasoning 2 b Working with a partner, use your ratio reasoning skills to solve the second question on your Scale Factor Talk Partner Activity Sheet. Large dog weighs 20 kg. This is four parts of the total weight. One part = 20 kg ÷ 4 = 5 kg. Small dog has three parts, so 5 kg × 3 = 15 kg. Judy has two dogs. The ratio of the large dog’s weight to the small dog is 4: 3. If the large dog weighs 20 kg, what is the weight of the small dog? The small dog weighs 15 kg. Answer

Ratio Reasoning 3 a ratio 1: 2: 3 ? + ? = 51 kg Read this reasoning question carefully. Leoni has three dogs. The ratio of the dogs’ weights is: 1: 2: 3. Together they weigh 51 kg. How much does each dog weigh? First, let’s highlight the important information and key vocabulary in the question to show we understand the question:

Ratio Reasoning 3 a Next, The let’ssmallest think dog has one part of I know thewe ratio about what the combined weight, is 1: 2: 3, so the already know indog the middle sized combined weight order help usand has to two parts inthe six has parts. answer question theislargest three correctly. parts. ratio 1: 2: 3 ? + ? = 51 kg Read this reasoning question carefully. Leoni has three dogs. The ratio of the dogs’ weights is: 1: 2: 3. Together they weigh 51 kg. How much does each dog weigh?

Ratio Reasoning 3 a ratio 1: 2: 3 8. 5 kg? ++ ? ? == 51 kg ÷ 6 = 8. 5 kg Leoni has three dogs. The ratio of the dogs’ weights is: 1: 2: 3. Together they weigh 51 kg. How much does each dog weigh? Question X The combined weight Now we are ready is divided into six to apply The our learning parts. smallest to solve the dog has one part, so question. to find out how much that is we divide 51 kg by 6.

Ratio Reasoning 3 a The medium sized dog has two of the six parts, so to find out how much that is we multiply 8. 5 kg by 2. ratio 1: 2: 3 8. 5 kg + 17 kg + ? ++ ? ? == 51 kg 8. 5 kg x 2 = 17 kg Leoni has three dogs. The ratio of the dogs’ weights is: 1: 2: 3. Together they weigh 51 kg. How much does each dog weigh? Question X

Ratio Reasoning 3 a The largest dog has three of the six parts, so to find out how much that is we multiply 8. 5 kg by 3. ratio 1: 2: 3 + ? = 51 kg 8. 5 kg + 17 kg+ +17 kg 25. 5 kg 8. 5 kg × 3 = 25. 5 kg Leoni has three dogs. The ratio of the dogs’ weights is: 1: 2: 3. Together they weigh 51 kg. How much does each dog weigh? Question X

Ratio Reasoning 3 a ratio 1: 2: 3 8. 5 kg + 17 kg + 25. 5 kg = 51 kg X Smallest dog: 8. 5 kg × 1 = 8. 5 kg Leoni has three dogs. The ratio of the dogs’ Medium dog: 8. 5 kg × 2 = 17 kg weights is: 1: 2: 3. Together they weigh 51 kg. How much does each weigh? Largest dog: 8. 5 kg × dog 3 = 25. 5 kg Question The combined Finally, let’s check weight has six parts. our answer with the One part = and key information 51 kg ÷ 6 = 8. 5 kg vocabulary in the question to check Add together the we have answered three dogs’ weight: the question 8. 5 kg + 17 kg + fully: 25. 5 kg = 51 kg

Scale Factor Reasoning 3 b Working with a partner, use your ratio reasoning skills to solve third question on your Scale Factor Talk Partner Activity Sheet. The combined weight has 10 parts, one part = 55 kg ÷ 10 = 5. 5 kg Smallest rabbit: 5. 5 kg × 1 = 5. 5 kg Medium rabbit: 5. 5 kg × 4 = 22 kg Suki has three rabbits. The ratio of the rabbits’ weight is: 1: 4: 5. Together, they weigh 55 kg. How much does each rabbit weigh? Largest rabbit: 5. 5 kg × 5 = 27. 5 kg Answer

Reasoning Practice Have a go at independently solving the reasoning questions on your activity sheet.

Reasoning Answers Did you correctly answer the reasoning questions about fractions, calculating missing amounts? The ratio of a baby’s weight from birth of they age brother isweigh 2: 5. If A mother sheep is brothers’ four timesweights the weight of 12 hermonths If three are: to 1: 2: 3. Iflamb. the middle the baby was how 5 kg when was born, what weight was he at 55 kg in 40 kg, total, does mother weigh? weighs muchhe do thethe three brothers weigh together? 12 -months-old? Mother sheep 120 kg weighs 44 kg. They in total. At 12 weigh months he would be 12. 5 kg.

Reasoning Answers Did you correctly answer the reasoning questions about fractions, calculating missing amounts? A bag of apples weighs of a bag of bananas. to. If the In a fruit smoothie, the half ratiothe of weight strawberries to raspberries bag of apples 1 kg, how muchofdoofboth bags weigh raspberries blackberries isisweighs 3: 2: 1. The total amount strawberries andtogether? raspberries strawberries is 3 kg. What and is theraspberries total weight is 2 kg. of the How three many fruits? grams of strawberries are there? The fruit weighs Both bags weigh 3600 g 3 kg. in total. 1200 g of strawberries.

Reasoning Answers Did you correctly answer the reasoning questions about fractions, calculating missing amounts? Onthe a map I am using, the is 0. 5 cm for everyof boys to girls is 1: 3. In art group, there are scale 28 boys children. The the ratio of to girls isratio 10 km. In real itmore is 300 km from one town to are girls? How many of life, the are and how many 5: 3. There are fourgroup boys than girls. another, how many cm would this be How many children in total attend theon artthe map? group and how many are boys? It would 15 cm on in the map. 10 are boys. There arebe 716 boys and 21 total. girls. children

Reasoning Answers How confident do you feel about finding missing amounts in ratio reasoning questions? Show me using a silent signal:

Aim • I can solve reasoning questions about ratio, calculating a missing amount. Success Criteria • I can break down complex problems into smaller steps. • I can use mathematical language to explain solutions to problems.